The document discusses the Pythagorean theorem and distance formula. It explains that the Pythagorean theorem can be written as a short equation and is used for right triangles, with the variables representing the lengths of the sides. It then discusses the distance formula, explaining that it is used to calculate the distance between two points by taking the square root of the sum of the squares of the differences between the x- and y-coordinates. Examples of using the distance formula to calculate distances are provided.
The document discusses linear inequalities and their representations on number lines. It provides examples of writing inequalities based on number lines and situations. It also describes how to form new inequalities by performing operations such as addition, subtraction, multiplication, and division on both sides of a given inequality.
The document discusses integration and the definition of the definite integral. It provides 30 rules of integration involving trigonometric, logarithmic, exponential and other common functions. It also briefly discusses integration by substitution and defines the process of making a u-substitution to evaluate integrals that can be written in a particular form.
The document discusses the calculation of the inverse of a 3x3 matrix. It defines the minor, cofactor, adjoint and determinant of a matrix which are used to calculate the inverse. The inverse of a 3x3 matrix A is calculated as the adjoint of A divided by the determinant of A. An example calculates each component and shows the full inverse of a 3x3 matrix.
This document provides information about parallel and perpendicular lines. It defines parallel lines as lines that never cross and have the same slope. Perpendicular lines are defined as lines that cross at a right angle, have slopes that are opposite reciprocals, and have a product of slopes equal to -1. The document contains examples of writing equations of lines parallel and perpendicular to given lines and determining whether pairs of lines are parallel, perpendicular, or neither. It concludes with homework problems from the text.
1) Standard form is the formal way to write the equation of a line as Ax + By = C, where A, B, and C are integers and A must be positive.
2) The document provides examples of writing a line equation in standard form and finding the slope, y-intercept, and x-intercept of lines written in standard form.
3) Students are instructed to complete practice problems involving writing equations in standard form, finding slopes and intercepts, and graphing lines.
The document discusses writing equations in point-slope form. It provides the point-slope form equation y - y1 = m(x - x1) and examples of writing equations in point-slope form given a point and slope, finding the slope and a point from an equation, writing an equation in slope-intercept form, and finding the equation of a line given two points in point-slope form. The homework assigned is to complete practice problems writing and identifying equations in point-slope form.
Translating vertex form into standard form when a is not equal to 1ChristianManzo5
The document provides steps for translating a quadratic function from vertex form to standard form when a ≠ 1. It explains that the vertex form can be written as the square of a binomial. Using FOIL multiplication and the distributive property, the terms can be distributed and combined to obtain the standard form. Two examples are provided and worked through to demonstrate the process.
Translating standard form into vertex form if a=1ChristianManzo5
Hello!
This presentation contains step by step process on how to translate quadratic function from standard form into vertex form when the value of a is equal to 1.
Translating vertex form into standard form when a=1ChristianManzo5
Hello!
This presentation contains step by step process on how to translate quadratic function from vertex form back to standard form when the value of a is equal to 1.
The document contains a list of 22 math word problems involving operations with integers. The problems involve combinations of addition, subtraction, multiplication, and division with both positive and negative integers. Students are instructed to copy the problems into their notebooks and solve them there. The problems range in complexity from single-step operations to longer multi-step expressions nested within brackets and parentheses.
Quicksort is a divide-and-conquer sorting algorithm that dynamically divides the array into subarrays rather than using static divisions like Mergesort. It has three steps - divide the array into subarrays separated by a pivot element, recursively sort the subarrays, and combine the sorted subarrays. The algorithm works by picking a pivot element and partitioning the array such that elements less than the pivot are moved before it and greater elements after it. It then recursively applies this process to the subarrays until the entire array is sorted. The performance depends on how evenly the array is divided during partitioning, with best case being a split in the middle and worst case being a skewed division.
This document discusses factoring polynomials by undoing the distributive property. It provides the example of factoring 3x - 12. To do this, the greatest common factor (GCF) of 3 is pulled out in front of the parentheses. Inside the parentheses, x is placed for the first term and -4 is placed for the second term, resulting in the factored form 3(x - 4).
1) The document presents the work of a student named Nurkhlifah Anwar solving a system of linear equations using Gaussian elimination and substitution methods.
2) Both methods resulted in the same solutions of x1 = -15/2, x2 = 15, x3 = 23/2.
3) Gaussian elimination uses row operations to transform the matrix into reduced row echelon form and directly obtain the variable values. Substitution sequentially substitutes values into the original equations to solve for each variable.
Properties of coefficient of correlationNadeem Uddin
The document discusses properties of the coefficient of correlation (r) including:
1) r always lies between -1 and 1
2) r is the geometric mean of the two regression coefficients
3) Several examples are shown calculating r from regression coefficients and comparing to Pearson's coefficient of correlation.
This document discusses different types of equations that can be reduced to quadratic form. It provides examples of each type:
1) Equations of the form ax4 - bx2 + c = 0 can be reduced to quadratic by substituting x2 = y.
2) Equations containing terms like apx + b/px can be reduced by substituting the x terms as y.
3) Reciprocal equations of the form ax2 + 1/x2 + bx + 1/x + c = 0 are reduced by substituting x - 1/x = y.
4) Exponential equations can be reduced by substituting a variable for the exponential term.
5) Equations
The document contains examples of evaluating mathematical expressions for given values of variables.
1) It evaluates the expressions x + y, 2xy, and 5x/3y for x = 3 and y = 5, obtaining answers of 8, 30, and 1.
2) It evaluates the expression 3x + 2y for x = 3 and y = 5, obtaining the answer 19.
3) It evaluates the expression m + 2n for m = 5 and n = 2, obtaining the answer 9.
4) It evaluates the expression 18m + 7 for m = 1/3, obtaining the answer 13.
The document discusses solving inequalities by multiplying or dividing both sides of an inequality by a negative number. It notes that this causes the inequality sign to flip (e.g. from > to < or vice versa). It also discusses graphing solutions to absolute value inequalities and notes that absolute value cannot be less than a negative number, so some absolute value inequalities have no solution.
1) The document discusses key theorems about parallel and perpendicular lines including: if two lines intersect to form congruent angles then they are perpendicular; if two lines are perpendicular they intersect to form four right angles; and if two sides of two adjacent acute angles are perpendicular then the angles are complementary.
2) It also discusses the perpendicular transversal theorem which states that if a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other line.
3) The document provides instructions for homework problems involving parallel and perpendicular lines and finding the distance between parallel lines.
1) To solve linear equations, we use the inverse operation of whatever has been done to one side of the equation and apply it to both sides.
2) This reduces the equation until it is in the form of a single variable equals a number, at which point the value of the variable can be determined.
3) Examples show solving equations by adding, subtracting, multiplying, and dividing both sides by the same quantity until the variable is isolated.
This geometry document covers writing equations of lines in slope-intercept form. It reviews the concepts of slope and y-intercept and teaches that an equation of a line needs a slope and y-intercept. Examples are given of writing equations given these components. The document also addresses writing equations of lines parallel or perpendicular to given lines and passing through given points. Students are provided practice problems to write equations of lines in different scenarios.
1. The given series converges based on the limit comparison test with bn = 5n. The limit of an/bn is 1/√2 which is between 0 and 1, so the series converges.
2. The given series converges by the integral test. Computing the integral of f(x) = 1/x√ln(x) from 1 to infinity gives a finite value, so the series converges.
3. The ratio test shows that the limit of an+1/an is 0, which is less than 1. Therefore, the series converges absolutely.
4. Partial fraction decomposition allows determining that the sum of the series is 1/6.
This document contains 20 multiple choice questions testing concepts in complex numbers and operations. The questions cover topics such as simplifying complex expressions, adding, subtracting and multiplying complex numbers, evaluating complex functions, finding conjugates and inverses, graphing complex numbers on an Argand diagram, and properties of complex exponents.
The document discusses three methods for solving the numeric expression 2(4+3):
1) Using the order of operations (BODMAS/PEMDAS) to evaluate the expression inside the parentheses first before multiplying.
2) Changing multiplication to addition by thinking of it as having "lots of" something.
3) Using the distributive property, where the number outside the parentheses is distributed across each term inside the parentheses.
To divide rational expressions, multiply the dividend by the reciprocal of the divisor. The reciprocal is obtained by interchanging the numerator and denominator. For fractions a/b divided by c/d, the division is performed as a/b * d/c. Examples are provided to demonstrate dividing rational expressions and fractions.
This document provides an overview of solving systems of linear equations through three methods: graphing, substitution, and elimination. It defines systems of linear equations as two or more linear equations with the same variables, where the point of intersection is the solution. Examples are worked through for each solving method. Graphing involves putting the equations in y-intercept form and finding the point where the lines intersect on a graph. Substitution involves solving one equation for a variable and substituting it into the other equation. Elimination involves adding or subtracting the equations to eliminate a variable and then solving for the remaining variable.
This document discusses higher order differential equations and their applications. It introduces second order homogeneous differential equations and their solutions based on the nature of the roots. Non-homogeneous differential equations are also discussed, along with their general solution being the sum of the solution to the homogeneous equation and a particular solution. Methods for solving non-homogeneous equations are presented, including undetermined coefficients and reduction of order. Applications to problems in various domains like physics, engineering, and circuits are also outlined.
Second order homogeneous linear differential equations Viraj Patel
1) The document discusses second order linear homogeneous differential equations, which have the general form P(x)y'' + Q(x)y' + R(x)y = 0.
2) It describes methods for finding the general solution including reduction of order, and discusses the solutions when the coefficients are constants.
3) The general solution depends on the nature of the roots of the auxiliary equation: distinct real roots, repeated real roots, or complex roots.
Translating vertex form into standard form when a is not equal to 1ChristianManzo5
The document provides steps for translating a quadratic function from vertex form to standard form when a ≠ 1. It explains that the vertex form can be written as the square of a binomial. Using FOIL multiplication and the distributive property, the terms can be distributed and combined to obtain the standard form. Two examples are provided and worked through to demonstrate the process.
Translating standard form into vertex form if a=1ChristianManzo5
Hello!
This presentation contains step by step process on how to translate quadratic function from standard form into vertex form when the value of a is equal to 1.
Translating vertex form into standard form when a=1ChristianManzo5
Hello!
This presentation contains step by step process on how to translate quadratic function from vertex form back to standard form when the value of a is equal to 1.
The document contains a list of 22 math word problems involving operations with integers. The problems involve combinations of addition, subtraction, multiplication, and division with both positive and negative integers. Students are instructed to copy the problems into their notebooks and solve them there. The problems range in complexity from single-step operations to longer multi-step expressions nested within brackets and parentheses.
Quicksort is a divide-and-conquer sorting algorithm that dynamically divides the array into subarrays rather than using static divisions like Mergesort. It has three steps - divide the array into subarrays separated by a pivot element, recursively sort the subarrays, and combine the sorted subarrays. The algorithm works by picking a pivot element and partitioning the array such that elements less than the pivot are moved before it and greater elements after it. It then recursively applies this process to the subarrays until the entire array is sorted. The performance depends on how evenly the array is divided during partitioning, with best case being a split in the middle and worst case being a skewed division.
This document discusses factoring polynomials by undoing the distributive property. It provides the example of factoring 3x - 12. To do this, the greatest common factor (GCF) of 3 is pulled out in front of the parentheses. Inside the parentheses, x is placed for the first term and -4 is placed for the second term, resulting in the factored form 3(x - 4).
1) The document presents the work of a student named Nurkhlifah Anwar solving a system of linear equations using Gaussian elimination and substitution methods.
2) Both methods resulted in the same solutions of x1 = -15/2, x2 = 15, x3 = 23/2.
3) Gaussian elimination uses row operations to transform the matrix into reduced row echelon form and directly obtain the variable values. Substitution sequentially substitutes values into the original equations to solve for each variable.
Properties of coefficient of correlationNadeem Uddin
The document discusses properties of the coefficient of correlation (r) including:
1) r always lies between -1 and 1
2) r is the geometric mean of the two regression coefficients
3) Several examples are shown calculating r from regression coefficients and comparing to Pearson's coefficient of correlation.
This document discusses different types of equations that can be reduced to quadratic form. It provides examples of each type:
1) Equations of the form ax4 - bx2 + c = 0 can be reduced to quadratic by substituting x2 = y.
2) Equations containing terms like apx + b/px can be reduced by substituting the x terms as y.
3) Reciprocal equations of the form ax2 + 1/x2 + bx + 1/x + c = 0 are reduced by substituting x - 1/x = y.
4) Exponential equations can be reduced by substituting a variable for the exponential term.
5) Equations
The document contains examples of evaluating mathematical expressions for given values of variables.
1) It evaluates the expressions x + y, 2xy, and 5x/3y for x = 3 and y = 5, obtaining answers of 8, 30, and 1.
2) It evaluates the expression 3x + 2y for x = 3 and y = 5, obtaining the answer 19.
3) It evaluates the expression m + 2n for m = 5 and n = 2, obtaining the answer 9.
4) It evaluates the expression 18m + 7 for m = 1/3, obtaining the answer 13.
The document discusses solving inequalities by multiplying or dividing both sides of an inequality by a negative number. It notes that this causes the inequality sign to flip (e.g. from > to < or vice versa). It also discusses graphing solutions to absolute value inequalities and notes that absolute value cannot be less than a negative number, so some absolute value inequalities have no solution.
1) The document discusses key theorems about parallel and perpendicular lines including: if two lines intersect to form congruent angles then they are perpendicular; if two lines are perpendicular they intersect to form four right angles; and if two sides of two adjacent acute angles are perpendicular then the angles are complementary.
2) It also discusses the perpendicular transversal theorem which states that if a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other line.
3) The document provides instructions for homework problems involving parallel and perpendicular lines and finding the distance between parallel lines.
1) To solve linear equations, we use the inverse operation of whatever has been done to one side of the equation and apply it to both sides.
2) This reduces the equation until it is in the form of a single variable equals a number, at which point the value of the variable can be determined.
3) Examples show solving equations by adding, subtracting, multiplying, and dividing both sides by the same quantity until the variable is isolated.
This geometry document covers writing equations of lines in slope-intercept form. It reviews the concepts of slope and y-intercept and teaches that an equation of a line needs a slope and y-intercept. Examples are given of writing equations given these components. The document also addresses writing equations of lines parallel or perpendicular to given lines and passing through given points. Students are provided practice problems to write equations of lines in different scenarios.
1. The given series converges based on the limit comparison test with bn = 5n. The limit of an/bn is 1/√2 which is between 0 and 1, so the series converges.
2. The given series converges by the integral test. Computing the integral of f(x) = 1/x√ln(x) from 1 to infinity gives a finite value, so the series converges.
3. The ratio test shows that the limit of an+1/an is 0, which is less than 1. Therefore, the series converges absolutely.
4. Partial fraction decomposition allows determining that the sum of the series is 1/6.
This document contains 20 multiple choice questions testing concepts in complex numbers and operations. The questions cover topics such as simplifying complex expressions, adding, subtracting and multiplying complex numbers, evaluating complex functions, finding conjugates and inverses, graphing complex numbers on an Argand diagram, and properties of complex exponents.
The document discusses three methods for solving the numeric expression 2(4+3):
1) Using the order of operations (BODMAS/PEMDAS) to evaluate the expression inside the parentheses first before multiplying.
2) Changing multiplication to addition by thinking of it as having "lots of" something.
3) Using the distributive property, where the number outside the parentheses is distributed across each term inside the parentheses.
To divide rational expressions, multiply the dividend by the reciprocal of the divisor. The reciprocal is obtained by interchanging the numerator and denominator. For fractions a/b divided by c/d, the division is performed as a/b * d/c. Examples are provided to demonstrate dividing rational expressions and fractions.
This document provides an overview of solving systems of linear equations through three methods: graphing, substitution, and elimination. It defines systems of linear equations as two or more linear equations with the same variables, where the point of intersection is the solution. Examples are worked through for each solving method. Graphing involves putting the equations in y-intercept form and finding the point where the lines intersect on a graph. Substitution involves solving one equation for a variable and substituting it into the other equation. Elimination involves adding or subtracting the equations to eliminate a variable and then solving for the remaining variable.
This document discusses higher order differential equations and their applications. It introduces second order homogeneous differential equations and their solutions based on the nature of the roots. Non-homogeneous differential equations are also discussed, along with their general solution being the sum of the solution to the homogeneous equation and a particular solution. Methods for solving non-homogeneous equations are presented, including undetermined coefficients and reduction of order. Applications to problems in various domains like physics, engineering, and circuits are also outlined.
Second order homogeneous linear differential equations Viraj Patel
1) The document discusses second order linear homogeneous differential equations, which have the general form P(x)y'' + Q(x)y' + R(x)y = 0.
2) It describes methods for finding the general solution including reduction of order, and discusses the solutions when the coefficients are constants.
3) The general solution depends on the nature of the roots of the auxiliary equation: distinct real roots, repeated real roots, or complex roots.
Differential equations can be used to model real-world phenomena like disease spread. An influenza outbreak in a village of 500 people is modeled using a differential equation where the rate of spread is proportional to the number of infected and uninfected individuals. The equation is solved, giving the number of infected people over time. After 3 months there were 30 infected, and the model predicts 205 infected after 5 months. Differential equations allow quantification of how factors like disease transmission rates impact outcomes over time.
This document discusses applications of differential equations. It begins by covering the invention of differential equations by Newton and Leibniz. It then defines differential equations and covers types like ordinary differential equations (ODEs) and partial differential equations (PDEs). Examples of commonly used differential equations are provided, such as the Laplace equation, heat equation, and wave equation. Applications of differential equations are discussed, including modeling mechanical oscillations, electrical circuits, and Newton's law of cooling.
This document contains information about a group project on differential equations. It lists the group members and covers topics like the invention of differential equations, types of ordinary and partial differential equations, applications, and examples. The group will discuss differential equations including the history, basic concepts of ODEs and PDEs, types like first and second order ODEs, linear and non-linear PDEs, and applications in fields like mechanics, physics, and engineering.
First order linear differential equationNofal Umair
1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.
The document presents information about differential equations including:
- A definition of a differential equation as an equation containing the derivative of one or more variables.
- Classification of differential equations by type (ordinary vs. partial), order, and linearity.
- Methods for solving different types of differential equations such as variable separable form, homogeneous equations, exact equations, and linear equations.
- An example problem demonstrating how to use the cooling rate formula to calculate the time of death based on measured body temperatures.
Adomian decomposition Method and Differential Transform Method to solve the H...IJERA Editor
In this paper, we consider the AdomianDecomposition Method (ADM) and the Differential Transform Method (DTM) for finding approximate and exact solution of the heat equation with a power nonlinearity. Moreover, the reliability and performance of ADM and DTM. Numerical results show that these methods are powerful tools for solving heat equation with a power nonlinearity.
The document discusses equations of lines, including:
1) The gradient-point form of a straight line equation which uses the gradient and coordinates of one point to determine the equation.
2) Calculating the gradient from two points on a line and using it to find the angle of inclination.
3) Determining the equation of a line parallel to another line, by setting their gradients equal since parallel lines have the same gradient.
Linear equations in two variables- By- PragyanPragyan Poudyal
This is a power point presentation on linear equations in two variables for class 10th. I have spent 3 hours on making this and all the equations you will see are written by me.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
The document discusses solving simultaneous linear equations using the substitution method. It begins by explaining how to reduce a set of simultaneous linear equations into a single linear equation with one unknown. This is done by substituting one equation into the other to eliminate one of the unknowns. Three examples are then worked through step-by-step to demonstrate the substitution method. The key steps are: 1) express one unknown in terms of the other, 2) substitute this into the other equation to get a single-variable equation, 3) solve for the value of the unknown, and 4) back-substitute to find the value of the other unknown. Checking the solution involves substituting the values back into the original equations.
The document outlines the key concepts covered in an engineering mathematics course, including:
- Types of differential equations such as ordinary, partial, linear, non-linear, homogeneous, and non-homogeneous equations.
- Solutions including general, particular, singular, explicit, and implicit solutions.
- Boundary and initial conditions.
- Methods for solving differential equations including separation of variables, homogeneous equations, linear equations, and Laplace transforms.
- Key concepts are defined and examples are provided to illustrate different types of equations and solutions.
Helmholtz equation (Motivations and Solutions)Hassaan Saleem
Solutions of Helmholtz equation in cartesian, cylindrical and spherical coordinates are discussed and the applications to the problem of a quantum mechanical particle in a cubical box is discussed.
1) The document presents a wavelet collocation method for numerically solving nth order Volterra integro-differential equations. It expands the unknown function as a series of Chebyshev wavelets of the second kind with unknown coefficients.
2) It states and proves a uniform convergence theorem that establishes the convergence of approximating the solution using truncated Chebyshev wavelet series expansions.
3) The paper demonstrates the validity and applicability of the proposed method through some illustrative examples of solving integro-differential equations using the Chebyshev wavelet collocation approach.
This document discusses Hermite polynomials and their properties. It begins by introducing the Hermite equation, which arises from the theory of the linear harmonic oscillator. The Hermite equation is then solved using a series solution approach. Explicit formulas for the Hermite polynomials Hn(x) are derived for n=0,1,2,3,... using properties of the Hermite equation like recursion relations. Key properties of the Hermite polynomials like generating functions, even/odd behavior, Rodrigue's formula, orthogonality, and recurrence relations are also proved.
- The document discusses new special functions K_n(x) defined in terms of Legendre polynomials P_n(x).
- Recurrence relations and differential equations for the new functions K_n(x) are derived.
- Properties of Legendre polynomials such as the generating function and orthogonality are used to derive relationships between the K_n(x) functions.
1. The document discusses differential equations of higher order, which are equations where the derivatives are functions of higher algebraic order.
2. It provides examples of functions that are of higher order, and explains that a differential equation is of higher order if the functions P(x,y) and Q(x,y) are of higher algebraic order.
3. Methods for solving higher order differential equations are presented, including reducing them to an equivalent ordinary differential equation using appropriate substitutions, and then solving using standard integration techniques.
This document discusses ordinary differential equations of first order and first degree. It is divided into three topics: 1) Homogeneous differential equations, where functions F(x,y) satisfy F(λx, λy)= λn F(x,y). Examples of homogeneous functions are given. 2) Equations reducible to homogeneous equations through variable substitution. Two cases are discussed: when lines are not parallel and when lines are parallel. 3) Exact differential equations, where the condition for exactness is that the partial derivatives of P and Q with respect to x and y are equal. Examples of finding the integral of exact equations are provided.
TRANSIENT AND STEADY STATE HEAT CONDUCTION WITH NO LATERAL CONVECTION SOLVED ...Wasswaderrick3
In this book we go ahead and solve for the transient and steady state heat conduction phenomena in one dimensional heat flow with no lateral convection. It is known that there exist a Fourier series method but the problem of this method is that it is an approximate method since it involves summing up to infinite number of terms which we can never achieve in practice without approximating. In this book we develop an analytic solution to the heat equation with no lateral convection by using the already derived hyperbolic temperature profile functions in literature and solve the heat equation using these functions and the integral equation method and get a solution of the time dependent parameter δ which we substitute in the temperature profile. We deal with different types of boundary conditions and get their solutions. In solving for the steady state temperatures, we use the L’hopital’s rule since we get undefined limits when we substitute for time tending to infinity in some cases. We realize that the steady state temperature profile agrees with theory.
Digital marketing strategy and planning | About BusinessGaditek
Introduction
Respondent profiles
About Business
Adoption of digital transformation programs
Investing In Digital Marketing
Top Online Marketing Channels
What should the planning horizon for digital planning be?
Integration Of Digital And Traditional Marketing Activities
EXECUTIVE SUMMARY
Intro to social network analysis | What is Network Analysis? | History of (So...Gaditek
Social network analysis examines the connections between individuals, groups, organizations, or other social entities. It focuses on interactions rather than individual behavior. Network analysis can be applied across many disciplines to study how the structure of relationships influences functioning. Early research in fields like sociology, anthropology, and educational psychology helped develop concepts still used today, such as examining homophily and interaction patterns. Key concepts in network analysis include nodes, edges, degree, clustering coefficients, and graph diameter. "Small world" networks are highly clustered with short path lengths, characteristics seen in many real-world networks. Social capital research also examines how network connections impact groups, organizations, and individuals.
Marketing ethics and social responsibility | Criticisms of MarketingGaditek
Identify the major social criticisms of marketing.
Define consumerism and environmentalism and explain how they affect marketing strategies.
Describe the principles of socially responsible marketing.
Explain the role of ethics in marketing.
understanding and capturing customer value | What Is a Price?Gaditek
Discuss the importance of understanding customer value perceptions and company costs when setting prices.
Identify and define the other important internal and external factors affecting a firm’s pricing decisions.
Describe the major strategies for pricing imitative and new products.
Explain how companies find a set of prices that maximizes the profits from the total product mix.
Discuss how companies adjust their prices to take into account different types of customers and situations.
Discuss key issues related to initiating and responding to price changes.
The marketing environment | Suppliers | Marketing intermediariesGaditek
The document summarizes the key elements of a company's marketing environment including:
- The microenvironment comprised of a company's internal operations as well as suppliers, intermediaries, customers, competitors, and publics.
- The macroenvironment including demographic, economic, natural, technological, political, and cultural forces outside a company's control that shape opportunities and threats.
- How changes in these environments like population aging, income shifts, resource scarcity, regulations, and cultural values influence marketing decisions and strategies.
- Approaches companies take to proactively manage their environments like lobbying, partnerships, and influencing public opinion.
strategic planning | Customer Relationships | Partnering to Build Gaditek
Explain companywide strategic planning and its four steps.
Discuss how to design business portfolios and growth strategies.
Explain marketing’s role in strategic planning and how marketing works with its partners to create and deliver customer value.
Describe the elements of a customer-driven marketing strategy and mix, and the forces that influence it.
List the marketing management functions, including the elements of a marketing plan.
Define marketing and the marketing process.
Explain the importance of understanding customers and identify the five core marketplace concepts.
Identify the elements of a customer-driven marketing strategy and discuss the marketing management orientations.
Discuss customer relationship management and creating value for and capturing value from customers.
Describe the major trends and forces changing the marketing landscape.
Fundamentals of Computer Design including performance measurements & quantita...Gaditek
This document provides an overview of the Computer Architecture course CNE-301 taught by Irfan Ali. The course outline covers topics like fundamentals of computer design, instruction set design, pipelining, memory hierarchy, multiprocessors, and case studies. Recommended books are also mentioned. The document then provides background on computer architecture and organization, the history of computers from first to fourth generations, and embedded systems.
Dealing with exceptions Computer Architecture part 2Gaditek
The document discusses exceptions in computer architecture. It describes two types of exceptions - interrupts and traps. Interrupts are caused by external events like I/O requests, while traps are caused by internal events like arithmetic overflow. When an exception occurs, the pipeline must stop executing the offending instruction, save state like the program counter, and jump to an exception handler. Handling exceptions in a pipelined processor is challenging as it can disrupt instruction flow. The document outlines some of the techniques used to handle exceptions in a pipeline, like writing exception information to registers and flushing instructions after the exception.
Dealing with Exceptions Computer Architecture part 1Gaditek
The document discusses exceptions in computer architecture. It describes two types of exceptions - interrupts and traps. Interrupts are caused by external events like I/O requests, while traps are caused by internal events like arithmetic overflow. When an exception occurs, the pipeline must stop executing the offending instruction, save state like the program counter, and jump to an exception handler. Handling exceptions in a pipelined processor is challenging as it can disrupt instruction flow. The document outlines some of the techniques used to handle exceptions in a pipeline, like writing exception information to registers and flushing instructions after the exception.
The document provides an overview of pipelining in computer processors. It discusses how pipelining works by dividing processor operations like fetch, decode, execute, memory, and write-back into discrete stages that can overlap, improving throughput. Key points made include:
- Pipelining allows multiple instructions to be in different stages of completion at the same time, improving instruction throughput.
- The document uses an example of a sequential laundry process versus a pipelined laundry process to illustrate how pipelining improves efficiency.
- It describes the five main stages of a RISC instruction set pipeline - fetch, decode, execute, memory, and write-back. The work done and data passed between each stage
This document discusses instruction set architectures (ISAs). It covers four main types of ISAs: accumulator, stack, memory-memory, and register-based. It also discusses different addressing modes like immediate, direct, indirect, register-indirect, and relative addressing. The key details provided are:
1) Accumulator ISAs use a dedicated register (accumulator) to hold operands and results, while stack ISAs use an implicit last-in, first-out stack. Memory-memory ISAs can have 2-3 operands specified directly in memory.
2) Register-based ISAs can be either register-memory (like 80x86) or load-store (like MIPS), which fully separate
The document discusses higher order non-homogeneous linear differential equations and methods for finding their particular integrals. It defines a general higher order non-homogeneous differential equation and explains that the general solution is the sum of the complementary solution and particular solution. It then presents three rules for finding the particular integral when the forcing term F(x) is an exponential, sine, or cosine function. The rules involve taking derivatives of the differential operator f(D) evaluated at constants related to the exponential, sine, or cosine function.
Introduction to ANN, McCulloch Pitts Neuron, Perceptron and its Learning
Algorithm, Sigmoid Neuron, Activation Functions: Tanh, ReLu Multi- layer Perceptron
Model – Introduction, learning parameters: Weight and Bias, Loss function: Mean
Square Error, Back Propagation Learning Convolutional Neural Network, Building
blocks of CNN, Transfer Learning, R-CNN,Auto encoders, LSTM Networks, Recent
Trends in Deep Learning.
AI-Powered Data Management and Governance in RetailIJDKP
Artificial intelligence (AI) is transforming the retail industry’s approach to data management and decisionmaking. This journal explores how AI-powered techniques enhance data governance in retail, ensuring data quality, security, and compliance in an era of big data and real-time analytics. We review the current landscape of AI adoption in retail, underscoring the need for robust data governance frameworks to handle the influx of data and support AI initiatives. Drawing on literature and industry examples, we examine established data governance frameworks and how AI technologies (such as machine learning and automation) are augmenting traditional data management practices. Key applications are identified, including AI-driven data quality improvement, automated metadata management, and intelligent data lineage tracking, illustrating how these innovations streamline operations and maintain data integrity. Ethical considerations including customer privacy, bias mitigation, transparency, and regulatory compliance are discussed to address the challenges of deploying AI in data governance responsibly.
Design of Variable Depth Single-Span Post.pdfKamel Farid
Hunched Single Span Bridge: -
(HSSBs) have maximum depth at ends and minimum depth at midspan.
Used for long-span river crossings or highway overpasses when:
Aesthetically pleasing shape is required or
Vertical clearance needs to be maximized
Optimization techniques can be divided to two groups: Traditional or numerical methods and methods based on stochastic. The essential problem of the traditional methods, that by searching the ideal variables are found for the point that differential reaches zero, is staying in local optimum points, can not solving the non-linear non-convex problems with lots of constraints and variables, and needs other complex mathematical operations such as derivative. In order to satisfy the aforementioned problems, the scientists become interested on meta-heuristic optimization techniques, those are classified into two essential kinds, which are single and population-based solutions. The method does not require unique knowledge to the problem. By general knowledge the optimal solution can be achieved. The optimization methods based on population can be divided into 4 classes from inspiration point of view and physical based optimization methods is one of them. Physical based optimization algorithm: that the physical rules are used for updating the solutions are:, Lighting Attachment Procedure Optimization (LAPO), Gravitational Search Algorithm (GSA) Water Evaporation Optimization Algorithm, Multi-Verse Optimizer (MVO), Galaxy-based Search Algorithm (GbSA), Small-World Optimization Algorithm (SWOA), Black Hole (BH) algorithm, Ray Optimization (RO) algorithm, Artificial Chemical Reaction Optimization Algorithm (ACROA), Central Force Optimization (CFO) and Charged System Search (CSS) are some of physical methods. In this paper physical and physic-chemical phenomena based optimization methods are discuss and compare with other optimization methods. Some examples of these methods are shown and results compared with other well known methods. The physical phenomena based methods are shown reasonable results.
Welcome to the May 2025 edition of WIPAC Monthly celebrating the 14th anniversary of the WIPAC Group and WIPAC monthly.
In this edition along with the usual news from around the industry we have three great articles for your contemplation
Firstly from Michael Dooley we have a feature article about ammonia ion selective electrodes and their online applications
Secondly we have an article from myself which highlights the increasing amount of wastewater monitoring and asks "what is the overall" strategy or are we installing monitoring for the sake of monitoring
Lastly we have an article on data as a service for resilient utility operations and how it can be used effectively.
The TRB AJE35 RIIM Coordination and Collaboration Subcommittee has organized a series of webinars focused on building coordination, collaboration, and cooperation across multiple groups. All webinars have been recorded and copies of the recording, transcripts, and slides are below. These resources are open-access following creative commons licensing agreements. The files may be found, organized by webinar date, below. The committee co-chairs would welcome any suggestions for future webinars. The support of the AASHTO RAC Coordination and Collaboration Task Force, the Council of University Transportation Centers, and AUTRI’s Alabama Transportation Assistance Program is gratefully acknowledged.
This webinar overviews proven methods for collaborating with USDOT University Transportation Centers (UTCs), emphasizing state departments of transportation and other stakeholders. It will cover partnerships at all UTC stages, from the Notice of Funding Opportunity (NOFO) release through proposal development, research and implementation. Successful USDOT UTC research, education, workforce development, and technology transfer best practices will be highlighted. Dr. Larry Rilett, Director of the Auburn University Transportation Research Institute will moderate.
For more information, visit: https://aub.ie/trbwebinars
Jacob Murphy Australia - Excels In Optimizing Software ApplicationsJacob Murphy Australia
In the world of technology, Jacob Murphy Australia stands out as a Junior Software Engineer with a passion for innovation. Holding a Bachelor of Science in Computer Science from Columbia University, Jacob's forte lies in software engineering and object-oriented programming. As a Freelance Software Engineer, he excels in optimizing software applications to deliver exceptional user experiences and operational efficiency. Jacob thrives in collaborative environments, actively engaging in design and code reviews to ensure top-notch solutions. With a diverse skill set encompassing Java, C++, Python, and Agile methodologies, Jacob is poised to be a valuable asset to any software development team.
Construction Materials (Paints) in Civil EngineeringLavish Kashyap
This file will provide you information about various types of Paints in Civil Engineering field under Construction Materials.
It will be very useful for all Civil Engineering students who wants to search about various Construction Materials used in Civil Engineering field.
Paint is a vital construction material used for protecting surfaces and enhancing the aesthetic appeal of buildings and structures. It consists of several components, including pigments (for color), binders (to hold the pigment together), solvents or thinners (to adjust viscosity), and additives (to improve properties like durability and drying time).
Paint is one of the material used in Civil Engineering field. It is especially used in final stages of construction project.
Paint plays a dual role in construction: it protects building materials and contributes to the overall appearance and ambiance of a space.
This research presents the optimization techniques for reinforced concrete waffle slab design because the EC2 code cannot provide an efficient and optimum design. Waffle slab is mostly used where there is necessity to avoid column interfering the spaces or for a slab with large span or as an aesthetic purpose. Design optimization has been carried out here with MATLAB, using genetic algorithm. The objective function include the overall cost of reinforcement, concrete and formwork while the variables comprise of the depth of the rib including the topping thickness, rib width, and ribs spacing. The optimization constraints are the minimum and maximum areas of steel, flexural moment capacity, shear capacity and the geometry. The optimized cost and slab dimensions are obtained through genetic algorithm in MATLAB. The optimum steel ratio is 2.2% with minimum slab dimensions. The outcomes indicate that the design of reinforced concrete waffle slabs can be effectively carried out using the optimization process of genetic algorithm.
1. DIFFERENTIAL EQUATION (MT-202) SYED AZEEM INAM
DIFFERENTIAL EQUATION (MT-202)
LECTURE #5
TYPE 3 EQUATIONS REDUCIBLE TO HOMOGENOUS:
If equation
𝑑𝑦
𝑑𝑥
= 𝑓(𝑥, 𝑦) is of the form
𝑑𝑦
𝑑𝑥
=
𝐴𝑥 + 𝐵𝑦 + 𝐶
𝐴′ 𝑥+𝐵′ 𝑦 + 𝐶′
(1)
It can be reduced to the homogenous form by substituting𝑥 = 𝑋 + ℎ, 𝑦 = 𝑌 + 𝑘.
Therefore
𝑑𝑦
𝑑𝑥
=
𝑑𝑌
𝑑𝑋
(2)
And the equation (1) reduces to
𝑑𝑌
𝑑𝑋
=
𝐴𝑋 + 𝐵𝑌 + 𝐴ℎ + 𝐵𝑘 + 𝐶
𝐴𝑋′ + 𝐵𝑌′ + 𝐴′ℎ + 𝐵′ 𝑘 + 𝐶′
Now, choose h and k so that 𝐴ℎ + 𝐵𝑘 + 𝐶 = 0 and 𝐴′
ℎ+𝐵′
𝑘 + 𝐶′
= 0 which
gives
ℎ =
𝐵𝐶′
− 𝐶𝐵′
𝐴𝐵′ − 𝐵𝐴′
, 𝑘 =
𝐶𝐴′
− 𝐴𝐶′
𝐴𝐵′ − 𝐵𝐴′
By substituting these values in (2), we get
𝑑𝑌
𝑑𝑋
=
𝐴𝑋 + 𝐵𝑌
𝐴′ 𝑋+𝐵′ 𝑌
Which is a homogenous differential equation and can be solved by the method
discussed in Type 2.
CASE OF FAILURE:
In this case, the differential equation reduces to variable separable type.
If
𝐴
𝐴′
=
𝐵
𝐵′
, then the value of h and k will not exist. In this case, let
𝐴
𝐴′
=
𝐵
𝐵′
=
1
𝑚
=> 𝐴′
= 𝑚𝐴 And 𝐵′
= 𝑚𝐵
Then the given equation becomes
2. DIFFERENTIAL EQUATION (MT-202) SYED AZEEM INAM
DIFFERENTIAL EQUATION (MT-202)
𝑑𝑦
𝑑𝑥
=
𝐴𝑥 + 𝐵𝑦 + 𝐶
𝑚(𝐴𝑥 + 𝐵𝑦) + 𝐶′
To solve it first we put 𝐴𝑥 + 𝐵𝑦 = 𝑧 and then apply the method of variable
separable to solve the transformed differential equation.