Schaum's Outline of Calculus for Business, Economics and Finance, Fourth Edition

The most useful tool for reviewing mathematical methods for economics classes—now with more content Schaum's Outline of Calculus for Business, Economics and Finance, Fourth Edition is the go-to study guide for help in economics courses, mirroring the courses in scope and sequence to help you understand basic concepts and get extra practice in topics like multivariable functions, exponential and logarithmic functions, and more. With an outline format that facilitates quick and easy review, Schaum's Outline of Calculus for Business, Economics and Finance, Fourth Edition supports the major bestselling textbooks in economics courses and is useful for a variety of classes, including Introduction to Economics, Economics, Econometrics, Microeconomics, Macroeconomics, Economics Theories, Mathematical Economics, Math for Economists and Math for Social Sciences. Chapters include Economic Applications of Graphs and Equations, The Derivative and the Rules of Differentiation, Calculus of Multivariable Functions, Exponential and Logarithmic Functions in Economics, Special Determinants and Matrices and Their Use in Economics, First-Order Differential Equations, and more. Features: NEW in this edition: Additional problems at the end of each chapter NEW in this edition: An additional chapter on sequences and series NEW in this edition: Two computer applications of Linear Programming in Excel 710 fully solved problems Outline format to provide a concise guide for study for standard college courses in mathematical economics Clear, concise explanations covers all course fundamentals Supplements the major bestselling textbooks in economics courses Appropriate for the following courses: Introduction to Economics, Economics, Econometrics, Microeconomics, Macroeconomics, Economics Theories, Mathematical Economics, Math for Economists, Math for Social Sciences Cover Title Page Copyright Page Contents CHAPTER 1 Review 1.1 Exponents 1.2 Polynomials 1.3 Equations: Linear and Quadratic 1.4 Simultaneous Equations 1.5 Functions 1.6 Graphs, Slopes, and Intercepts CHAPTER 2 Economic Applications of Graphs and Equations 2.1 Isocost Lines 2.2 Supply and Demand Analysis 2.3 Income Determination Models 2.4 IS-LM Analysis CHAPTER 3 The Derivative and the Rules of Differentiation 3.1 Limits 3.2 Continuity 3.3 The Slope of a Curvilinear Function 3.4 The Derivative 3.5 Differentiability and Continuity 3.6 Derivative Notation 3.7 Rules of Differentiation 3.8 Higher-Order Derivatives 3.9 Implicit Differentiation CHAPTER 4 Uses of the Derivative in Mathematics and Economics 4.1 Increasing and Decreasing Functions 4.2 Concavity and Convexity 4.3 Relative Extrema 4.4 Inflection Points 4.5 Optimization of Functions 4.6 Successive-Derivative Test for Optimization 4.7 Marginal Concepts 4.8 Optimizing Economic Functions 4.9 Relationship among Total, Marginal, and Average Concepts CHAPTER 5 Calculus of Multivariable Functions 5.1 Functions of Several Variables and Partial Derivatives 5.2 Rules of Partial Differentiation 5.3 Second-Order Partial Derivatives 5.4 Optimization of Multivariable Func tions 5.5 Constrained Optimization with Lagrange Multipliers 5.6 Significance of the Lagrange Multiplier 5.7 Differentials 5.8 Total and Partial Differentials 5.9 Total Derivatives 5.10 Implicit and Inverse Function Rules CHAPTER 6 Calculus of Multivariable Functions in Economics 6.1 Marginal Productivity 6.2 Income Determination Multipliers and Comparative Statics 6.3 Income and Cross Price Elasticities of Demand 6.4 Differentials and Incremental Changes 6.5 Optimization of Multivariable Functions in Economics 6.6 Constrained Optimization of Multivariable Functions in Economics 6.7 Homogeneous Production Functions 6.8 Returns to Scale 6.9 Optimization of Cobb-Douglas Production Functions 6.10 Optimization of Constant Elasticity of Substitution Production Functions CHAPTER 7 Exponential and Logarithmic Functions 7.1 Exponential Functions 7.2 Logarithmic Functions 7.3 Properties of Exponents and Logarithms 7.4 Natural Exponential and Logarithmic Functions 7.5 Solving Natural Exponential and Logarithmic Functions 7.6 Logarithmic Transformation of Nonlinear Functions CHAPTER 8 Exponential and Logarithmic Functions in Economics 8.1 Interest Compounding 8.2 Effective vs. Nominal Rates of Interest 8.3 Discounting 8.4 Converting Exponential to Natural Exponential Functions 8.5 Estimating Growth Rates from Data Points CHAPTER 9 Differentiation of Exponential and Logarithmic Functions 9.1 Rules of Differentiation 9.2 Higher-Order Derivatives 9.3 Partial Derivatives 9.4 Optimization of Exponential and Logarithmic Functions 9.5 Logarithmic Differentiation 9.6 Alternative Measures of Growth 9.7 Optimal Timing 9.8 Derivation of a Cobb-Douglas Demand Function Using a Logarithmic Transformation CHAPTER 10 The Fundamentals of Linear (or Matrix) Algebra 10.1 The Role of Linear Algebra 10.2 Definitions and Terms 10.3 Addition and Subtraction of Matrices 10.4 Scalar Multiplication 10.5 Vector Multiplication 10.6 Multiplication of Matrices 10.7 Commutative, Associative, and Distributive Laws in Matrix Algebra 10.8 Identity and Null Matrices 10.9 Matrix Expression of a System of Linear Equations CHAPTER 11 Matrix Inversion 11.1 Determinants and Nonsingularity 11.2 Third-Order Determinants 11.3 Minors and Cofactors 11.4 Laplace Expansion and Higher-Order Determinants 11.5 Properties of a Determinant 11.6 Cofactor and Adjoint Matrices 11.7 Inverse Matrices 11.8 Solving Linear Equations with the Inverse 11.9 Cramer’s Rule for Matrix Solutions CHAPTER 12 Special Determinants and Matrices and Their Use in Economics 12.1 The Jacobian 12.2 The Hessian 12.3 The Discriminant 12.4 Higher-Order Hessians 12.5 The Bordered Hessian for Constrained Optimization 12.6 Input-Output Analysis 12.7 Characteristic Roots and Vectors (Eigenvalues, Eigenvectors) CHAPTER 13 Comparative Statics and Concave Programming 13.1 Introduction to Comparative Statics 13.2 Comparative Statics with One Endogenous Variable 13.3 Comparative Statics with More Than One Endogenous Variable 13.4 Comparative Statics for Optimization Problems 13.5 Comparative Statics Used in Constrained Optimization 13.6 The Envelope Theorem 13.7 Concave Programming and Inequality Constraints CHAPTER 14 Integral Calculus: The Indefinite Integral 14.1 Integration 14.2 Rules of Integration 14.3 Initial Conditions and Boundary Conditions 14.4 Integration by Substitution 14.5 Integration by Parts 14.6 Economic Applications CHAPTER 15 Integral Calculus: The Definite Integral 15.1 Area Under a Curve 15.2 The Definite Integral 15.3 The Fundamental Theorem of Calculus 15.4 Properties of Definite Integrals 15.5 Area Between Curves 15.6 Improper Integrals 15.7 L’HÔpital’s Rule 15.8 Consumers’ and Producers’ Surplus 15.9 The Definite Integral and Probability CHAPTER 16 First-Order Differential Equations 16.1 Definitions and Concepts 16.2 General Formula for First-Order Linear Differential Equations 16.3 Exact Differential Equations and Partial Integration 16.4 Integrating Factors 16.5 Rules for the Integrating Factor 16.6 Separation of Variables 16.7 Economic Applications 16.8 Phase Diagrams for Differential Equations CHAPTER 17 First-Order Difference Equations 17.1 Definitions and Concepts 17.2 General Formula for First-Order Linear Difference Equations 17.3 Stability Conditions 17.4 Lagged Income Determination Model 17.5 The Cobweb Model 17.6 The Harrod Model 17.7 Phase Diagrams for Difference Equations CHAPTER 18 Second-Order Differential Equations and Difference Equations 18.1 Second-Order Differential Equations 18.2 Second-Order Difference Equations 18.3 Characteristic Roots 18.4 Conjugate Complex Numbers 18.5 Trigonometric Functions 18.6 Derivatives of Trigonometric Functions 18.7 Transformation of Imaginary and Complex Numbers 18.8 Stability Conditions CHAPTER 19 Simultaneous Differential and Difference Equations 19.1 Matrix Solution of Simultaneous Differential Equations, Part 1 19.2 Matrix Solution of Simultaneous Differential Equations, Part 2 19.3 Matrix Solution of Simultaneous Difference Equations, Part 1 19.4 Matrix Solution of Simultaneous Difference Equations, Part 2 19.5 Stability and Phase Diagrams for Simultaneous Differential Equations CHAPTER 20 The Calculus of Variations 20.1 Dynamic Optimization 20.2 Distance Between Two Points on a Plane 20.3 Euler’s Equation and the Necessary Condition for Dynamic Optimization 20.4 Finding Candidates for Extremals 20.5 The Sufficiency Conditions for the Calculus of Variations 20.6 Dynamic Optimization Subject to Functional Constraints 20.7 Variational Notation 20.8 Applications to Economics CHAPTER 21 Optimal Control Theory 21.1 Terminology 21.2 The Hamiltonian and the Necessary Conditions for Maximization in Optimal Control Theory 21.3 Sufficiency Conditions for Maximization in Optimal Control 21.4 Optimal Control Theory with a Free Endpoint 21.5 Inequality Constraints in the Endpoints 21.6 The Current-Valued Hamiltonian CHAPTER 22 Series in Economics: Descriptive Statistics and Linear Regression 22.1 Series 22.2 Properties of Summations 22.3 Descriptive Statistics: Frequency, Mean, and Variance 22.4 Probability: The Discrete Case 22.5 The Weighted Average 22.6 The Expected Value 22.7 Economic Applications: Regression Analysis EXCEL PRACTICE Excel Practice A Excel Practice B Additional Practice Problems Additional Practice Problems: Solutions Index 'Schaum's Outline of Calculus for Business, Economics and Finance' is the go-to study guide for help in economics courses, mirroring the courses in scope and sequence to help you understand basic concepts and get extra practice in topics like multivariable functions, exponential and logarithmic functions, and more. The most useful tool for reviewing mathematical methods for economics classes-now with more contentSchaum's Outline of Calculus for Business, Economics and Finance, Fourth Edition is the go-to study guide for help in economics courses, mirroring the courses in scope and sequence to help you understand basic concepts and get extra practice in topics like multivariable functions, exponential and logarithmic functions, and more. With an outline format that facilitates quick and easy review, Schaum's Outline of Calculus for Business, Economics and Finance, Fourth Edition supports the major bestselling textbooks in economics courses and is useful for a variety of classes, including Introduction to Economics, Economics, Econometrics, Microeconomics, Macroeconomics, Economics Theories, Mathematical Economics, Math for Economists and Math for Social Sciences. Chapters include Economic Applications of Graphs and Equations, The Derivative and the Rules of Differentiation, Calculus of Multivariable Functions, Exponential and Logarithmic Functions in Economics, Special Determinants and Matrices and Their Use in Economics, First-Order Differential Equations, and more.Features:NEW in this edition: Additional problems at the end of each chapterNEW in this edition: An additional chapter on sequences and seriesNEW in this edition: Two computer applications of Linear Programming in Excel710 fully solved problemsOutline format to provide a concise guide for study for standard college courses in mathematical economicsClear, concise explanations covers all course fundamentalsSupplements the major bestselling textbooks in economics coursesAppropriate for the following courses: Introduction to Economics, Economics, Econometrics, Microeconomics, Macroeconomics, Economics Theories, Mathematical Economics, Math for Economists, Math for Social Sciences