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

by Luis Moises Pena-Levano, Edward T. Dowling

Overview

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
  
  
  

Product Details

ISBN-13:	9781264266852
Publisher:	McGraw Hill LLC
Publication date:	12/08/2021
Edition description:	4th ed.
Pages:	752
Sales rank:	637,822
Product dimensions:	8.20(w) x 10.70(h) x 1.80(d)

About the Author

Dr. Luis Peña-Lévano is Assistant Professor in the Department of Agricultural Economics at the University of Wisconsin–River Falls, and Dairy Innovation Hub Faculty in the Department of Agricultural and Applied Economics at the University of Wisconsin – Madison. He is also the Chair of the International Section at the Agricultural and Applied Economics Association. His areas of expertise include climate change, international trade, optimization programming, agricultural finance and labor economics. Luis has also taught econometrics at the graduate level, and upper undergraduate level courses including Financial Management, Microeconomics, International Trade, Contemporary Issues in Agribusiness, among others.

Table of Contents

Chapter 1 Review 1

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 14

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 32

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 58

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 82

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 Functions.

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 110

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 146

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 160

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 173

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 199

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 224

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 254

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 284

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 326

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 342

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 362

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 391

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 408

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 428

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 460

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 493

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 515

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 537

Excel Practice B 554

Additional Practice Problems 570

Additional Practice Problems: Solutions 647

Index 725