Designed for students, faculty, and professionals, this book describes the role of mathematics in the world of economics and business. Beginning with the fundamental nature of numbers and progressing into more complex realms like hyperreal numbers and the intricacies of set theory, this book constructs a strong foundational understanding of mathematical concepts. The book uses PYTHON code throughout the text to illustrate problems numerically. As readers advance, the text seamlessly integrates essential topics such as linear simultaneous equations, which are pivotal in analyzing market equilibrium, and covers the mechanics of matrices for solving larger equation systems. Furthermore, chapters dedicated to calculus, especially its applications in economics and the innovative use of infinitesimal methods, equip learners with tools to tackle profit maximization challenges, factor optimization, and beyond. Later chapters unfold the world of differential and difference equations, revealing their significance in analyzing dynamic systems. All these concepts are illuminated through practical examples and numerous images from economics and business, ensuring relevance and clarity.
FEATURES:
Integrates computational understanding with chapters dedicated to PYTHON code examples that illuminate mathematical concepts
Covers infinitesimal methods, a distinct approach that emphasizes intuition and comprehensive technique development
Includes differential and difference equations, vital for understanding how variables evolve over time in response to external influences
Author(s): Paul Turner; Justine Wood
Publisher: Mercury Learning and Information
Year: 2024
Language: English
Pages: xiv; 360
City: Boston
Tags: Computer science; Mathematics; Economics; Business; Calculus; Infinitesimal methods; Difference Equations; Factor optimization; Profit maximization challenges; Linear simultaneous equations
Cover
Half-Title
Title
Copyright
Dedication
Contents
Preface
Chapter 1: Sets, Numbers, and Algebra
1.1 Sets and Numbers
Review Exercises – Section 1.1
1.2 Rules of Algebra
Commutative Property
Associative Property
Distributive Property
Review Exercises – Section 1.2
1.3 Complex Numbers and Hyperreal Numbers
Complex Numbers
Hyperreal Numbers
Principle 1: The Extension Principle
Principle 2: The Transfer Principle
Principle 3: The Standard Part Principle
Rules for Infinitesimal Numbers
Rules for Infinite Numbers
Review Exercises – Section 1.3
1.4 Intervals
Review Exercises – Section 1.4
1.5 Expanding and Factorizing Mathematical Expressions
Review Exercises – Section 1.5
1.6 A Numerical Method for Finding Roots
Review Exercises Section 1.6
Chapter 2: Lines, Curves, Functions, and Equations
2.1 The Cartesian Plane
Review Exercises – Section 2.1
2.2 Functions
Review Exercises – Section 2.2
2.3 Limits
Review Exercises – Section 2.3
2.4 Power Functions
Review Exercises – Section 2.4
2.5 Exponential and Logarithmic Functions
Review Exercises – Section 2.5
2.6 Polynomial Functions
Review Exercises – Section 2.6
2.7 Sine, Cosine, and Tangent Functions
Review Exercises – Section 2.7
Chapter 3: Simultaneous Equations
3.1 Linear Equations
Review Exercises – Section 3.1
3.2 Systems of Linear Simultaneous Equations
Review Exercises – Section 3.2
3.3 Some Examples from Economics
Review Exercises – Section 3.3
3.4 Nonlinear Simultaneous Equations
Review Exercises – Section 3.4
3.5 Numerical Methods
Review Exercises – Section 3.5
Chapter 4: Derivatives and Differentiation
4.1 Differential Calculus
Review Exercises – Section 4.1
4.2 Differentiation from First Principles
Review Exercises – Section 4.2
4.3 Rules for Differentiation
Rule 1: Multiplication by a Constant
Rule 2: Sum–Difference Rule
Rule 3: The Product Rule
Rule 4: The Quotient Rule
Rule 5: The Power Function Rule
Rule 6: The Chain Rule
Rule 7: The Inverse Function Rule
Generalization of the Power Function Rule
Review Exercises – Section 4.3
4.4 Some Economic Examples
Review Exercises – Section 4.4
4.5 Higher-Order Derivatives
Review Exercises – Section 4.5
4.6 Numerical Methods
Review Exercises – Section 4.6
Chapter 5: Optimization
5.1 Identifying Critical Points
Review Exercises – Section 5.1
5.2 Some Economic Examples
Review Exercises – Section 5.2
5.3 Convexity and Concavity
Review Exercises – Section 5.3
5.4 Numerical Methods for Finding Turning Points
Review Exercises – Section 5.4
Chapter 6: Optimization of Multivariable Functions
6.1 Multivariable Functions
Review Exercises – Section 6.1
6.2 Partial Derivatives
Review Exercise – Section 6.2
6.3 Differentials and the Total Derivative
Review Exercises – Section 6.3
6.4 Optimization with Multivariable Functions
Review Exercises – Section 6.4
6.5 Optimization with Constraints
Review Exercises – Section 6.5
6.6 Numerical Methods
Review Exercises – Section 6.6
Chapter 7: Integration
7.1 Definite Integration
Review Exercises – Section 7.1
7.2 The Fundamental Theorem of Calculus
Review Exercises – Section 7.2
7.3 Integration by Substitution and by Parts
Review Exercises – Section 7.3
7.4 Some Economic Applications
Review Exercises – Section 7.4
7.5 Numerical Methods of Integration
Review Exercises – Section 7.5
Chapter 8: Matrices
8.1 Matrix Algebra
Addition or Subtraction of Matrices
Matrix Transposition
Scalar Multiplication
Vector Multiplication
Matrix Multiplication
Review Exercises – Section 8.1
8.2 Determinants
Review Exercises – Section 8.2
8.3 Matrix Inversion
Review Exercises – Section 8.3
8.4 Solving Simultaneous Equations with Matrices
Review Exercises – Section 8.4
8.5 Eigenvalues and Eigenvectors
Review Exercises – Section 8.5
Chapter 9: First-Order Differential Equations
9.1 Separable Differential Equations
Review Exercises – Section 9.1
9.2 First-order Linear Differential Equations with Constant Coefficients
Review Exercises – Section 9.2
9.3 Solutions Using an Integrating Factor
Review Exercises – Section 9.3
9.4 The Method of Undetermined Coefficients
Review Exercises – Section 9.4
9.5 Numerical Methods
Review Exercises – Section 9.5
9.6 Some Economic Examples
Review Exercises – Section 9.6
Chapter 10: Second-Order Differential Equations
10.1 Homogeneous Second-Order Linear Differential Equations
Review Exercises – Section 10.1
10.2 Initial Value Problems with Second-Order Differential Equations
Review Exercises – Section 10.2
10.3 Nonhomogeneous Second-Order Linear Differential Equations
Review Exercises – Section 10.3
10.4 Numerical Solution for Second-Order Equations
Review Exercises – Section 10.4
Appendix: The Principle of Superposition
Appendix: Derivation of the Complementary Function When the Roots are Complex
Chapter 11: Difference Equations
11.1 First-Order Difference Equations
Review Exercises – Section 11.1
11.2 Second-Order Difference Equations
Review Exercises – Section 11.2
11.3 Solution by Backward Substitution
Review Exercises – Section 11.3
11.4 Boundary Conditions and Expectations
Review Exercises – Section 11.4
Appendix: Solution for the Case of Complex Roots
Appendix A: Coding in Python
Appendix B: Odd Numbered Exercises Answers
Index
