Essential Mathematics for Economic Analysis. (2021)

• Record Type: Book
• Further Information: Note: Knut Sydsaeter, Peter Hammond, Arne Strom, Andrés Carvajal.
• Authors: Sydsæter, Knut; Hammond, Peter; Strøm, Arne; Carvajal, Andrés
• Contents: 1 Essentials of Logic and Set Theory 1.1 Essentials of Set Theory 1.2 Essentials of Logic 1.3 Mathematical Proofs 1.4 Mathematical Induction Review Exercises 2 Algebra 2.1 The Real Numbers 2.2 Integer Powers 2.3 Rules of Algebra 2.4 Fractions 2.5 Fractional Powers 2.6 Inequalities 2.7 Intervals and Absolute Values 2.8 Sign Diagrams 2.9 Summation Notation 2.10 Rules for Sums 2.11 Newton's Binomial Formula 2.12 Double Sums Review Exercises 3 Solving Equations 3.1 Solving Equations 3.2 Equations and Their Parameters 3.3 Quadratic Equations 3.4 Some Nonlinear Equations 3.5 Using Implication Arrows 3.6 Two Linear Equations in Two Unknowns Review Exercises 4 Functions of One Variable 4.1 Introduction 4.2 Definitions 4.3 Graphs of Functions 4.4 Linear Functions 4.5 Linear Models 4.6 Quadratic Functions 4.7 Polynomials 4.8 Power Functions 4.9 Exponential Functions 4.10 Logarithmic Functions Review Exercises 5 Properties of Functions 5.1 Shifting Graphs 5.2 New Functions From Old 5.3 Inverse Functions 5.4 Graphs of Equations 5.5 Distance in The Plane 5.6 General Functions Review Exercises II SINGLE-VARIABLE CALCULUS 6 Differentiation 6.1 Slopes of Curves 6.2 Tangents and Derivatives 6.3 Increasing and Decreasing Functions 6.4 Economic Applications 6.5 A Brief Introduction to Limits 6.6 Simple Rules for Differentiation 6.7 Sums, Products, and Quotients 6.8 The Chain Rule 6.9 Higher-Order Derivatives 6.10 Exponential Functions 6.11 Logarithmic Functions Review Exercises 7 Derivatives in Use 7.1 Implicit Differentiation 7.2 Economic Examples 7.3 The Inverse Function Theorem 7.4 Linear Approximations 7.5 Polynomial Approximations 7.6 Taylor's Formula 7.7 Elasticities 7.8 Continuity 7.9 More on Limits 7.10 The Intermediate Value Theorem 7.11 Infinite Sequences 7.12 L'Hôpital's Rule Review Exercises 8 Concave and Convex Functions 8.1 Intuition 8.2 Definitions 8.3 General Properties 8.4 First Derivative Tests 8.5 Second Derivative Tests 8.6 Inflection Points Review Exercises 9 Optimization 9.1 Extreme Points 9.2 Simple Tests for Extreme Points 9.3 Economic Examples 9.4 The Extreme and Mean Value Theorems 9.5 Further Economic Examples 9.6 Local Extreme Points Review Exercises 10 Integration 10.1 Indefinite Integrals 10.2 Area and Definite Integrals 10.3 Properties of Definite Integrals 10.4 Economic Applications 10.5 Integration by Parts 10.6 Integration by Substitution 10.7 Infinite Intervals of Integration Review Exercises 11 Topics in Finance and Dynamics 11.1 Interest Periods and Effective Rates 11.2 Continuous Compounding 11.3 Present Value 11.4 Geometric Series 11.5 Total Present Value 11.6 Mortgage Repayments 11.7 Internal Rate of Return 11.8 A Glimpse at Difference Equations 11.9 Essentials of Differential Equations 11.10 Separable and Linear Differential Equations Review Exercises III MULTI-VARIABLE ALGEBRA 12 Matrix Algebra 12.1 Matrices and Vectors 12.2 Systems of Linear Equations 12.3 Matrix Addition 12.4 Algebra of Vectors 12.5 Matrix Multiplication 12.6 Rules for Matrix Multiplication 12.7 The Transpose 12.8 Gaussian Elimination 12.9 Geometric Interpretation of Vectors 12.10 Lines and Planes Review Exercises 13 Determinants, Inverses, and Quadratic Forms 13.1 Determinants of Order 2 13.2 Determinants of Order 3 13.3 Determinants in General 13.4 Basic Rules for Determinants 13.5 Expansion by Cofactors 13.6 The Inverse of a Matrix 13.7 A General Formula for The Inverse 13.8 Cramer's Rule 13.9 The Leontief Model 13.10 Eigenvalues and Eigenvectors 13.11 Diagonalization 13.12 Quadratic Forms Review Exercises IV MULTI-VARIABLE CALCULUS 14 Multivariable Functions 14.1 Functions of Two Variables 14.2 Partial Derivatives with Two Variables 14.3 Geometric Representation 14.4 Surfaces and Distance 14.5 Functions of More Variables 14.6 Partial Derivatives with More Variables 14.7 Convex Sets 14.8 Concave and Convex Functions 14.9 Economic Applications 14.10 Partial Elasticities Review Exercises 15 Partial Derivatives in Use 15.1 A Simple Chain Rule 15.2 Chain Rules for Many Variables 15.3 Implicit Differentiation Along A Level Curve 15.4 Level Surfaces 15.5 Elasticity of Substitution 15.6 Homogeneous Functions of Two Variables 15.7 Homogeneous and Homothetic Functions 15.8 Linear Approximations 15.9 Differentials 15.10 Systems of Equations 15.11 Differentiating Systems of Equations Review Exercises 16 Multiple Integrals 16.1 Double Integrals Over Finite Rectangles 16.2 Infinite Rectangles of Integration 16.3 Discontinuous Integrands and Other Extensions 16.4 Integration Over Many Variables V MULTI-VARIABLE OPTIMIZATION 17 Unconstrained Optimization 17.1 Two Choice Variables: Necessary Conditions 17.2 Two Choice Variables: Sufficient Conditions 17.3 Local Extreme Points 17.4 Linear Models with Quadratic Objectives 17.5 The Extreme Value Theorem 17.6 Functions of More Variables 17.7 Comparative Statics and the Envelope Theorem Review Exercises 18 Equality Constraints 18.1 The Lagrange Multiplier Method 18.2 Interpreting the Lagrange Multiplier 18.3 Multiple Solution Candidates 18.4 Why Does the Lagrange Multiplier Method Work? 18.5 Sufficient Conditions 18.6 Additional Variables and Constraints 18.7 Comparative Statics Review Exercises 19 Linear Programming 19.1 A Graphical Approach 19.2 Introduction to Duality Theory 19.3 The Duality Theorem 19.4 A General Economic Interpretation 19.5 Complementary Slackness Review Exercises 20 Nonlinear Programming 20.1 Two Variables and One Constraint 20.2 Many Variables and Inequality Constraints 20.3 Nonnegativity Constraints Review Exercises Appendix: Geometry Solutions to the Exercises Index.
• Edition: Sixth edition
• Publisher Details: Harlow : Pearson
• Publication Date: 2021
• Copyright Date: 2021
• Extent: 1 online resource
• Subjects: Economics
• Languages: English
• ISBNs: 9781292359298; 1292359293
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.