Sydsaeter Essential Mathematics for Economic Analysis – 5e TOC   Ch01: Essentials of Logic and Set Theory 1.1 Essentials of set theory 1.2 Some aspects of logic 1.3 Mathematical proofs 1.4 Mathematical induction   Ch02: 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 Summation 2.9 Rules for sums 2. 10 Newton’s binomial formula 2. 11 Double sums   Ch03: Solving Equations 3.1 Solving equations 3.2 Equations and their parameters 3.3 Quadratic equations 3.4 Nonlinear equations 3.5 Using implication arrows 3.6 Two linear equations in two unknowns   Ch04: Functions of One Variable 4.1 Introduction 4.2 Basic 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   Ch05: 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   Ch06: Differentiation 6.1 Slopes of curves 6.2 Tangents and derivatives 6.3 Increasing and decreasing functions 6.4 Rates of change 6.5 A dash of 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   Ch07: Derivatives in Use 7.1 Implicit differentiation 7.2 Economic examples 7.3 Differentiating the inverse 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 and Newton’s method 7. 11 Infinite sequences 7. 12 L'Hôpital's Rule   Ch08: Single-Variable Optimization 8.1 Extreme points 8.2 Simple tests for extreme points 8.3 Economic examples 8.4 The Extreme Value Theorem 8.5 Further economic examples 8.6 Local extreme points 8.7 Inflection points   Ch09: Integration 9.1 Indefinite integrals 9.2 Area and definite integrals 9.3 Properties of definite integrals 9.4 Economic applications 9.5 Integration by parts 9.6 Integration by substitution 9.7 Infinite intervals of integration 9.8 A glimpse at differential equations 9.9 Separable and linear differential equations       Ch10: Topics in Financial Mathematics 10.1   Interest periods and effective rates 10.2   Continuous compounding 10.3   Present value 10.4   Geometric series 10.5   Total present value 10.6   Mortgage repayments 10.7   Internal rate of return 10.8   A glimpse at difference equations   Ch11: Functions of Many Variables 11.1   Functions of two variables 11.2   Partial derivatives with two variables 11.3   Geometric representation 11.4   Surfaces and distance 11.5   Functions of more variables 11.6   Partial derivatives with more variables 11.7   Economic applications 11.8   Partial elasticities   Ch12: Tools for Comparative Statics 12.1   A simple chain rule 12.2   Chain rules for many variables 12.3   Implicit differentiation along a level curve 12.4   More general cases 12.5   Elasticity of substitution 12.6   Homogeneous functions of two variables 12.7   Homogeneous and homothetic functions 12.8   Linear approximations 12.9   Differentials 12. 10 Systems of equations 12. 11 Differentiating systems of equations   Ch13: Multivariable Optimization 13.1   Two variables: necessary conditions 13.2   Two variables: sufficient conditions 13.3   Local extreme points 13.4   Linear models with quadratic objectives 13.5   The Extreme Value Theorem 13.6   The general case 13.7   Comparative statics and the envelope theorem   Ch14: Constrained Optimization 14.1   The Lagrange Multiplier Method 14.2   Interpreting the Lagrange multiplier 14.3   Multiple solution candidates 14.4   Why the Lagrange method works 14.5   Sufficient conditions 14.6   Additional variables and constraints 14.7   Comparative statics 14.8   Nonlinear programming: a simple case 14.9   Multiple inequality constraints 14. 10 Nonnegativity constraints   Ch15: Matrix and Vector Algebra 15.1   Systems of linear equations 15.2   Matrices and matrix operations 15.3   Matrix multiplication 15.4   Rules for matrix multiplication 15.5   The transpose 15.6   Gaussian elimination 15.7   Vectors 15.8   Geometric interpretation of vectors 15.9   Lines and planes   Ch16: Determinants and Inverse Matrices 16.1   Determinants of order 2 16.2   Determinants of order 3 16.3   Determinants in general 16.4   Basic rules for determinants 16.5   Expansion by cofactors 16.6   The inverse of a matrix 16.7   A general formula for the inverse 16.8   Cramer's Rule 16.9   The Leontief Model   Ch17: Linear Programming 17.1   A graphical approach 17.2   Introduction to Duality Theory 17.3   The Duality Theorem 17.4   A general economic interpretation 17.5   Complementary slackness