Essential mathematics for economic analysis

Table of Contents;
Seedeater Essential Mathematics for Economic Analysis – 5e TOC;
Chat 1: 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;
Chat 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 Summation;
2.9 Rules for sums;
2. 10 Newton’s binomial formula;
2. 11 Double sums;
Chat 3: 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;
Chat 4: 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;
Chat 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;
Chat 6: 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;
Chat 7: 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;
Chat 8: Single-Variable Optimization;
8.1 Extreme points;
8.2 Simple tests for extreme point;
8.3 Economic example;
8.4 The Extreme Value Theorem;
8.5 Further economic examples;
8.6 Local extreme points;
8.7 Inflection points;
Chat 9: 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;
Chat 10: 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;
Chat 12: Tools for Comparative Statics;
12.1 A simple chain rule;
12.2 Chain rules for many variable;
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;
Chat 13: 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;
Chat 14: 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 No negativity constraints;
Chat 15: 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;
Chat 16: 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 Duality Theory;
17.3 The Duality Leontief Model;
Chat 17: Linear Programming;
17.1 A graphical approach;
17.2 Introduction to
Theorem;