Essential Mathematics for Economic Analysis/ Knut Sydsaeter, Peter Hammond, Arne Strom, et.al., english

Essentials of Logic and Set Theory
Essentials of Set Theory
Essentials of Logic
Mathematical Proofs
Mathematical Induction
Review Exercises
Algebra
The Real Numbers
Integer Powers
Rules of Algebra
Fractions
Fractional Powers
Inequalities
Intervals and Absolute Values
Sign Diagrams
Summation Notation
Rules for Sums
Newton's Binomial Formula
Double Sums
Review Exercises
Solving Equations
Solving Equations
Equations and Their Parameters
Quadratic Equations
Some Nonlinear Equations
Using Implication Arrows
Two Linear Equations in Two Unknowns
Review Exercises
Functions of One Variable
Introduction
Definitions
Graphs of Functions
Linear Functions
Linear Models
Quadratic Functions
Polynomials
Power Functions
Exponential Functions
Logarithmic Functions
Review Exercises
Properties of Functions
Shifting Graphs
New Functions From Old
Inverse Functions
Graphs of Equations
Distance in The Plane
General Functions
Review Exercises
II SINGLE-VARIABLE CALCULUS
Differentiation
Slopes of Curves
Tangents and Derivatives
Increasing and Decreasing Functions
Economic Applications
A Brief Introduction to Limits
Simple Rules for Differentiation
Sums, Products, and Quotients
The Chain Rule
Higher-Order Derivatives
Exponential Functions
Logarithmic Functions
Review Exercises
Derivatives in Use
Implicit Differentiation
Economic Examples
The Inverse Function Theorem
Linear Approximations
Polynomial Approximations
Taylor's Formula
Elasticities
Continuity
More on Limits
The Intermediate Value Theorem
Infinite Sequences
L'Hôpital's Rule Review Exercises
Review Exercises
Concave and Convex Functions
Intuition
Definitions
General Properties
First Derivative Tests
Second Derivative Tests
Inflection Points
Review Exercises
Optimization
Extreme Points
Simple Tests for Extreme Points
Economic Examples
The Extreme and Mean Value Theorems
Further Economic Examples
Local Extreme Points
Review Exercises
Integration
Indefinite Integrals
Area and Definite Integrals
Properties of Definite Integrals
Economic Applications
Integration by Parts
Integration by Substitution
Infinite Intervals of Integration
Review Exercises
Topics in Finance and Dynamics
Interest Periods and Effective Rates
Continuous Compounding
Present Value
Geometric Series
Total Present Value
Mortgage Repayments
Internal Rate of Return
A Glimpse at Difference Equations
Essentials of Differential Equations
Separable and Linear Differential Equations
Review Exercises
III MULTI-VARIABLE ALGEBRA
Matrix Algebra
Matrices and Vectors
Systems of Linear Equations
Matrix Addition
Algebra of Vectors
Matrix Multiplication
Rules for Matrix Multiplication
The Transpose
Gaussian Elimination
Geometric Interpretation of Vectors
Lines and Planes
Review Exercises
Determinants, Inverses, and Quadratic Forms
Determinants of Order 2
Determinants of Order 3
Determinants in General
Basic Rules for Determinants
Expansion by Cofactors
The Inverse of a Matrix
A General Formula for The Inverse
Cramer's Rule
The Leontief Mode
Eigenvalues and Eigenvectors
Diagonalization
Quadratic Forms
Review Exercises
IV MULTI-VARIABLE CALCULUS
Multivariable Functions
Functions of Two Variables
Partial Derivatives with Two Variables
Geometric Representation
Surfaces and Distance
Functions of More Variables
Partial Derivatives with More Variables
Convex Sets
Concave and Convex Functions
Economic Applications
Partial Elasticities
Review Exercises
Partial Derivatives in Use
A Simple Chain Rule
Chain Rules for Many Variables
Implicit Differentiation Along A Level Curve
Level Surfaces
Elasticity of Substitution
Homogeneous Functions of Two Variables
Homogeneous and Homothetic Functions
Linear Approximations
Differentials
Systems of Equations
Differentiating Systems of Equations
Review Exercises
Multiple Integrals
Double Integrals Over Finite Rectangles
Infinite Rectangles of Integration
Discontinuous Integrands and Other Extensions
Integration Over Many Variables
Review Exercises
V MULTI-VARIABLE OPTIMIZATION
Unconstrained Optimization
Two Choice Variables: Necessary Conditions
Two Choice Variables: Sufficient Conditions
Local Extreme Points
Linear Models with Quadratic Objectives
The Extreme Value Theorem
Functions of More Variables
Comparative Statics and the Envelope Theorem
Review Exercises
Equality Constraints
The Lagrange Multiplier Method
Interpreting the Lagrange Multiplier
Multiple Solution Candidates
Why Does the Lagrange Multiplier Method Work?
Sufficient Conditions
Additional Variables and Constraints
Comparative Statics
Review Exercises
Linear Programming
A Graphical Approach
Introduction to Duality Theory
The Duality Theorem
A General Economic Interpretation
Complementary Slackness
Review Exercises
Nonlinear Programming
Two Variables and One Constraint
Many Variables and Inequality Constraints
Nonnegativity Constraints