Mathematics Handbook for Science and Engineering
1 Fundamentals, Discrete Mathematics
1.1 Logic
1.2 Set Theory
1.3 Binary Relations and Functions
1.4 Algebraic Structures
1.5 Graph Theory
1.6 Codes
2 Algebra
3 Geometry and Trigonometry
4 Linear Algebra
4.1 Matrices
4.2 Determinants
4.3 Systems of Linear Equations
4.4 Linear Coordinate Transformation
4.5 Eigenvalues, Diagonalization
4.6 Quadratic Forms
4.7 Linear Spaces
4.8 Linear Mappings
4.9 Tensors
4.8 Complex matrices
5 The Elementary Functions
6 Differential Calculus (one variable)
6.1 Some Basic Concepts
6.2 Limits and Continuity
6.3 Derivatives
6.4 Monotonicity, Extremes of Functions
7 Integral Calculus
7.1 Indefinite Integrals
7.2 Definite Integrals
7.3 Applications of Differential and Integral Calculus
7.4 Tables of Indefinite Integrals
7.5 Tables of Definite Integrals
8 Sequences and Series
8.1 Sequences of Numbers
8.2 Sequences of Functions
8.3 Series of Constant Terms
8.4 Series of Functions
8.5 Taylor Series
8.6 Special Sums and Series
9 Ordinary Differential Equations (ODE)
9.1 Differential Equations of the First Order
9.2 Differential Equations of the Second Order
9.3 Linear Differential Equations
9.4 Autonomous systems
9.5 General Concepts and Results
9.6 Linear Differential Equations
10 Multidimensional Calculus
10.1 The Space R^n
10.2 Surfaces. Tangent Planes
10.3 Limits and Continuity
10.4 Partial Derivatives
10.5 Extremes of Functions
10.6 Functions f:R^n -> R^m (R^n -> R^m)
10.7 Double Integrals
10.8 Triple Integrals
10.9 Partial Differential Equations
11 Vector Analysis
11.1 Curves
11.2 Vector Fields
11.3 Line Integrals
11.4 Surface Integrals
12 Orthogonal Series and Special Functions
13 Transforms
14 Complex Analysis
15 Optimizations
15.1 Calculus of Variations
15.2 Linear Optimizations
15.3 Integer and Combinatorial Optimization
15.4 Nonlinear Optimization
15.5 Dynamic Optimization
16 Numerical Analysis
17 Probability Theory
17.1 Basic Probability Theory
17.2 Probability Distributions
17.3 Stochastic Processes
17.4 Algorithms for Calculation of Probability Distributions
17.5 Simulation
17.6 Queueing Systems
17.7 Reliability
17.8 Tables
18 Statistics
18.1 Descriptive Statistics
18.2 Point Estimation
18.3 Confidence Intervals
18.4 Table for Confidence Intervals
18.5 Tests of Significance
18.6 Linear Models
18.7 Distribution-free Methods
18.8 Statistical Quality Control
18.9 Factorial Experiments
18.10 Analysis of life time (failure time) data
18.11 Statistical glossary
