Contents
Chapter 1: MATLAB Introduction and Working Environment
Introduction to Working with MATLAB
Numerical Calculations with MATLAB
Symbolic Calculations with MATLAB
Chapter 2: Numbers, Operators, Variables and Functions
Integers and Integer Variable Functions
Real Numbers and Functions of Real Variables
Exponential and Logarithmic Functions
Numeric Variable-Specific Functions
One-Dimensional, Vector and Matrix Variables
Symbolic Functions and Functional Operations: Composite and Inverse Functions
Commands that Handle Variables in the Workspace and Store them in Files
Chapter 3: Complex Numbers and Functions of Complex Variables
General Functions of Complex Variables
Trigonometric Functions of a Complex Variable
Hyperbolic Functions of a Complex Variable
Exponential and Logarithmic Functions of a Complex Variable
Specific Functions of a Complex Variable
Basic Functions with a Complex Vector Argument
Basic Functions with a Complex Matrix Argument
General Functions with a Complex Matrix Argument
Trigonometric Functions of a Complex Matrix Variable
Hyperbolic Functions of a Complex Matrix Variable
Exponential and Logarithmic Functions of a Complex Matrix Variable
Specific Functions of Complex Matrix Variables
Operations with Real and Complex Matrix Variables
Chapter 4: Graphics in MATLAB. Curves, Surfaces and Volumes
Curves in Explicit, Implicit, Parametric and Polar Coordinates
Explicit and Parametric Surfaces: Contour Plots
Three-Dimensional Geometric Forms
Chapter 5: Limits of Sequences and Functions. Continuity in One and Several Variables
Limits in Several Variables. Iterated and Directional Limits
Continuity in Several Variables
Chapter 6: Numerical Series and Power Series
Numerical Series of Non-negative Terms
Convergence Criteria: The Ratio Test
Alternating Numerical Series. Dirichlet and Abel’s Criteria
Chapter 7: Derivatives. One and Several Variables
Applications of Differentiation. Tangents, Asymptotes, Extreme Points and Points of Inflection
Differentiation in Several Variables
Extreme Points in Several Variables
Conditional minima and maxima. The method of “Lagrange multipliers”
The Composite Function Theorem
The Change of Variables Theorem
Series Expansions in Several Variables
Curl, Divergence and the Laplacian
Rectangular, Spherical and Cylindrical Coordinates
Chapter 8: Integration in One and Several Variables. Applications
Indefinite Integrals, Change of Variables and Integration by Parts
Integration by Reduction and Cyclic Integration
Rational and Irrational Integrals. Binomial Integrals
Definite Integrals and Applications
Approximate Numerical Integration
Definite Integrals and Applications. Several Variables
Planar Areas and Double Integration
Calculation of Surface Area by Double Integration
Calculation of Volumes by Double Integration
Calculation of Volumes and Triple Integrals
Chapter 9: Differential Equations
First Order Differential Equations
Numerical Solutions of Differential Equations
Ordinary Differential Equations with Initial Values