Book description
MATLAB Mathematical Analysis is a reference book that presents the techniques of mathematical analysis through examples and exercises resolved with MATLAB software. The purpose is to give you examples of the mathematical analysis functions offered by MATLAB so that you can use them in your daily work regardless of the application. The book supposes proper training in the mathematics and so presents the basic knowledge required to be able to use MATLAB for calculational or symbolic solutions to your problems for a vast amount of MATLAB functions.
The book begins by introducing the reader to the use of numbers, operators, variables and functions in the MATLAB environment. Then it delves into working with complex variables. A large section is devoted to working with and developing graphical representations of curves, surfaces and volumes. MATLAB functions allow working with twodimensional and threedimensional graphics, statistical graphs, curves and surfaces in explicit, implicit, parametric and polar coordinates. Additional work implements twisted curves, surfaces, meshes, contours, volumes and graphical interpolation.
The following part covers limits, functions, continuity and numerical and power series. Then differentiation is addressed in one and several variables including differential theorems for vector fields. Thereafter the topic of integration is handled including improper integrals, definite and indefinite integration, integration in multiple variables and multiple integrals and their applications.
Differential equations are exemplified in detail, Laplace transforms, Tayor series, and the RungaKutta method and partial differential equations.
Table of contents
 Cover
 Title
 Copyright
 Contents at a Glance
 Contents
 About the Author
 About the Technical Reviewer
 Introduction
 Also Available
 Chapter 1: MATLAB Introduction and Working Environment

Chapter 2: Numbers, Operators, Variables and Functions
 Numbers
 Integers and Integer Variable Functions
 Real Numbers and Functions of Real Variables
 Trigonometric Functions
 Hyperbolic Functions
 Exponential and Logarithmic Functions
 Numeric VariableSpecific Functions
 OneDimensional, Vector and Matrix Variables
 Elements of Vector Variables
 Elements of Matrix Variables
 Specific Matrix Functions
 Random Numbers
 Operators
 Symbolic 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
 Chapter 4: Graphics in MATLAB. Curves, Surfaces and Volumes
 Chapter 5: Limits of Sequences and Functions. Continuity in One and Several Variables
 Chapter 6: Numerical Series and Power Series

Chapter 7: Derivatives. One and Several Variables
 Derivatives
 Partial Derivatives
 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”
 Vector Differential Calculus
 The Composite Function Theorem
 The Implicit Function Theorem
 The Inverse 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
 Integrals
 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
 Curve Arc Length
 The Area between Two Curves
 Surfaces of Revolution
 Volumes of Revolution
 Curvilinear Integrals
 Improper Integrals
 Parameter Dependent Integrals
 Approximate Numerical Integration
 Special Integrals
 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
 Green’s Theorem
 The Divergence Theorem
 Stokes’ Theorem
 Chapter 9: Differential Equations
Product information
 Title: MATLAB Mathematical Analysis
 Author(s):
 Release date: December 2014
 Publisher(s): Apress
 ISBN: 9781484203491
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