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 two-dimensional and three-dimensional 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 Runga-Kutta 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 Variable-Specific Functions
- One-Dimensional, 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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