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MATLAB Mathematical Analysis

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

  1. Cover
  2. Title
  3. Copyright
  4. Contents at a Glance
  5. Contents
  6. About the Author
  7. About the Technical Reviewer
  8. Introduction
  9. Also Available
  10. Chapter 1: MATLAB Introduction and Working Environment
    1. Introduction to Working with MATLAB
    2. Numerical Calculations with MATLAB
    3. Symbolic Calculations with MATLAB
    4. Graphics with MATLAB
    5. MATLAB and Programming
  11. Chapter 2: Numbers, Operators, Variables and Functions
    1. Numbers
    2. Integers and Integer Variable Functions
    3. Real Numbers and Functions of Real Variables
    4. Trigonometric Functions
    5. Hyperbolic Functions
    6. Exponential and Logarithmic Functions
    7. Numeric Variable-Specific Functions
    8. One-Dimensional, Vector and Matrix Variables
    9. Elements of Vector Variables
    10. Elements of Matrix Variables
    11. Specific Matrix Functions
    12. Random Numbers
    13. Operators
      1. Arithmetic Operators
      2. Logical Operators
      3. Relational Operators
    14. Symbolic Variables
    15. Symbolic Functions and Functional Operations: Composite and Inverse Functions
    16. Commands that Handle Variables in the Workspace and Store them in Files
  12. Chapter 3: Complex Numbers and Functions of Complex Variables
    1. Complex Numbers
    2. General Functions of Complex Variables
      1. Trigonometric Functions of a Complex Variable
      2. Hyperbolic Functions of a Complex Variable
      3. Exponential and Logarithmic Functions of a Complex Variable
      4. Specific Functions of a Complex Variable
    3. Basic Functions with a Complex Vector Argument
    4. Basic Functions with a Complex Matrix Argument
    5. General Functions with a Complex Matrix Argument
      1. Trigonometric Functions of a Complex Matrix Variable
      2. Hyperbolic Functions of a Complex Matrix Variable
      3. Exponential and Logarithmic Functions of a Complex Matrix Variable
      4. Specific Functions of Complex Matrix Variables
    6. Operations with Real and Complex Matrix Variables
  13. Chapter 4: Graphics in MATLAB. Curves, Surfaces and Volumes
    1. Introduction
    2. Exploratory Graphics
    3. Curves in Explicit, Implicit, Parametric and Polar Coordinates
    4. Three-Dimensional (3D) Curves
    5. Explicit and Parametric Surfaces: Contour Plots
    6. Three-Dimensional Geometric Forms
    7. Specialized Graphics
    8. 2D and 3D Graphics Options
  14. Chapter 5: Limits of Sequences and Functions. Continuity in One and Several Variables
    1. Limits
    2. Sequences of Functions
    3. Continuity
    4. Limits in Several Variables. Iterated and Directional Limits
    5. Continuity in Several Variables
  15. Chapter 6: Numerical Series and Power Series
    1. Numerical Series of Non-negative Terms
    2. Convergence Criteria: The Ratio Test
    3. Raabe’s Criterion
    4. The Root Test
    5. Other Convergence Criteria
    6. Alternating Numerical Series. Dirichlet and Abel’s Criteria
    7. Power Series
    8. Power Series Expansions
  16. Chapter 7: Derivatives. One and Several Variables
    1. Derivatives
    2. Partial Derivatives
    3. Applications of Differentiation. Tangents, Asymptotes, Extreme Points and Points of Inflection
    4. Differentiation in Several Variables
    5. Extreme Points in Several Variables
    6. Conditional minima and maxima. The method of “Lagrange multipliers”
    7. Vector Differential Calculus
    8. The Composite Function Theorem
    9. The Implicit Function Theorem
    10. The Inverse Function Theorem
    11. The Change of Variables Theorem
    12. Series Expansions in Several Variables
    13. Curl, Divergence and the Laplacian
    14. Rectangular, Spherical and Cylindrical Coordinates
  17. Chapter 8: Integration in One and Several Variables. Applications
    1. Integrals
    2. Indefinite Integrals, Change of Variables and Integration by Parts
    3. Integration by Reduction and Cyclic Integration
    4. Rational and Irrational Integrals. Binomial Integrals
    5. Definite Integrals and Applications
    6. Curve Arc Length
    7. The Area between Two Curves
    8. Surfaces of Revolution
    9. Volumes of Revolution
    10. Curvilinear Integrals
    11. Improper Integrals
    12. Parameter Dependent Integrals
    13. Approximate Numerical Integration
    14. Special Integrals
    15. Definite Integrals and Applications. Several Variables
    16. Planar Areas and Double Integration
    17. Calculation of Surface Area by Double Integration
    18. Calculation of Volumes by Double Integration
    19. Calculation of Volumes and Triple Integrals
    20. Green’s Theorem
    21. The Divergence Theorem
    22. Stokes’ Theorem
  18. Chapter 9: Differential Equations
    1. First Order Differential Equations
    2. Numerical Solutions of Differential Equations
    3. Ordinary Differential Equations with Initial Values
    4. Ordinary Differential Equations with Boundary Values
    5. Partial Differential Equations