Academic Press Programming Mathematics Using MATLAB 1st edition by Lisa Oberbroeckling 0128177993 9780128177990

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ISBN 10:0128177993 
ISBN 13:9780128177990
Author:Lisa Oberbroeckling

Providing an alternative to engineering-focused resources in the area, Programming Mathematics Using MATLAB® introduces the basics of programming and of using MATLAB® by highlighting many mathematical examples. Emphasizing mathematical concepts through the visualization of programming throughout the book, this useful resource utilizes examples that may be familiar to math students (such as numerical integration) and others that may be new (such as fractals). Additionally, the text uniquely offers a variety of MATLAB® projects, all of which have been class-tested thoroughly, and which enable students to put MATLAB® programming into practice while expanding their comprehension of concepts such as Taylor polynomials and the Gram–Schmidt process.

Programming Mathematics Using MATLAB® is appropriate for readers familiar with sophomore-level mathematics (vectors, matrices, multivariable calculus), and is useful for math courses focused on MATLAB® specifically and those focused on mathematical concepts which seek to utilize MATLAB® in the classroom.

Provides useful visual examples throughout for student comprehension

Includes valuable, class-tested projects to reinforce both familiarity with MATLAB® and a deeper understanding of mathematical principles

Offers downloadable MATLAB® scripts to supplement practice and provide useful example

 

Academic Press Programming Mathematics Using MATLAB 1st edition Table of contents:

Part 1 MATLAB®

1 Introduction to MATLAB®

1.1 Basic MATLAB® information

1.1.1 Starting MATLAB

1.1.2 Good commands to know

1.2 Basic mathematics

1.2.1 Built-in mathematical functions

1.2.2 Precedence rules

1.2.3 Formats

1.3 Variables

1.4 Diaries and script files

1.5 Exercises

2 Vectors and Matrices (Arrays)

2.1 One-dimensional arrays (vectors)

2.1.1 Constant spaced vectors

2.1.2 Equally spaced vectors

2.2 Two-dimensional arrays (matrices)

2.3 Addressing elements of vectors/arrays

2.4 Component-wise calculations

2.5 Random numbers

2.6 Exercises

3 Plotting in MATLAB®

3.1 Basic 2D plots

3.2 Bad domain examples

3.3 Axis settings

3.4 Multiple plots

3.5 Color, line, and marker modifications

3.5.1 Clf/close all

3.5.2 Subplots

3.6 Other 2D plots

3.6.1 Parametric curves

3.6.2 Polar curves

3.7 Exercises

4 Three-Dimensional Plots

4.1 Vector functions or space curves

4.2 Plotting surfaces

4.2.1 The meshgrid command

4.2.2 Domain issues

4.2.3 Level curves

4.2.4 Multiple plots and modifying colors

4.3 View command

4.4 Axis settings, revisited

4.5 Other coordinate systems and 3D graphs

4.5.1 The sphere and cylinder commands

4.5.2 Cylindrical coordinates

4.5.3 Spherical coordinates

4.6 Exercises

5 Functions

5.1 The lookfor and help commands

5.2 File format

5.3 Function examples

5.3.1 Basic function examples

5.3.2 More function examples – multiple inputs

5.3.3 Multiple outputs

5.3.4 Bad examples

5.4 Exercises

6 Control Flow

6.1 Relational and logical operators

6.2 If statements

6.3 Switch/case

6.4 Use of characteristic functions

6.5 For loops

6.6 While loops

6.7 Useful commands break, continue, return, and error

6.8 Optional inputs and outputs of functions

6.9 Exercises

7 Miscellaneous Commands and Code Improvement

7.1 Miscellaneous commands

7.1.1 The fprintf command

7.1.2 The sprintf command

7.1.3 Formats revisited

7.1.4 The save/load commands

7.1.5 The tic/toc commands

7.1.6 The fill command

7.1.7 The command alpha

7.1.8 The syms, diff, int, and subs commands

7.1.9 Commands for polynomials

7.2 Code improvement

7.2.1 Vectorization of code

7.2.2 Preallocation

Part 2 Mathematics and MATLAB®

8 Transformations and Fern Fractals

8.1 Linear transformations

8.2 Affine transformations

8.3 Fern fractals

8.4 Exercises

9 Complex Numbers and Fractals

9.1 Complex numbers

9.1.1 Adding complex numbers

9.1.2 Multiplication by a real numbers (scalars)

9.1.3 Multiplication and de Moivre’s theorem/formula

9.1.4 Plotting complex numbers in MATLAB®

9.1.5 Creating line segments with complex numbers

9.2 The Chaos Game

9.3 Line replacement fractals

9.3.1 Snowflake fractals

9.3.2 Gosper Island

9.4 Geometric series

9.5 Exercises

10 Series and Taylor Polynomials

10.1 Review of series

10.2 Power series

10.3 Taylor polynomials and Taylor series

10.4 Exercises

11 Numerical Integration

11.1 Approximating integrals/numerical integration

11.2 Riemann sums

11.3 Error bounds

11.4 Simpson’s rule

11.5 Exercises

12 The Gram-Schmidt Process

12.1 General vector spaces and subspaces

12.1.1 Vector spaces

12.1.2 Subspaces

12.2 Linear combinations of vectors

12.3 Linear independence and bases

12.3.1 Linear independence

12.3.2 Bases

12.4 Rank

12.5 Orthonormal vectors and the Gram-Schmidt process

12.5.1 Orthogonal and orthonormal vectors

12.5.2 The Gram-Schmidt process

12.6 Answers to example problems

12.7 Exercises

A Publishing and Live Scripts

A.1 Live scripts

A.2 Basic scripts or M-files

A.3 Publishing M-files

A.4 Using sections

A.4.1 Using sections for publishing

A.4.2 Using sections for running/debugging files

A.5 Formatting text

A.5.1 Basic text formatting

A.5.2 Lists

A.5.3 HTML links

A.5.4 Inserting images

A.5.5 Pre-formatted text

A.5.6 Inserting HTML code

A.5.7 Inserting LaTeX equations

B Final Projects

B.1 Ciphers

B.1.1 Substitution cipher

B.1.2 Columnar transposition cipher

B.2 Game of Pig

B.3 Linearization and Newton’s method

B.3.1 Linearization

B.3.2 Newton’s method

B.4 Disk and Shell method

B.5 Power ball data

C Linear Algebra Projects

C.1 Matrix calculations and linear systems

C.1.1 First handout

C.1.2 Exercises

C.2 The Hill cipher

C.2.1 Useful commands

C.2.2 Exercises

C.3 Least-squares solutions

C.3.1 Brief overview

C.3.2 Curve fitting

C.3.3 Exercises

C.4 Markov matrices

C.4.1 Brief overview

C.4.2 Exercises

D Multivariable Calculus Projects

D.1 Lines and planes

D.2 Vector functions

D.2.1 2D example plots

D.2.2 3D example plot

D.2.3 Bad domain example

D.2.4 Adjusting the view

D.2.5 Sphere command

D.2.6 Multiple plots on one figure

D.2.7 Exercises

D.3 Applications of double integrals

D.3.1 Calculating integrals and viewing regions

D.3.2 Exercises

 

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