Programming Mathematics Using MATLAB

Contents
Preface
	Supplements
Introduction
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 [basicstyle=]|lookfor| and [basicstyle=]|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
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
References
Index