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Introduction to Programming and Numerical Methods in MATLAB

ISBN-10: 1852339195
ISBN-13: 9781852339197
Edition: 2005
List price: $49.95 Buy it from $20.46
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Description: This text provides a first course in numerical methods and programming taught through the medium of MATLAB. It is designed to give readers their first exposure to any kind of programming. The first three chapters introduce readers to the power of  More...

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Book details

List price: $49.95
Copyright year: 2005
Publisher: Springer
Publication date: 5/31/2005
Binding: Paperback
Pages: 464
Size: 6.75" wide x 9.00" long x 0.75" tall
Weight: 1.672
Language: English

This text provides a first course in numerical methods and programming taught through the medium of MATLAB. It is designed to give readers their first exposure to any kind of programming. The first three chapters introduce readers to the power of MATLAB without overwhelming them with its advanced features; the text then covers all the elementary material associated with numerical methods, and helps students develop skills in algorithm design. Examples of code are provided to debug, hence accentuating the need for precision, and developing readersb skills in finding errors in their own work. At the end of each chapter, tasks are provided to reinforce the ideas introduced, with full solutions at the back of the book. A glossary of terms is provided, with each term supported by an example of the syntaxes commonly encountered. Aimed at first and second year undergraduates in mathematics and engineering, this book will also be invaluable for engineers who need to use MATLAB in their work environment.

Simple Calculations with MATLAB
Introduction and a Word of Warning
Scalar Quantities and Variables
Rules for Naming of Variables
Precedence: The Order in Which Calculations Are Performed
Mathematical Functions
Format: The Way in Which Numbers Appear
Vectors in MATLAB
Initialising Vector Objects
Manipulating Vectors and Dot Arithmetic
Setting Up Mathematical Functions
Some MATLAB Specific Commands
Looking at Variables and Their Sizes
Accessing Elements of Arrays
Tasks
Writing Scripts and Functions
Creating Scripts and Functions
Functions
Brief Aside
Plotting Simple Functions
Evaluating Polynomials and Plotting Curves
More on Plotting
Functions of Functions
Errors
Numerical Errors
User Error
Tasks
Loops and Conditional Statements
Introduction
Loops Structures
Summing Series
Sums of Series of the Form [characters not reproducible] j[superscript p], p [set membership] [characters not reproducible]
Summing Infinite Series
Summing Series Using MATLAB Specific Commands
Loops Within Loops (Nested)
Conditional Statements
Constructing Logical Statements
The MATLAB Command switch
Conditional loops
The break Command
MATLAB Specific Commands
Error Checking
Tasks
Root Finding
Introduction
Initial Estimates
Fixed Point Iteration
Bisection
Newton-Raphson and Secant Methods
Derivation of the Newton-Raphson Method
Repeated Roots of Functions
Zeros of Higher-Dimensional Functions(*)
MATLAB Routines for Finding Zeros
Roots of a Polynomial
The Command fzero
Tasks
Interpolation and Extrapolation
Introduction
Saving and Reading Data
Which Points to Use?
Newton Forward Differences and Lagrange Polynomials
Linear Interpolation/Extrapolation
Calculating Interpolated and Extrapolated Values
Splines
Curves of Best Fit
Interpolation of Non-Smooth Data
Insufficient Data Points
Minimisation of Functions and Parameter Retrieval
Parameter Retrieval
Using fmins for Parameter Retrieval
Tasks
Matrices
Introduction
Initialising Matrices Within MATLAB
Matrix Operations
Operations on Elements of Matrices
More on Special Matrices
Matrices Containing Strings
Properties of Matrices and Systems of Equations
Determinants of Matrices
Elementary Row Operations
Solving Many Equations at Once
Matrix Decomposition
Eigenvalues and Eigenvectors
Specific MATLAB Commands
Characteristic Polynomials
Exponentials of Matrices
Tasks
Numerical Integration
Introduction
Integration Using Straight Lines
Errors in the Trapezium Method
Integration Using Quadratics
Integration Using Cubic Polynomials
Integrating Using MATLAB Commands
Specific Examples of Integrals
Infinite Integrals and Removable Singularities
Indefinite Integrals
Tasks
Solving Differential Equations
Introduction
Euler's Method and Crank-Nicolson
Analytical Comparisons
Banded Matrices
Runge-Kutta Methods
Higher-Order Systems
Second-Order Systems
Bessel's equation
Airy's Equation
Shooting Methods
Boundary-Value Problems
Population Dynamics
Eigenvalues of Differential Systems
Tasks
Simulations and Random Numbers
Introduction
Statistical quantities
Averages
Other Statistical Measures
Random Numbers and Distributions
Normal Distribution
Calculating Probabilities
Permutations
Maps and White Noise
Modelling Discrete Systems
Periodicity and Chaos
Random Motion
Tasks
A Mathematical Introduction to Matrices
Special Matrices
Inverses of Matrices
Glossary of Useful Terms
Arithmetic and Logical Operators
Symbols
Plotting Commands
General MATLAB Commands
Solutions to Tasks
Solutions for Tasks from Chapter 1
Solutions for Tasks from Chapter 2
Solutions for Tasks from Chapter 3
Solutions for Tasks from Chapter 4
Solutions for Tasks from Chapter 5
Solutions for Tasks from Chapter 6
Solutions for Tasks from Chapter 7
Solutions for Tasks from Chapter 8
Solutions for Tasks from Chapter 9
Index

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