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9781852339197

An Introduction To Programming And Numerical Methods In Matlab

by ;
  • ISBN13:

    9781852339197

  • ISBN10:

    1852339195

  • Format: Paperback
  • Copyright: 2005-06-30
  • Publisher: SPRINGER - VERLAG

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Summary

MATLAB is a powerful programme, which naturally lends itself to the rapid implementation of most numerical algorithms. This text, which uses MATLAB, gives a detailed overview of structured programming and numerical methods for the undergraduate student. The book covers numerical methods for solving a wide range of problems, from integration to the numerical solution of differential equations or the simulation of random processes. Each chapter includes extensive examples and tasks, at varying levels of complexity. For practice, the early chapters include programmes that require debugging by the reader, while full solutions are given for all the tasks. The book also includes: a glossary of MATLAB commands appendices of mathematical techniques used in numerical methods. Designed as a text for a first course in programming and algorithm design, as well as in numerical methods courses, the book will be of benefit to a wide range of students from mathematics and engineering, to commerce.

Author Biography

Steve Otto was formerly a lecturer at Birmingham University but now heads a research unit at St. Andrews, UK. This book is based on courses taught at Birmingham and at Adelaide to students in mathematics, engineering and economics.

Table of Contents

Simple Calculations with MATLAB
1(26)
Introduction and a Word of Warning
1(1)
Scalar Quantities and Variables
2(10)
Rules for Naming of Variables
4(1)
Precedence: The Order in Which Calculations Are Performed
5(3)
Mathematical Functions
8(4)
Format: The Way in Which Numbers Appear
12(1)
Vectors in MATLAB
13(4)
Initialising Vector Objects
13(1)
Manipulating Vectors and Dot Arithmetic
14(3)
Setting Up Mathematical Functions
17(3)
Some MATLAB Specific Commands
20(3)
Looking at Variables and Their Sizes
22(1)
Accessing Elements of Arrays
23(1)
Tasks
24(3)
Writing Scripts and Functions
27(36)
Creating Scripts and Functions
27(9)
Functions
30(5)
Brief Aside
35(1)
Plotting Simple Functions
36(13)
Evaluating Polynomials and Plotting Curves
41(3)
More on Plotting
44(5)
Functions of Functions
49(2)
Errors
51(6)
Numerical Errors
51(3)
User Error
54(3)
Tasks
57(6)
Loops and Conditional Statements
63(40)
Introduction
63(1)
Loops Structures
63(5)
Summing Series
68(15)
Sums of Series of the Form NΣ j=4 jp, p ε N
73(3)
Summing Infinite Series
76(3)
Summing Series Using MATLAB Specific Commands
79(3)
Loops Within Loops (Nested)
82(1)
Conditional Statements
83(7)
Constructing Logical Statements
85(3)
The MATLAB Command switch
88(2)
Conditional loops
90(2)
The break Command
92(1)
MATLAB Specific Commands
92(2)
Error Checking
94(3)
Tasks
97(6)
Root Finding
103(30)
Introduction
103(1)
Initial Estimates
104(5)
Fixed Point Iteration
109(4)
Bisection
113(4)
Newton--Raphson and Secant Methods
117(6)
Derivation of the Newton--Raphson Method
117(6)
Repeated Roots of Functions
123(2)
Zeros of Higher-Dimensional Functions(*)
125(3)
MATLAB Routines for Finding Zeros
128(2)
Roots of a Polynomial
128(1)
The Command fzero
128(2)
Tasks
130(3)
Interpolation and Extrapolation
133(36)
Introduction
133(1)
Saving and Reading Data
134(5)
Which Points to Use?
139(2)
Newton Forward Differences and Lagrange Polynomials
141(7)
Linear Interpolation/Extrapolation
147(1)
Calculating Interpolated and Extrapolated Values
148(2)
Splines
150(2)
Curves of Best Fit
152(3)
Interpolation of Non-Smooth Data
155(6)
Insufficient Data Points
158(3)
Minimisation of Functions and Parameter Retrieval
161(5)
Parameter Retrieval
163(1)
Using fmins for Parameter Retrieval
164(2)
Tasks
166(3)
Matrices
169(56)
Introduction
169(17)
Initialising Matrices Within MATLAB
169(5)
Matrix Operations
174(6)
Operations on Elements of Matrices
180(2)
More on Special Matrices
182(3)
Matrices Containing Strings
185(1)
Properties of Matrices and Systems of Equations
186(5)
Determinants of Matrices
190(1)
Elementary Row Operations
191(8)
Solving Many Equations at Once
198(1)
Matrix Decomposition
199(5)
Eigenvalues and Eigenvectors
204(4)
Specific MATLAB Commands
208(4)
Characteristic Polynomials
212(2)
Exponentials of Matrices
214(3)
Tasks
217(8)
Numerical Integration
225(22)
Introduction
225(1)
Integration Using Straight Lines
226(4)
Errors in the Trapezium Method
229(1)
Integration Using Quadratics
230(5)
Integration Using Cubic Polynomials
235(2)
Integrating Using MATLAB Commands
237(1)
Specific Examples of Integrals
238(4)
Infinite Integrals and Removable Singularities
238(2)
Indefinite Integrals
240(2)
Tasks
242(5)
Solving Differential Equations
247(44)
Introduction
247(1)
Euler's Method and Crank--Nicolson
247(12)
Analytical Comparisons
253(6)
Banded Matrices
259(4)
Runge--Kutta Methods
263(3)
Higher-Order Systems
266(12)
Second-Order Systems
266(4)
Bessel's equation
270(3)
Airy's Equation
273(1)
Shooting Methods
274(4)
Boundary-Value Problems
278(4)
Population Dynamics
282(3)
Eigenvalues of Differential Systems
285(1)
Tasks
286(5)
Simulations and Random Numbers
291(32)
Introduction
291(1)
Statistical quantities
291(4)
Averages
291(2)
Other Statistical Measures
293(2)
Random Numbers and Distributions
295(5)
Normal Distribution
298(1)
Calculating Probabilities
299(1)
Permutations
300(1)
Maps and White Noise
300(19)
Modelling Discrete Systems
307(2)
Periodicity and Chaos
309(7)
Random Motion
316(3)
Tasks
319(4)
A. Mathematical Introduction to Matrices
323(12)
Special Matrices
330(1)
Inverses of Matrices
331(4)
B. Glossary of Useful Terms
335(54)
Arithmetic and Logical Operators
335(8)
Symbols
343(4)
Plotting Commands
347(18)
General MATLAB Commands
365(24)
C. Solutions to Tasks
389(70)
Solutions for Tasks from Chapter 1
389(5)
Solutions for Tasks from Chapter 2
394(6)
Solutions for Tasks from Chapter 3
400(8)
Solutions for Tasks from Chapter 4
408(6)
Solutions for Tasks from Chapter 5
414(4)
Solutions for Tasks from Chapter 6
418(11)
Solutions for Tasks from Chapter 7
429(7)
Solutions for Tasks from Chapter 8
436(18)
Solutions for Tasks from Chapter 9
454(5)
Index 459

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