Numerical Analysis Using MATLAB and Spreadsheets

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Orchard Publications, 2004 - Education - 570 pages
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Annotation This text provides complete, clear, and detailed explanations of the principal numerical analysis methods and well known functions used in science and engineering. These are illustrated with many practical examples. With this text the reader learns numerical analysis with many real-world applications, MATLAB, and spreadsheets simultaneously.This text includes the following chapters:? Introduction to MATLAB ? Root Approximations ? Sinusoids and Complex Numbers ? Matrices and Determinants ? Review of Differential Equations ? Fourier, Taylor, and Maclaurin Series ? Finite Differences and Interpolation ? Linear and Parabolic Regression ? Solution of Differential Equations by Numerical Methods ? Integration by Numerical Methods ? Difference Equations? Partial Fraction Expansion ? The Gamma and Beta Functions ? Orthogonal Functions and Matrix Factorizations ? Bessel, Legendre, and Chebyshev Polynomials ? Optimization MethodsEach chapter contains numerous practical applications supplemented with detailed instructionsfor using MATLAB and/or Microsoft Excel? to obtain quick solutions.
 

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Contents

Chapter 2
1
Chapter 6
6
Approximations with Spreadsheets
9
The Bisection Method for Root Approximation 219
23
Solutions to Exercises 229
29
Chapter 3
1
Exponential and Polar Forms of Phasors 313
15
Inverse Trigonometric Functions 310
19
Parabolic Regression
8
Summary 824
25
Solutions to Exercises 828
31
Chapter 9
1
RungeKutta Method
9
Adams Method 913
19
Chapter 10
27
Summary 1013
39

Exercises 321
25
Addition and Subtraction of Phasors 311
3
Minors and Cofactors 412
12
Gaussian Elimination Method 418
18
Solution of Simultaneous Equations with Matrices 423
25
Summary 429
31
Exercises 433
39
Solutions of Ordinary Differential Equations ODE
5
Using the Method of Variation of Parameters for the Forced Response 519
19
Solution of Single State Equations 527
27
The State Transition Matrix 528
35
Eigenvectors 537
45
Fourier Taylor and Maclaurin Series
1
Symmetry
17
Line Spectra 633
34
Summary 647
49
Factorial Polynomials
7
Antidifferences 711
40
Chapter 11
49
Summary 1110
59
Chapter 12
65
ii
69
Alternate Method of Partial Fraction Expansion 1213
77
Summary 1218
83
Chapter 13
93
The Gamma Distribution 1315
74
Exercises 1324
85
Orthogonal Vectors 144
91
The LU Factorization 149
99
The QR Factorization 1417
105
Exercises 1423
115
The Bessel Function 151
143
Exercises 1532
151
Optimization Methods
155
Dynamic Programming 164
173
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