# Numerical Analysis Using MATLAB and Spreadsheets

Orchard Publications, 2004 - Education - 570 pages
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 Copyright