<p>Table of Contents<br/>Chapter 1<br/>Introduction to MATLAB<br/>Command Window....................................................................................................................... 1-1<br/>Roots of Polynomials.................................................................................................................... 1-3<br/>Polynomial Construction from Known Roots .............................................................................. 1-4<br/>Evaluation of a Polynomial at Specified Values ........................................................................... 1-5<br/>Rational Polynomials .................................................................................................................... 1-7<br/>Using MATLAB to Make Plots.................................................................................................... 1-9<br/>Subplots...................................................................................................................................... 1-18<br/>Multiplication, Division and Exponentiation............................................................................. 1-18<br/>Script and Function Files............................................................................................................ 1-25<br/>Display Formats .......................................................................................................................... 1-29<br/>Summary .................................................................................................................................... 1-30<br/>Exercises..................................................................................................................................... 1-35<br/>Solutions to Exercises ................................................................................................................. 1-36<br/>Chapter 2<br/>Root Approximations<br/>Newton’s Method for Root Approximation ................................................................................. 2-1<br/>Approximations with Spreadsheets .............................................................................................. 2-7<br/>The Bisection Method for Root Approximation........................................................................ 2-19<br/>Summary .................................................................................................................................... 2-27<br/>Exercises..................................................................................................................................... 2-28<br/>Solutions to Exercises ................................................................................................................. 2-29<br/>Chapter 3<br/>Sinusoids and Phasors<br/>Alternating Voltages and Currents .............................................................................................. 3-1<br/>Characteristics of Sinusoids .......................................................................................................... 3-2<br/>Inverse Trigonometric Functions ............................................................................................... 3-10<br/>Phasors ....................................................................................................................................... 3-10<br/>Addition and Subtraction of Phasors ......................................................................................... 3-11<br/>Multiplication of Phasors............................................................................................................ 3-12<br/>Division of Phasors ..................................................................................................................... 3-12</p><p>Exponential and Polar Forms of Phasors ....................................................................................3-13<br/>Summary.....................................................................................................................................3-18<br/>Exercises .....................................................................................................................................3-21<br/>Solutions to Exercises..................................................................................................................3-22<br/>Chapter 4<br/>Matrices and Determinants<br/>Matrix Definition ......................................................................................................................... 4-1<br/>Matrix Operations....................................................................................................................... 4-2<br/>Special Forms of Matrices ............................................................................................................ 4-5<br/>Determinants............................................................................................................................... 4-9<br/>Minors and Cofactors................................................................................................................. 4-12<br/>Cramer’s Rule............................................................................................................................ 4-16<br/>Gaussian Elimination Method ................................................................................................... 4-18<br/>The Adjoint of a Matrix............................................................................................................. 4-19<br/>Singular and Non-Singular Matrices ......................................................................................... 4-20<br/>The Inverse of a Matrix.............................................................................................................. 4-21<br/>Solution of Simultaneous Equations with Matrices................................................................... 4-23<br/>Summary.................................................................................................................................... 4-29<br/>Exercises .................................................................................................................................... 4-33<br/>Solutions to Exercises................................................................................................................. 4-35<br/>Chapter 5<br/>Differential Equations, State Variables, and State Equations<br/>Simple Differential Equations .......................................................................................................5-1<br/>Classification ................................................................................................................................5-2<br/>Solutions of Ordinary Differential Equations (ODE)...................................................................5-5<br/>Solution of the Homogeneous ODE .............................................................................................5-8<br/>Using the Method of Undetermined Coefficients for the Forced Response...............................5-10<br/>Using the Method of Variation of Parameters for the Forced Response....................................5-19<br/>Expressing Differential Equations in State Equation Form ........................................................5-23<br/>Solution of Single State Equations..............................................................................................5-27<br/>The State Transition Matrix.......................................................................................................5-28<br/>Computation of the State Transition Matrix..............................................................................5-30<br/>Eigenvectors ...............................................................................................................................5-37<br/>Summary.....................................................................................................................................5-41<br/>Exercises .....................................................................................................................................5-46<br/>Solutions to Exercises..................................................................................................................5-47</p><p>Chapter 6<br/>Fourier, Taylor, and Maclaurin Series<br/>Wave Analysis .............................................................................................................................. 6-1<br/>Evaluation of the Coefficients ...................................................................................................... 6-2<br/>Symmetry ..................................................................................................................................... 6-7<br/>Waveforms in Trigonometric Form of Fourier Series................................................................. 6-12<br/>Alternate Forms of the Trigonometric Fourier Series ................................................................ 6-25<br/>The Exponential Form of the Fourier Series .............................................................................. 6-28<br/>Line Spectra ............................................................................................................................... 6-33<br/>Numerical Evaluation of Fourier Coefficients............................................................................ 6-36<br/>Power Series Expansion of Functions ......................................................................................... 6-37<br/>Taylor and Maclaurin Series....................................................................................................... 6-40<br/>Summary .................................................................................................................................... 6-47<br/>Exercises..................................................................................................................................... 6-50<br/>Solutions to Exercises ................................................................................................................. 6-52<br/>Chapter 7<br/>Finite Differences and Interpolation<br/>Divided Differences ...................................................................................................................... 7-1<br/>Factorial Polynomials.................................................................................................................... 7-6<br/>Antidifferences........................................................................................................................... 7-11<br/>Newton’s Divided Difference Interpolation Method ................................................................. 7-15<br/>Lagrange’s Interpolation Method ............................................................................................... 7-18<br/>Gregory-Newton Forward Interpolation Method....................................................................... 7-19<br/>Gregory-Newton Backward Interpolation Method .................................................................... 7-20<br/>Interpolation with MATLAB..................................................................................................... 7-23<br/>Summary .................................................................................................................................... 7-37<br/>Exercises..................................................................................................................................... 7-42<br/>Solutions to Exercises ................................................................................................................. 7-43<br/>Chapter 8<br/>Linear and Parabolic Regression<br/>Curve Fitting................................................................................................................................ 8-1<br/>Linear Regression......................................................................................................................... 8-2<br/>Parabolic Regression ..................................................................................................................... 8-7<br/>Regression with Power Series Approximations .......................................................................... 8-14<br/>Summary .................................................................................................................................... 8-24</p><p>Exercises .................................................................................................................................... 8-26<br/>Solutions to Exercises................................................................................................................. 8-28<br/>Chapter 9<br/>Solution of Differential Equations by Numerical Methods<br/>Taylor Series Method................................................................................................................... 9-1<br/>Runge-Kutta Method................................................................................................................... 9-5<br/>Adams’ Method......................................................................................................................... 9-13<br/>Milne’s Method .......................................................................................................................... 9-16<br/>Summary.................................................................................................................................... 9-17<br/>Exercises .................................................................................................................................... 9-20<br/>Solutions to Exercises................................................................................................................. 9-21<br/>Chapter 10<br/>Integration by Numerical Methods<br/>The Trapezoidal Rule................................................................................................................. 10-1<br/>Simpson’s Rule ........................................................................................................................... 10-6<br/>Summary.................................................................................................................................. 10-13<br/>Exercises .................................................................................................................................. 10-15<br/>Solution to Exercises ................................................................................................................ 10-16<br/>Chapter 11<br/>Difference Equations<br/>Definition, Solutions, and Applications..................................................................................... 11-1<br/>Fibonacci Numbers .................................................................................................................... 11-7<br/>Summary.................................................................................................................................. 11-10<br/>Exercises .................................................................................................................................. 11-13<br/>Solutions to Exercises............................................................................................................... 11-14<br/>Chapter 12<br/>Partial Fraction Expansion<br/>Partial Fraction Expansion.........................................................................................................12-1<br/>Alternate Method of Partial Fraction Expansion ....................................................................12-13<br/>Summary..................................................................................................................................12-18<br/>Exercises ..................................................................................................................................12-21<br/>Solutions to Exercises...............................................................................................................12-22</p><p>Chapter 13<br/>The Gamma and Beta Functions and Distributions<br/>The Gamma Function ................................................................................................................ 13-1<br/>The Gamma Distribution ......................................................................................................... 13-15<br/>The Beta Function.................................................................................................................... 13-17<br/>The Beta Distribution............................................................................................................... 13-20<br/>Summary .................................................................................................................................. 13-21<br/>Exercises................................................................................................................................... 13-24<br/>Solutions to Exercises ............................................................................................................... 13-25<br/>Chapter 14<br/>Orthogonal Functions and Matrix Factorizations<br/>Orthogonal Functions ................................................................................................................14-1<br/>Orthogonal Trajectories .............................................................................................................14-2<br/>Orthogonal Vectors....................................................................................................................14-4<br/>The Gram-Schmidt Orthogonalization Procedure .....................................................................14-7<br/>The LU Factorization.................................................................................................................14-9<br/>The Cholesky Factorization .....................................................................................................14-15<br/>The QR Factorization...............................................................................................................14-17<br/>Singular Value Decomposition ................................................................................................14-20<br/>Summary.................................................................................................................................14-21<br/>Exercises .................................................................................................................................14-23<br/>Solutions to Exercises ..............................................................................................................14-25<br/>Chapter 15<br/>Bessel, Legendre, and Chebyshev Functions<br/>The Bessel Function ................................................................................................................... 15-1<br/>Legendre Functions .................................................................................................................. 15-10<br/>Laguerre Polynomials................................................................................................................ 15-20<br/>Chebyshev Polynomials ............................................................................................................ 15-21<br/>Summary .................................................................................................................................. 15-26<br/>Exercises................................................................................................................................... 15-32<br/>Solutions to Exercises ............................................................................................................... 15-33</p><p>Chapter 16<br/>Optimization Methods<br/>Linear Programming................................................................................................................... 16-1<br/>Dynamic Programming............................................................................................................... 16-4<br/>Network Analysis ..................................................................................................................... 16-14<br/>Summary.................................................................................................................................. 16-19<br/>Exercises .................................................................................................................................. 16-20<br/>Solutions to Exercises............................................................................................................... 16-22</p><br/><br>squarekiss
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