Solving Applied Mathematical Problems with MATLAB

1 Solving Applied Mathematical Problems WITH MATLAB 19/19/08 4:21:15 PMThis page intentionally left blank Solving Applied Mathematical Problems WITH MATLAB Dingy XueYangQuan 39/19/08 4:21:15 PMChapman & Hall/CRCT aylor & Francis Group6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 2009 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa businessNo claim to original Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4200-8250-0 (Hardcover)This book contains information obtained from authentic and highly regarded sources.

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4 Engineering mathematics--Data processing. 2. MATLAB . 3. Numerical analysis--Data processing. 4. Mathematical optimization--Data processing. I. Chen, YangQuan, 1966- II. Title. 5133--dc22 2008025953 Visit the Taylor & Francis Web site the CRC Press Web site 49/19/08 4:21:15 PMContentsPrefacexi1 Computer Mathematics Languages An Computer Solutions to Mathematics Problems .. Why should we study computer mathematics language? Analytical solutions versus numerical solutions .. Mathematics software packages: an overview.

5 Summary of Computer Mathematics Languages .. A brief historic review of MATLAB .. Three widely used computer mathematics languages . Introduction to free scientific open-source softwares .. Outline of the Book..8 Exercises ..92 Fundamentals of MATLAB Fundamentals of MATLAB Programming .. Variables and constants in MATLAB .. Data structure .. Basic structure of MATLAB .. Colon expressions and sub-matrices extraction .. Fundamental Mathematical Calculations .. Algebraic operations of matrices.

6 Logic operations of matrices .. Relationship operations of matrices .. Simplifications and presentations of analytical results . Basic number theory computations .. Flow Control Structures of MATLAB Language.. Loop control structures .. Conditional control structures .. Switch structure .. Trial structure .. Writing and Debugging MATLAB Functions.. Basic structure of MATLAB functions .. Programming of functions with variable Inline functions and anonymous functions.

7 Two-Dimensional Graphics .. Basic statements of two-dimensional plotting .. Other two-dimensional plotting statements .. Implicit function plotting and applications ..36vviSolving Applied Mathematical Problems with Graphics decorations .. Three-Dimensional Graphics.. Plotting of three-dimensional curves .. Plotting of three-dimensional surfaces .. Viewpoint setting in 3D graphs ..43 Exercises ..443 Calculus Analytical Solutions to Calculus Problems .. Analytical solutions to limit Problems .

8 Analytical solutions to derivative Problems .. Analytical solutions to integral Problems .. Series Expansions and Series Evaluations.. Taylor series expansion .. Fourier series expansion .. Series .. Sequence product .. Numerical Differentiation .. Numerical differentiation algorithms .. Central-point difference algorithm .. Gradient computations of functions with two Numerical Integration Problems .. Numerical integration from given data using trapezoidalmethod.

9 Numerical integration of single variable functions .. Numerical solutions to double integrals .. Numerical solutions to triple integrals .. Path Integrals and Line Integrals .. Path integrals .. Line integrals .. Surface Integrals .. Scalar surface integrals .. Vector surface integrals ..84 Exercises ..854 Linear Algebra Inputting Special Matrices.. Numerical matrix input .. Defining symbolic matrices .. Fundamental Matrix Operations .. Basic concepts and properties of matrices.

10 Matrix inversion and generalized inverse of a matrix . Matrix eigenvalue Problems .. Fundamental Matrix Transformations .. Similarity transformations and orthogonal matrices .. Triangular and Cholesky decompositions .. Jordan transformations .. Singular value decompositions .. Solving Matrix Equations .. Solutions to linear algebraic equations .. Solutions to Lyapunov equations .. Solutions to Sylvester equations .. Solutions to Riccati equations .. Nonlinear Functions and Matrix Function Evaluations.