دانلود کتاب Programming Mathematics Using MATLAB

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Contents Preface Supplements Introduction 1 Introduction to MATLAB® 1.1 Basic MATLAB® information 1.1.1 Starting MATLAB 1.1.2 Good commands to know 1.2 Basic mathematics 1.2.1 Built-in mathematical functions 1.2.2 Precedence rules 1.2.3 Formats 1.3 Variables 1.4 Diaries and script files 1.5 Exercises 2 Vectors and Matrices (Arrays) 2.1 One-dimensional arrays (vectors) 2.1.1 Constant spaced vectors 2.1.2 Equally spaced vectors 2.2 Two-dimensional arrays (matrices) 2.3 Addressing elements of vectors/arrays 2.4 Component-wise calculations 2.5 Random numbers 2.6 Exercises 3 Plotting in MATLAB® 3.1 Basic 2D plots 3.2 Bad domain examples 3.3 Axis settings 3.4 Multiple plots 3.5 Color, line, and marker modifications 3.5.1 Clf/close all 3.5.2 Subplots 3.6 Other 2D plots 3.6.1 Parametric curves 3.6.2 Polar curves 3.7 Exercises 4 Three-Dimensional Plots 4.1 Vector functions or space curves 4.2 Plotting surfaces 4.2.1 The meshgrid command 4.2.2 Domain issues 4.2.3 Level curves 4.2.4 Multiple plots and modifying colors 4.3 View command 4.4 Axis settings, revisited 4.5 Other coordinate systems and 3D graphs 4.5.1 The sphere and cylinder commands 4.5.2 Cylindrical coordinates 4.5.3 Spherical coordinates 4.6 Exercises 5 Functions 5.1 The [basicstyle=]|lookfor| and [basicstyle=]|help| commands 5.2 File format 5.3 Function examples 5.3.1 Basic function examples 5.3.2 More function examples - multiple inputs 5.3.3 Multiple outputs 5.3.4 Bad examples 5.4 Exercises 6 Control Flow 6.1 Relational and logical operators 6.2 If statements 6.3 Switch/case 6.4 Use of characteristic functions 6.5 For loops 6.6 While loops 6.7 Useful commands break, continue, return, and error 6.8 Optional inputs and outputs of functions 6.9 Exercises 7 Miscellaneous Commands and Code Improvement 7.1 Miscellaneous commands 7.1.1 The fprintf command 7.1.2 The sprintf command 7.1.3 Formats revisited 7.1.4 The save/load commands 7.1.5 The tic/toc commands 7.1.6 The fill command 7.1.7 The command alpha 7.1.8 The syms, diff, int, and subs commands 7.1.9 Commands for polynomials 7.2 Code improvement 7.2.1 Vectorization of code 7.2.2 Preallocation 8 Transformations and Fern Fractals 8.1 Linear transformations 8.2 Affine transformations 8.3 Fern fractals 8.4 Exercises 9 Complex Numbers and Fractals 9.1 Complex numbers 9.1.1 Adding complex numbers 9.1.2 Multiplication by a real numbers (scalars) 9.1.3 Multiplication and de Moivre's theorem/formula 9.1.4 Plotting complex numbers in MATLAB® 9.1.5 Creating line segments with complex numbers 9.2 The Chaos Game 9.3 Line replacement fractals 9.3.1 Snowflake fractals 9.3.2 Gosper Island 9.4 Geometric series 9.5 Exercises 10 Series and Taylor Polynomials 10.1 Review of series 10.2 Power series 10.3 Taylor polynomials and Taylor series 10.4 Exercises 11 Numerical Integration 11.1 Approximating integrals/numerical integration 11.2 Riemann sums 11.3 Error bounds 11.4 Simpson's rule 11.5 Exercises 12 The Gram-Schmidt Process 12.1 General vector spaces and subspaces 12.1.1 Vector spaces 12.1.2 Subspaces 12.2 Linear combinations of vectors 12.3 Linear independence and bases 12.3.1 Linear independence 12.3.2 Bases 12.4 Rank 12.5 Orthonormal vectors and the Gram-Schmidt process 12.5.1 Orthogonal and orthonormal vectors 12.5.2 The Gram-Schmidt process 12.6 Answers to example problems 12.7 Exercises A Publishing and Live Scripts A.1 Live scripts A.2 Basic scripts or M-files A.3 Publishing M-files A.4 Using sections A.4.1 Using sections for publishing A.4.2 Using sections for running/debugging files A.5 Formatting text A.5.1 Basic text formatting A.5.2 Lists A.5.3 HTML links A.5.4 Inserting images A.5.5 Pre-formatted text A.5.6 Inserting HTML code A.5.7 Inserting LaTeX equations B Final Projects B.1 Ciphers B.1.1 Substitution cipher B.1.2 Columnar transposition cipher B.2 Game of Pig B.3 Linearization and Newton's method B.3.1 Linearization B.3.2 Newton's method B.4 Disk and Shell method B.5 Power ball data C Linear Algebra Projects C.1 Matrix calculations and linear systems C.1.1 First handout C.1.2 Exercises C.2 The Hill cipher C.2.1 Useful commands C.2.2 Exercises C.3 Least-squares solutions C.3.1 Brief overview C.3.2 Curve fitting C.3.3 Exercises C.4 Markov matrices C.4.1 Brief overview C.4.2 Exercises D Multivariable Calculus Projects D.1 Lines and planes D.2 Vector functions D.2.1 2D example plots D.2.2 3D example plot D.2.3 Bad domain example D.2.4 Adjusting the view D.2.5 Sphere command D.2.6 Multiple plots on one figure D.2.7 Exercises D.3 Applications of double integrals D.3.1 Calculating integrals and viewing regions D.3.2 Exercises References Index