ماتماتیکا به‌وسیلهٔ مثال، ویرایش پنجم

A desk reference for the beginning Mathematica user, providing step-by-step instructions on achieving results. The book fully accounts for the changes to functionality and visualization capabilities in version 11. The book is written with a view to practical implementation and problem-solving, without jargon, and uses representative biological, physical, and engineering problems.--;1. Getting started -- 2. Basic operations on numbers, expressions, and functions -- 3. Calculus -- 4. Introduction to lists and tables -- 5. Matrices and vectors: topics from linear algebra and vector calculus -- 6. Applications related to ordinary and partial differential equations. front-matter-2017......Page 1 copyright-2017......Page 4 Preface......Page 5 1.1 Introduction to Mathematica......Page 7 A Note Regarding Different Versions of Mathematica......Page 8 1.1.1 Getting Started with Mathematica......Page 9 Preview......Page 19 Five Basic Rules of Mathematica Syntax......Page 20 1.2 Getting Help from Mathematica......Page 21 Mathematica Help......Page 27 2.1.1 Numerical Calculations......Page 33 2.1.2 Built-In Constants......Page 35 2.1.3 Built-In Functions......Page 36 A Word of Caution......Page 39 2.2.1 Basic Algebraic Operations on Expressions......Page 41 2.2.2 Naming and Evaluating Expressions......Page 45 2.2.3 Defining and Evaluating Functions......Page 47 2.3.1 Functions of a Single Variable......Page 53 2.3.2 Parametric and Polar Plots in Two Dimensions......Page 66 2.3.3 Three-Dimensional and Contour Plots; Graphing Equations......Page 74 2.3.4 Parametric Curves and Surfaces in Space......Page 84 2.3.5 Miscellaneous Comments......Page 96 2.4.1 Exact Solutions of Equations......Page 101 2.4.2 Approximate Solutions of Equations......Page 110 3.1.1 Using Graphs and Tables to Predict Limits......Page 115 3.1.2 Computing Limits......Page 118 3.1.3 One-Sided Limits......Page 120 3.1.4 Continuity......Page 122 3.2.1 Definition of the Derivative......Page 125 3.2.2 Calculating Derivatives......Page 131 3.2.3 Implicit Differentiation......Page 135 3.2.4 Tangent Lines......Page 137 Tangent Lines of Implicit Functions......Page 139 Parametric Equations and Polar Coordinates......Page 141 3.2.5 The First Derivative Test and Second Derivative Test......Page 147 3.2.6 Applied Max/Min Problems......Page 155 3.2.7.1 Antiderivatives......Page 165 u-Substitutions......Page 166 3.3.1 Area......Page 168 3.3.2 The Definite Integral......Page 174 3.3.4 Area......Page 180 Parametric Equations......Page 184 Polar Coordinates......Page 185 3.3.5 Arc Length......Page 186 Parametric Equations......Page 187 Polar Coordinates......Page 190 Volume......Page 191 Surface Area......Page 202 3.4.1 Introduction to Sequences......Page 204 3.4.2 Introduction to Infinite Series......Page 208 3.4.3 Convergence Tests......Page 211 3.4.4 Alternating Series......Page 215 3.4.5 Power Series......Page 216 3.4.6 Taylor and Maclaurin Series......Page 220 3.4.7 Taylor's Theorem......Page 224 3.4.8 Other Series......Page 235 3.5.1 Limits of Functions of Two Variables......Page 237 3.5.2 Partial and Directional Derivatives......Page 239 Classifying Critical Points......Page 246 Tangent Planes......Page 249 Lagrange Multipliers......Page 252 3.5.3 Iterated Integrals......Page 255 Area, Volume, and Surface Area......Page 256 Triple Iterated Integrals......Page 262 4.1.1 Defining Lists......Page 265 4.1.2 Plotting Lists of Points......Page 270 4.2 Manipulating Lists: More on Part and Map......Page 283 4.2.1 More on Graphing Lists; Graphing Lists of Points Using Graphics Primitives......Page 292 4.3 Other Applications......Page 300 4.3.1 Approximating Lists with Functions......Page 301 4.3.2 Introduction to Fourier Series......Page 305 Application: The One-Dimensional Heat Equation......Page 309 Application: The Wave Equation on a Circular Plate......Page 312 4.3.3 The Mandelbrot Set and Julia Sets......Page 316 5.1.1 Defining Nested Lists, Matrices, and Vectors......Page 331 5.1.2 Extracting Elements of Matrices......Page 338 5.1.3 Basic Computations with Matrices......Page 340 5.1.4.1 Basic Operations on Vectors......Page 345 5.1.4.2 Basic Operations on Vectors in 3-Space......Page 346 5.2.1 Calculating Solutions of Linear Systems of Equations......Page 353 5.2.2 Gauss-Jordan Elimination......Page 357 5.3.1 Fundamental Subspaces Associated with Matrices......Page 364 5.3.2 The Gram-Schmidt Process......Page 366 5.3.3 Linear Transformations......Page 370 Application: Rotations......Page 371 5.3.4 Eigenvalues and Eigenvectors......Page 372 5.3.5 Jordan Canonical Form......Page 376 5.3.6 The QR Method......Page 379 5.4.1 The Standard Form of a Linear Programming Problem......Page 381 5.4.2 The Dual Problem......Page 383 Application: A Transportation Problem......Page 386 5.5.1 Vector-Valued Functions......Page 389 5.5.2 Line Integrals......Page 400 5.5.3 Surface Integrals......Page 403 5.5.4 A Note on Nonorientability......Page 407 5.5.5 More on Tangents, Normals, and Curvature in R3......Page 420 5.6.1 Manipulating Photographs with Built-In Functions......Page 430 5.6.2 Manipulating Photographs by Viewing Them as a Matrix or Array......Page 433 6.1.1 Separable Equations......Page 445 6.1.2 Linear Equations......Page 452 6.1.2.1 Application: Free-Falling Bodies......Page 456 6.1.3 Nonlinear Equations......Page 459 6.1.4 Numerical Methods......Page 462 6.2.1 Basic Theory......Page 466 6.2.2 Constant Coefficients......Page 467 Application: Harmonic Motion......Page 470 6.2.3 Undetermined Coefficients......Page 472 6.2.4 Variation of Parameters......Page 478 6.3.1 Basic Theory......Page 481 6.3.2 Constant Coefficients......Page 482 6.3.3 Undetermined Coefficients......Page 484 Variation of Parameters......Page 488 6.3.4 Laplace Transform Methods......Page 490 Application: The Convolution Theorem......Page 495 Application: The Dirac Delta Function......Page 498 6.3.5 Nonlinear Higher-Order Equations......Page 500 A(t) Constant......Page 501 Application: The Double Pendulum......Page 509 6.4.2 Nonhomogeneous Linear Systems......Page 515 6.4.3 Nonlinear Systems......Page 519 Linearization......Page 522 6.5.1 The One-Dimensional Wave Equation......Page 543 6.5.2 The Two-Dimensional Wave Equation......Page 549 6.5.3 Other Partial Differential Equations......Page 559 Bibliography......Page 563 Index......Page 564 Mathematica by Example, Fifth Edition is an essential desk reference for the beginning Mathematica user, providing step-by-step instructions on achieving results from this powerful software tool. The book fully accounts for the dramatic changes to functionality and visualization capabilities in the most recent version of Mathematica (10.4). It accommodates the full array of new extensions in the types of data and problems that Mathematica can immediately handle, including cloud services and systems, geographic and geometric computation, dynamic visualization, interactive applications and other improvements. It is an ideal text for scientific students, researchers and aspiring programmers seeking further understanding of Mathematica. Written by seasoned practitioners with a view to practical implementation and problem-solving, the book's pedagogy is delivered clearly and without jargon using representative biological, physical and engineering problems. Code is provided on an ancillary website to support the use of Mathematica across diverse applications. Provides a clear organization, integrated topic coverage, and accessible exposition for novices Includes step-by-step instructions for the most popular implementations Contains new applications, exercises and examples from a variety of fields, including biology, physics and engineering Supported by a website providing Mathematica code derived from examples in the book A desk reference for the beginning Mathematica user, providing step-by-step instructions on achieving results. The book fully accounts for the changes to functionality and visualization capabilities in version 11. The book is written with a view to practical implementation and problem-solving, without jargon, and uses representative biological, physical, and engineering problems.-- From publisher's description