{"product_id":"mathematical-methods-in-engineering-and-physics-isbn-9781118449608","title":"Mathematical Methods in Engineering and Physics","description":"\u003cp\u003eThis text is intended for the undergraduate course in math methods, with an audience of physics and engineering majors. As a required course in most departments, the text relies heavily on explained examples, real-world applications and student engagement. Supporting the use of active learning, a strong focus is placed upon physical motivation combined with a versatile coverage of topics that can be used as a reference after students complete the course.\u003c\/p\u003e \u003cp\u003eEach chapter begins with an overview that includes a list of prerequisite knowledge, a list of skills that will be covered in the chapter, and an outline of the sections. Next comes the motivating exercise, which steps the students through a real-world physical problem that requires the techniques taught in each chapter.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Ordinary Differential Equations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Motivating Exercise: The Simple Harmonic Oscillator 2\u003c\/p\u003e \u003cp\u003e1.2 Overview of Differential Equations 3\u003c\/p\u003e \u003cp\u003e1.3 Arbitrary Constants 15\u003c\/p\u003e \u003cp\u003e1.4 Slope Fields and Equilibrium 25\u003c\/p\u003e \u003cp\u003e1.5 Separation of Variables 34\u003c\/p\u003e \u003cp\u003e1.6 Guess and Check, and Linear Superposition 39\u003c\/p\u003e \u003cp\u003e1.7 Coupled Equations (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e1.8 Differential Equations on a Computer (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e1.9 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Taylor Series and Series Convergence 50\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Motivating Exercise: Vibrations in a Crystal 51\u003c\/p\u003e \u003cp\u003e2.2 Linear Approximations 52\u003c\/p\u003e \u003cp\u003e2.3 Maclaurin Series 60\u003c\/p\u003e \u003cp\u003e2.4 Taylor Series 70\u003c\/p\u003e \u003cp\u003e2.5 Finding One Taylor Series from Another 76\u003c\/p\u003e \u003cp\u003e2.6 Sequences and Series 80\u003c\/p\u003e \u003cp\u003e2.7 Tests for Series Convergence 92\u003c\/p\u003e \u003cp\u003e2.8 Asymptotic Expansions (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e2.9 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Complex Numbers 104\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Motivating Exercise: The Underdamped Harmonic Oscillator 104\u003c\/p\u003e \u003cp\u003e3.2 Complex Numbers 105\u003c\/p\u003e \u003cp\u003e3.3 The Complex Plane 113\u003c\/p\u003e \u003cp\u003e3.4 Euler’s Formula I—The Complex Exponential Function 117\u003c\/p\u003e \u003cp\u003e3.5 Euler’s Formula II—Modeling Oscillations 126\u003c\/p\u003e \u003cp\u003e3.6 Special Application: Electric Circuits (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e3.7 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Partial Derivatives 136\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Motivating Exercise: The Wave Equation 136\u003c\/p\u003e \u003cp\u003e4.2 Partial Derivatives 137\u003c\/p\u003e \u003cp\u003e4.3 The Chain Rule 145\u003c\/p\u003e \u003cp\u003e4.4 Implicit Differentiation 153\u003c\/p\u003e \u003cp\u003e4.5 Directional Derivatives 158\u003c\/p\u003e \u003cp\u003e4.6 The Gradient 163\u003c\/p\u003e \u003cp\u003e4.7 Tangent Plane Approximations and Power Series (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e4.8 Optimization and the Gradient 172\u003c\/p\u003e \u003cp\u003e4.9 Lagrange Multipliers 181\u003c\/p\u003e \u003cp\u003e4.10 Special Application: Thermodynamics (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e4.11 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Integrals in Two or More Dimensions 188\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Motivating Exercise: Newton’s Problem (or) The Gravitational Field of a Sphere 188\u003c\/p\u003e \u003cp\u003e5.2 Setting Up Integrals 189\u003c\/p\u003e \u003cp\u003e5.3 Cartesian Double Integrals over a Rectangular Region 204\u003c\/p\u003e \u003cp\u003e5.4 Cartesian Double Integrals over a Non-Rectangular Region 211\u003c\/p\u003e \u003cp\u003e5.5 Triple Integrals in Cartesian Coordinates 216\u003c\/p\u003e \u003cp\u003e5.6 Double Integrals in Polar Coordinates 221\u003c\/p\u003e \u003cp\u003e5.7 Cylindrical and Spherical Coordinates 229\u003c\/p\u003e \u003cp\u003e5.8 Line Integrals 240\u003c\/p\u003e \u003cp\u003e5.9 Parametrically Expressed Surfaces 249\u003c\/p\u003e \u003cp\u003e5.10 Surface Integrals 253\u003c\/p\u003e \u003cp\u003e5.11 Special Application: Gravitational Forces (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e5.12 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Linear Algebra I 266\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Motivating Example on which We’re Going to Base the Whole Chapter: The Three-Spring Problem 266\u003c\/p\u003e \u003cp\u003e6.2 Matrices: The Easy Stuff 276\u003c\/p\u003e \u003cp\u003e6.3 Matrix Times Column 280\u003c\/p\u003e \u003cp\u003e6.4 Basis Vectors 286\u003c\/p\u003e \u003cp\u003e6.5 Matrix Times Matrix 294\u003c\/p\u003e \u003cp\u003e6.6 The Identity and Inverse Matrices 303\u003c\/p\u003e \u003cp\u003e6.7 Linear Dependence and the Determinant 312\u003c\/p\u003e \u003cp\u003e6.8 Eigenvectors and Eigenvalues 325\u003c\/p\u003e \u003cp\u003e6.9 Putting It Together: Revisiting the Three-Spring Problem 336\u003c\/p\u003e \u003cp\u003e6.10 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Linear Algebra II 346\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Geometric Transformations 347\u003c\/p\u003e \u003cp\u003e7.2 Tensors 358\u003c\/p\u003e \u003cp\u003e7.3 Vector Spaces and Complex Vectors 369\u003c\/p\u003e \u003cp\u003e7.4 Row Reduction (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e7.5 Linear Programming and the Simplex Method (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e7.6 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Vector Calculus 378\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Motivating Exercise: Flowing Fluids 378\u003c\/p\u003e \u003cp\u003e8.2 Scalar and Vector Fields 379\u003c\/p\u003e \u003cp\u003e8.3 Potential in One Dimension 387\u003c\/p\u003e \u003cp\u003e8.4 From Potential to Gradient 396\u003c\/p\u003e \u003cp\u003e8.5 From Gradient to Potential: The Gradient Theorem 402\u003c\/p\u003e \u003cp\u003e8.6 Divergence, Curl, and Laplacian 407\u003c\/p\u003e \u003cp\u003e8.7 Divergence and Curl II—The Math Behind the Pictures 416\u003c\/p\u003e \u003cp\u003e8.8 Vectors in Curvilinear Coordinates 419\u003c\/p\u003e \u003cp\u003e8.9 The Divergence Theorem 426\u003c\/p\u003e \u003cp\u003e8.10 Stokes’ Theorem 432\u003c\/p\u003e \u003cp\u003e8.11 Conservative Vector Fields 437\u003c\/p\u003e \u003cp\u003e8.12 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Fourier Series and Transforms 445\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Motivating Exercise: Discovering Extrasolar Planets 445\u003c\/p\u003e \u003cp\u003e9.2 Introduction to Fourier Series 447\u003c\/p\u003e \u003cp\u003e9.3 Deriving the Formula for a Fourier Series 457\u003c\/p\u003e \u003cp\u003e9.4 Different Periods and Finite Domains 459\u003c\/p\u003e \u003cp\u003e9.5 Fourier Series with Complex Exponentials 467\u003c\/p\u003e \u003cp\u003e9.6 Fourier Transforms 472\u003c\/p\u003e \u003cp\u003e9.7 Discrete Fourier Transforms (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e9.8 Multivariate Fourier Series (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e9.9 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Methods of Solving Ordinary Differential Equations 484\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Motivating Exercise: A Damped, Driven Oscillator 485\u003c\/p\u003e \u003cp\u003e10.2 Guess and Check 485\u003c\/p\u003e \u003cp\u003e10.3 Phase Portraits (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e10.4 Linear First-Order Differential Equations (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e10.5 Exact Differential Equations (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e10.6 Linearly Independent Solutions and the Wronskian (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e10.7 Variable Substitution 494\u003c\/p\u003e \u003cp\u003e10.8 Three Special Cases of Variable Substitution 505\u003c\/p\u003e \u003cp\u003e10.9 Reduction of Order and Variation of Parameters (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e10.10 Heaviside, Dirac, and Laplace 512\u003c\/p\u003e \u003cp\u003e10.11 Using Laplace Transforms to Solve Differential Equations 522\u003c\/p\u003e \u003cp\u003e10.12 Green’s Functions 531\u003c\/p\u003e \u003cp\u003e10.13 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Partial Differential Equations 541\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Motivating Exercise: The Heat Equation 542\u003c\/p\u003e \u003cp\u003e11.2 Overview of Partial Differential Equations 544\u003c\/p\u003e \u003cp\u003e11.3 Normal Modes 555\u003c\/p\u003e \u003cp\u003e11.4 Separation of Variables—The Basic Method 567\u003c\/p\u003e \u003cp\u003e11.5 Separation of Variables—More than Two Variables 580\u003c\/p\u003e \u003cp\u003e11.6 Separation of Variables—Polar Coordinates and Bessel Functions 589\u003c\/p\u003e \u003cp\u003e11.7 Separation of Variables—Spherical Coordinates and Legendre Polynomials 607\u003c\/p\u003e \u003cp\u003e11.8 Inhomogeneous Boundary Conditions 616\u003c\/p\u003e \u003cp\u003e11.9 The Method of Eigenfunction Expansion 623\u003c\/p\u003e \u003cp\u003e11.10 The Method of Fourier Transforms 636\u003c\/p\u003e \u003cp\u003e11.11 The Method of Laplace Transforms 646\u003c\/p\u003e \u003cp\u003e11.12 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Special Functions and ODE Series Solutions 652\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Motivating Exercise: The Circular Drum 652\u003c\/p\u003e \u003cp\u003e12.2 Some Handy Summation Tricks 654\u003c\/p\u003e \u003cp\u003e12.3 A Few Special Functions 658\u003c\/p\u003e \u003cp\u003e12.4 Solving Differential Equations with Power Series 666\u003c\/p\u003e \u003cp\u003e12.5 Legendre Polynomials 673\u003c\/p\u003e \u003cp\u003e12.6 The Method of Frobenius 682\u003c\/p\u003e \u003cp\u003e12.7 Bessel Functions 688\u003c\/p\u003e \u003cp\u003e12.8 Sturm-Liouville Theory and Series Expansions 697\u003c\/p\u003e \u003cp\u003e12.9 Proof of the Orthgonality of Sturm-Liouville Eigenfunctions (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e12.10 Special Application: The Quantum Harmonic Oscillator and Ladder Operators (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e12.11 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Calculus with Complex Numbers 708\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Motivating Exercise: Laplace’s Equation 709\u003c\/p\u003e \u003cp\u003e13.2 Functions of Complex Numbers 710\u003c\/p\u003e \u003cp\u003e13.3 Derivatives, Analytic Functions, and Laplace’s Equation 716\u003c\/p\u003e \u003cp\u003e13.4 Contour Integration 726\u003c\/p\u003e \u003cp\u003e13.5 Some Uses of Contour Integration 733\u003c\/p\u003e \u003cp\u003e13.6 Integrating Along Branch Cuts and Through Poles (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e13.7 Complex Power Series 742\u003c\/p\u003e \u003cp\u003e13.8 Mapping Curves and Regions 747\u003c\/p\u003e \u003cp\u003e13.9 Conformal Mapping and Laplace’s Equation 754\u003c\/p\u003e \u003cp\u003e13.10 Special Application: Fluid Flow (see felderbooks.com)\u003c\/p\u003e \u003cp\u003e13.11 Additional Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003eAppendix A Different Types of Differential Equations 765\u003c\/p\u003e \u003cp\u003eAppendix B Taylor Series 768\u003c\/p\u003e \u003cp\u003eAppendix C Summary of Tests for Series Convergence 770\u003c\/p\u003e \u003cp\u003eAppendix D Curvilinear Coordinates 772\u003c\/p\u003e \u003cp\u003eAppendix E Matrices 774\u003c\/p\u003e \u003cp\u003eAppendix F Vector Calculus 777\u003c\/p\u003e \u003cp\u003eAppendix G Fourier Series and Transforms 779\u003c\/p\u003e \u003cp\u003eAppendix H Laplace Transforms 782\u003c\/p\u003e \u003cp\u003eAppendix I Summary: Which PDE Technique Do I Use? 787\u003c\/p\u003e \u003cp\u003eAppendix J Some Common Differential Equations and Their Solutions 790\u003c\/p\u003e \u003cp\u003eAppendix K Special Functions 798\u003c\/p\u003e \u003cp\u003eAppendix L Answers to “Check Yourself” in Exercises 801\u003c\/p\u003e \u003cp\u003eAppendix M Answers to Odd-Numbered Problems (see felderbooks.com)\u003c\/p\u003e \u003cp\u003eIndex 805\u003c\/p\u003e \u003cp\u003e\"[\u003ci\u003eMathematical Methods in Engineering and Physics\u003c\/i\u003e] is my book of choice for teaching undergraduates...I honestly never thought that I could be so enchanted by the heat equation before seeing how Felder and Felder effectively have students derive it as part of honing their intuition for how to think about partial differential equations.\" - \u003cb\u003eChristine Aidala, PhD, Associate Professor of Physics at University of Michigan for the \u003ci\u003eAmerican Journal of Physics \u003c\/i\u003e\u003cbr\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDidYou\u003cb\u003eKnow?\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eThis book is available as a Wiley E-Text.\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eThe Wiley E-Text is a complete digital version of the text that makes time spent studying more efficient. Course materials can be accessed on a desktop, laptop, or mobile device—so that learning can take place anytime, anywhere.\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eA more affordable alternative to traditional print, the Wiley E-Text creates a flexible user experience:\u003c\/b\u003e \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\u003cb\u003eAccess on-the-go\u003c\/b\u003e\u003c\/li\u003e \u003cli\u003e\u003cb\u003eSearch across content\u003c\/b\u003e\u003c\/li\u003e \u003cli\u003e\u003cb\u003eHighlight and take notes\u003c\/b\u003e\u003c\/li\u003e \u003cli\u003e\u003cb\u003eSave money!\u003c\/b\u003e\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003cb\u003eThe Wiley E-Text can be purchased in the following ways:\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eVia your campus bookstore:\u003c\/b\u003e Wiley E-Text: Powered by VitalSource® \u003c\/p\u003e\u003cp\u003eISBN 978-1-119-04598-4 \u003c\/p\u003e\u003cp\u003e* Instructors: This ISBN is needed when placing an order. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eDirectly from:\u003c\/b\u003e www.wiley.com\/college\/felder\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989586755813,"sku":"NP9781118449608","price":163.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118449608.jpg?v=1761784706","url":"https:\/\/k12savings.com\/es\/products\/mathematical-methods-in-engineering-and-physics-isbn-9781118449608","provider":"K12savings","version":"1.0","type":"link"}