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Zill NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC Loyola Marymount University © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LL NOT FOR SALE OR DISTRIBUT © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION Learn More at https://www.jblearning.com/catalog/productdetails/9781284206241 © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION World Headquarters Jones & Bartlett Learning 5 Wall Street Burlington, MA 01803 978-443-5000 info@jblearning.com www.jblearning.com © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LL NOT FOR SALE OR DISTRIBUT Jones & Bartlett Learning books and products are available through most bookstores and online booksellers. 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Title: Advanced engineering mathematics / Dennis G. Zill. Description:© Seventh edition.&| Burlington, MALearning, : Jones & Bartlett Learning, Jones Bartlett LLC [2022] | Includes index. | NOT FOR SALE OR DISTRIBUTION Identifiers: LCCN 2020022145 | ISBN 9781284206241 (hardcover) Subjects: LCSH: Engineering mathematics. 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Definitions and Terminology NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION 1.2 1.3 Initial-Value Problems Differential Equations as Mathematical Models Chapter 1 in Review © Jones & Bartlett Learning, LLC NOT SALE OR DISTRIBUTION 2 FOR First-Order Differential Equations 2 3 14 19 30 © Jones & Bartlett Learning, LL NOT FOR SALE OR 34DISTRIBUT 2.1 Solution Curves Without a Solution 35 2.1.1 Direction Fields 35 2.1.2 Autonomous First-Order DEs 37 © Jones & Bartlett Learning, LLC © Jones & Bartlett Learning, LLC 2.2 Separable Equations 44 NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION 2.3 Linear Equations 53 2.4 Exact Equations 61 2.5 Solutions by Substitutions 68 2.6 A Numerical Method 73 © Jones & Bartlett Learning, LLC © Jones & Bartlett Learning, LLC 2.7 Linear Models 77 NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION 2.8 Nonlinear Models 88 2.9 Modeling with Systems of First-Order DEs 97 Chapter 2 in Review 104 © Jones & Bartlett Learning, LLC © Jones & 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Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION viii | Contents 889 893 898 905 © Jones & Bartlett Learning, LL NOT FOR SALE OR DISTRIBUT 908 913 919 © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION Learn More at https://www.jblearning.com/catalog/productdetails/9781284206241 © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION 20 Conformal Mappings 20.1 Complex Functions as Mappings 20.2 Conformal Mappings ©20.3 JonesLinear & Bartlett Learning, LLC Fractional Transformations NOT FOR SALE OR DISTRIBUTION 20.4 Schwarz–Christoffel Transformations 20.5 Poisson Integral Formulas 20.6 Applications Chapter 20 in Review © Jones & Bartlett Learning, LLC Appendices NOT FOR SALE OR DISTRIBUTION 923 927 © Jones & Bartlett933 Learning, LL NOT FOR SALE OR 939DISTRIBUT 943 947 953 © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION A Integral-Defined Functions B Derivative and Integral Formulas C Laplace Transforms © Jones & Bartlett Learning, LLC D Conformal Mappings © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION Answers to Selected Odd-Numbered Problems Index © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION ANS-1 © Jones & Bartlett Learning, LL NOT FOR SALE OR DISTRIBUT © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION APP-2 APP-10 APP-12 APP-17 I-1 © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION 922 © Jones & Bartlett Learning, LL NOT FOR SALE OR DISTRIBUT © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION Contents | Learn More at https://www.jblearning.com/catalog/productdetails/9781284206241 ix © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION Preface © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION © Jones & Bartlett Learning, LLC © Jones & Bartlett Learning, LL NOT FOR SALE OR DISTRIBUT © Jones & Bartlett Learning, LLC functions, directional derivatives, line integrals, double and SALE ORtheorem, DISTRIBUTION triple integrals, NOT surfaceFOR integrals, Green’s Stokes’ theorem, and the divergence theorem. In Section 7.6 the vector concept is generalized; by defining vectors analytically we lose their geometric interpretation but keep many of their in n-dimensional and infinite-dimensional vector ©properties Jones & Bartlett Learning, LLC spaces. Chapter 8, Matrices, is an introduction to systems of NOT FORequations, SALE OR DISTRIBUTION algebraic determinants, and matrix algebra, with special emphasis on those types of matrices that are useful in solving systems of linear differential equations. Optional sections on cryptography, error correcting codes, the method of least squares, and discrete compartmental models are pre© Jones & Bartlett Learning, LLC © Jones & Bartlett Learning, LL sented as applications of matrix algebra. In courses such as calculus or differential equations, the conNOT FOR SALE DISTRIBUTION tent is fairly standardized, but the OR content of a course entitled engineering mathematics often varies considerably between two different academic institutions. Therefore a text entitled Advanced Engineering Mathematics is a compendium of many mathematical topics, all of which are loosely related © Jones & Bartlett Learning, LLC by the expedient of either being needed or useful in courses NOT FOR SALE OR DISTRIBUTION in science and engineering or in subsequent careers in these areas. There is literally no upper bound to the number of topics that could be included in a text such as this. Consequently, this book represents the author’s opinion of what constitutes engineering mathematics. NOT FOR SALE OR DISTRIBUT NOT FOR SALE OR DISTRIBUTION PART 3: Systems of Differential Equations For flexibility in topic selection this text is divided into five (Chapters 10 and 11) Content of the Text major parts. As can be seen from the titles of these various parts, it should be obvious that it is my belief that the & Bartlett Learning, LLC backbone © of Jones science/engineering-related mathematics is the FOR SALE ORand DISTRIBUTION theory andNOT applications of ordinary partial differential equations. PART 1: Ordinary Differential Equations (Chapters 1–6) © Jones & Bartlett Learning, LLC The sixSALE chapters in Part 1 constitute a complete short course NOT FOR OR DISTRIBUTION There are two chapters in Part 3. Chapter 10, Systems of © Jones & Bartlett Learning, Linear Differential Equations, and Chapter 11, SystemsLLC of NOT Equations, FOR SALE DISTRIBUTION Nonlinear Differential drawOR heavily on the matrix material presented in Chapter 8 of Part 2. In Chapter 10, systems of linear first-order equations are solved utilizing the concepts of eigenvalues and eigenvectors, diagonalization, and by means of a matrix exponential function. In ©Chapter Jones11, & qualitative Bartlett Learning, LLC aspects of autonomous linear and nonlinear considered in depth. NOT FORsystems SALEareOR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION in ordinary differential equations. These chapters, with some modifications, correspond to Chapters 1, 2, 3, 4, 5, 6, 7, and PART 4: Partial Differential Equations 9 in the text A First Course in Differential Equations with (Chapters 12–16) Modeling Applications, Eleventh Edition, by Dennis G. Zill © Jones & Bartlett Learning, Jones & Bartlett TheLLC core material on Fourier series© and boundary-value prob- Learning, LL (Cengage Learning). In Chapter 2 the focus is on methods lems involving second-order partialNOT differential for solving first-order differential equations FORequations SALEwas OR DISTRIBUT NOT FOR SALEand ORtheir DISTRIBUTION drawn from the text Differential Equations with Boundaryapplications. Chapter 3 deals mainly with linear second-order Value Problems, Ninth Edition, by Dennis G. Zill (Cengage differential equations and their applications. Chapter 4 is Learning). In Chapter 12, Fourier Series, the fundamental devoted to the solution of differential equations and systems topics of sets of orthogonal functions and expansions of funcof differential equations by the important Laplace transform. © Jones & Bartlett Learning, LLC & Bartlett Learning, tions in terms of©anJones infinite series of orthogonal functions LLC are presented. These topics are then utilized in Chapters 13 and 14 NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION PART 2: Vectors, Matrices, and Vector Calculus where boundary-value problems in rectangular, polar, cylin(Chapters 7–9) drical, and spherical coordinates are solved using the method of separation of variables. In Chapter 15, Integral Transforms, Chapter 7, Vectors, and Chapter 9, Vector Calculus, include boundary-value problems are solved by means of the Laplace the standard topics that are usually covered in the third semes© Jones Learning, LLC Jones Bartlett Learning, LLC Fourier&integral transforms. ter of&a Bartlett calculus sequence: vectors in 2- and 3-space, vector © and x | Preface Learn More at https://www.jblearning.com/catalog/productdetails/9781284206241 © Jones & Bartlett Learning, LLC © Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION NOT FOR SALE OR DISTRIBUTION New figures and photos have been added to highlight PART 5: Complex Analysis (Chapters 17–20) some of the older problems and discussions. 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