Straightforward and easy to read, Zill's DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 10th EDITION, gives you a thorough overview of the topics typically taught in a differential equations first course as well as an introduction to boundary-value problems and partial differential equations. Your study will be supported by a bounty of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions and more.
1. INTRODUCTION TO DIFFERENTIAL EQUATIONS.
Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review.
2. FIRST-ORDER DIFFERENTIAL EQUATIONS.
Solution Curves Without a Solution. Separable Equations. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review.
3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS.
Linear Models. Nonlinear Models. Modeling with Systems of First-Order DEs. Chapter 3 in Review.
4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Theory of Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients-Superposition Approach. Undetermined Coefficients-Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Green's Functions. Solving Systems of Linear DEs by Elimination. Nonlinear Differential Equations. Chapter 4 in Review.
5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review.
6. SERIES SOLUTIONS OF LINEAR EQUATIONS.
Review of Power Series. Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review.
7. THE LAPLACE TRANSFORM.
Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review.
8. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS.
Theory of Linear Systems. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review.
9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.
Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review.
10. SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS.
Autonomous Systems. Stability of Linear Systems. Linearization and Local Stability. Autonomous Systems as Mathematical Models. Chapter 10 in Review.
11. FOURIER SERIES.
Orthogonal Functions. Fourier Series. Fourier Cosine and Sine Series. Sturm-Liouville Problem. Bessel and Legendre Series. Chapter 11 in Review.
12. BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES.
Separable Partial Differential Equations. Classical PDEs and Boundary-Value Problems. Heat Equation. Wave Equation. Laplace's Equation. Nonhomogeneous Boundary-Value Problems. Orthogonal Series Expansions. Higher-Dimensional Problems. Chapter 12 in Review.
13. BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS.
Polar Coordinates. Polar and Cylindrical Coordinates. Spherical Coordinates. Chapter 13 in Review.
14. INTEGRAL TRANSFORM METHOD.
Error Function. Laplace Transform. Fourier Integral. Fourier Transforms. Finite Fourier Transforms. Chapter 14 in Review.
15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS.
Laplace's Equation. Heat Equation. Wave Equation. Chapter 15 in Review.
Appendix A: Integral-Defined Functions.
Appendix B: Matrices.
Appendix C: Table of Laplace Transforms.
Answers to Selected Odd-Numbered Problems.
Index.
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Dennis G. Zill
Dennis Zill received a PhD in Applied Mathematics from Iowa State University, and is a former professor of Mathematics at Loyola Marymount University in Los Angeles, Loras College in Iowa, and California Polytechnic State University. He is also the former chair of the Mathematics department at Loyola Marymount University, where he currently holds a rank as Professor Emeritus of Mathematics. Zill holds interests in astronomy, modern literature, music, golf, and good wine, while his research interests include Special Functions, Differential Equations, Integral Transformations, and Complex Analysis.
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In addition to new examples, figures and exposition, other new material includes the new section (14.5) Finite Fourier Transforms, an expanded table of Laplace transforms in Appendix C, and a greater emphasis on the concepts of piecewise-linear differential equations and solutions that involve nonelementary integrals.
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This text guides students through material necessary to progress to the next level of study; its clear presentation and mathematical precision make it an excellent reference tool in future courses.
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Many exercise sets have been updated by the addition of new problems. Some of these problems involve new and interesting mathematical models.
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WebAssign: DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 10th EDITION, continues to be fully supported by WebAssign. The powerful online learning, homework and course management system engages students in learning the math. WebAssign includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts, online learning tools like lecture videos and PowerPoint slides, as well as robust course, section, assignment and question settings and online testing. WebAssign also has a Differential Equations boot camp, providing a review of important calculus prerequisite topics.
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The development of material in this text progresses intuitively, and explanations are clear and concise. Exercises reinforce and build on chapter content.
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This text guides students through material necessary to progress to the next level of study; its clear presentation and mathematical precision make it an excellent reference tool in future courses.
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While this text is time-tested and widely accepted, it remains current with the addition of new exercises and examples.
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While this text is time-tested and widely accepted, it has remained current with the addition of new exercises and examples.
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The four-color design adds depth of meaning to all of the graphics, particularly three-dimensional pieces and visuals that involve multiple curves in a graph. The author directed the creation of each piece of art to ensure that it is as mathematically correct as the text.
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