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DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of Differential Equations. This proven text speaks to students of varied majors through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, and definitions. Now fully supported by two strong digital learning solutions, Enhanced WebAssign and MindTap® Math, the book provides a thorough overview of the topics typically taught in a first course in Differential Equations as well as an introduction to boundary-value problems and partial Differential Equations written in a straightforward, readable, and helpful style.
- Exercises in this edition have been updated to better test and challenge students.
- A new design helps students quickly identify resources in the text and emphasizes the application of Differential Equations in the world around them.
- NEW TECHNOLOGY. MindTap® Math for DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS is the all-in-one digital learning solution built with input from today’s students and instructors to enhance the learning experience. Complete with a modern design, student diagnostic and improvement plan, end-of-chapter exercises, automatically-graded algorithmic questions with just-in-time homework help and immediate feedback, MindTap helps instructors reduce distraction and keep students focused and engaged in learning course concepts.
- ENHANCED WEBASSIGN: DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, Ninth Edition, is fully supported by Enhanced WebAssign (EWA), the powerful online homework and course management system that engages students in learning the math. EWA includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.
- Extended homework problems at the end of selected section exercises were submitted and classroom-tested by members of the differential equations instructors.
- The development of material in this text progresses intuitively, and explanations are clear and concise. Exercises reinforce and build on chapter content.
- 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.
- While this text is time-tested and widely accepted, it has remained current with the addition of new exercises, and the enhanced four-color presentation.
- 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.
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 Variables. Linear Equations. Exact Equations and Integrating Factors. 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 Differential Equations. Chapter 3 in Review.
4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory-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. Solving Systems of Linear Differential Equations 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. 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 FIRST-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review.
9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.
Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review.
10. PLANE AUTONOMOUS SYSTEMS.
Autonomous Systems. Stability of Linear Systems. Linearization and Local Stability. Autonomous Systems as Mathematical Models. Chapter 10 in Review.
11. ORTHOGONAL FUNCTIONS AND FOURIER SERIES.
Orthogonal Functions. Fourier Series and Orthogonal Functions. 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 PDE''s 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. Chapter 14 in Review.
15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS.
Laplace''s Equation. Heat Equation. Wave Equation. Chapter 15 in Review.
Appendix I: Gamma Function.
Appendix II: Matrices.
Appendix III: Laplace Transforms.
Answers for Selected Odd-Numbered Problems.
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Instructor's Solutions Manual
This time-saving manual provides complete solutions to all the problems in the text.
Everything you need for your course in one place! This collection of product-specific lecture and class tools is available online via the instructor resource center at www.cengage.com/login. You'll be able to access and download materials such as PowerPoint presentations, images, instructor’s manual, videos, and more.
PowerPoint® with Image Library on Instructor's Website
Available via the instructor companion site, the PowerPoint® Image Library helps you make your lectures more engaging while effectively reaching your visually oriented students.
Cengage Learning Testing, powered by Cognero Instant Access
Cengage Learning Testing Powered by Cognero® is a flexible, online system that allows you to: import, edit, and manipulate content from the text’s test bank or elsewhere, including your own favorite test questions; create multiple test versions in an instant; and deliver tests from your LMS, your classroom, or wherever you want.
Student Solutions Manual
This manual contains fully worked-out solutions to select odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Student Solutions Manual
Go beyond the answers -- see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to select odd-numbered problems in the text, giving you the information you need to truly understand how these problems are solved. Each section begins with a list of key terms and concepts. The solutions sections also include hints and examples to guide you to greater understanding.