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Differential Equations: An Introduction to Modern Methods and Applications, Student Solutions Manual, 2nd Edition
John Wiley and Sons Ltd, Dec 2011, Pages: 600
Unlike other texts in the market, this second edition presents differential equations consistent with the way scientists and engineers use modern methods in their work. Technology is used freely, with more emphasis on modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. It also refers to larger-scale computations that computer algebra systems and DE solvers make possible. More exercises and examples involving working with data and devising the model provide scientists and engineers with the tools needed to model complex real-world situations.
New to this Edition:
- Clarity of Applications: Based on the advice of first-edition users and others, the authors have reorganized some topics to make key ideas stand out more clearly, and have added applications that will motivate students by catching their interest and will help to build their skills in modeling with differential equations.
- User Friendliness: The 2nd edition is designed to be more student-friendly by adjusting the level and strengthening the emphasis on applications, modeling and the use of computers.
- Additional Problems and Exercises: New exercises, projects, and problems invite the student to make conjectures or reach conclusions about complex situations based on computer-generated data and graphs, rather than closed-form solutions.
- Stressed Topics: The important link between linear second-order equations and linear systems of dimension two is strengthened in the second edition.
- Real-World Applications: New introduction to two-dimensional systems of first-order differential equations in Chapter 3. The author demonstrates the usefulness of eigenvalues in the context of a timely application involving solar energy transfer and storage in a greenhouse.
- Reorganization: Sections 4.2 through 4.4 reorganized into two sections. The sections are streamlined and simplified, with optional advanced material moved to exercise sets.
Hallmark Features:
Flexible Organization: Organization of chapters, sections, and projects allows for a variety of course configurations depending on desired course goals, topics, and depth of coverage.
Numerous and Varied Problems: Throughout the text, section exercises of varying levels of difficulty give students hands-on experience in modeling, analysis, and computer experimentation.
Emphasis on Systems: Systems of first order equations, a central and unifying theme of the text, are introduced early, in Chapter 3, and are used frequently thereafter.
Linear Algebra and Matrix Methods: Two-dimensional linear algebra sufficient for the study of two first order equations, taken up in Chapter 3, is presented in Section 3.1. Linear algebra and matrix methods required for the study of linear systems of dimension n (Chapter 6) are treated in Appendix A.
Contemporary Project Applications: Optional projects at the end of Chapters 2 through 10 integrate subject matter in the context of exciting, contemporary applications in science and engineering, such as controlling the attitude of a satellite, ray theory of wave propagation, uniformly distributing points on a sphere, and vibration analysis of tall buildings.
Computing Exercises: In most cases, problems requiring computer generated solutions and graphics are indicated by an icon.
Visual Elements: In addition to a large number of illustrations and graphs within the text, physical representations of dynamical systems and interactive animations available in WileyPLUS provide students with a strong visual component to the subject.
Laplace Transforms: A detailed chapter on Laplace transforms discusses systems, discontinuous and impulsive input functions, transfer functions, feedback control systems, poles, and stability.
Control Theory: Ideas and methods from the important application area of control theory are introduced in some examples and projects, and in the last section on Laplace Transforms, all of which are optional.
Recurring Themes and Applications: Important themes and applications, such as dynamical system formulation, phase portraits, linearization, stability of equilibrium solutions, vibrating systems, and frequency response are revisited and reexamined in different applications and mathematical settings.
Chapter Summaries: A summary at the end of each chapter provides students and instructors with a birds-eye view of the most important ideas in the chapter.
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