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Differential Equations 4/e

作者：Blanchard
原價：NT$ 1,400

ISBN：9781133110590
版次：4
年份：2012
出版商：Cengage Learning
頁數/規格：836頁/平裝雙色

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Description
Incorporating an innovative modeling approach, this text for a one-semester differential equations course emphasizes conceptual understanding to help students relate information taught in the classroom to real-world experiences. Going beyond a traditional emphasis on technique, the authors focus on understanding how differential equations are formulated and interpreting their meaning to applied models from a variety of disciplines. A three-pronged qualitative, numeric, and analytic approach stresses visualizing differential equations geometrically, utilizing the latest computational technology to investigate the behavior of solutions, and predicting the behavior of solutions as they apply to models. The presentation weaves various points of view together so students become adept at moving between different representations to solve nonlinear differential equations equally well as traditional linear equations. Certain models reappear throughout the text as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Students will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom.

Features

The book's modeling approach emphasizes understanding of the meaning of variables and parameters in a differential equation and interpreting this meaning in an applied setting.

Revisited models in the text reinforce recurring themes and synthesize multiple concepts to solve practical problems. This helps students develop a natural intuition for how to approach an applied problem in real life without a road map.

A large number of well-chosen exercises integrate the qualitative, numerical, and analytic arguments behind a solution and require students to demonstrate understanding of the concepts behind the problem.

Lab activities at the end of each chapter offer deeper explorations of models, and require students to summarize their results in a report that demonstrates the necessary qualitative, numerical, and analytic arguments.
Certain exercises make optional use of specific applets in the DE Tools suite to harness the power of technology in solving differential equations.

New to This Edition

New in-depth models on timely and relevant applications such as SIR infectious disease modeling.

Chapters on First-Order Systems, Linear Systems, and Forcing and Resonance have been extensively rewritten for better clarity and readability.

Several sections, particularly in Chapters 2-4, have been reorganized for teaching flexibility and to better fit into class time constraints.

Exercise sets have been thoroughly refreshed with updated problems throughout the text.

Table of Contents
1. FIRST-ORDER DIFFERENTIAL EQUATIONS.
2. FIRST-ORDER SYSTEMS.
3. LINEAR SYSTEMS.
4. FORCING AND RESONANCE.
5. NONLINEAR SYSTEMS.
6. LAPLACE TRANSFORMS.
7. NUMERICAL METHODS.
8. DISCRETE DYNAMICAL SYSTEMS.

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