## Fundamentals of differential equations / R. Kent Nagle, Edward B. Saff, Arthur David Snider.

Material type: TextHarlow, United Kingdom : Pearson Education Limited, 2019Edition: Ninth edition, global editionDescription: 717 pages : illustrations ; 26 cmISBN: 9781292240992; 1292240997Subject(s): Differential equations -- Textbooks | Differential equationsGenre/Form: Textbooks.DDC classification: 515.352Item type | Current location | Call number | Copy number | Status | Date due | Barcode |
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Foreign books | Library (men) - مكتبة الخدمات وقاعات الاطلاع (رجال) فرع خريص | 515.352 N.R.F (Browse shelf) | 1 | Available | e126037 |

Chapter 5: Introduction to Systems and Phase Plane Analysis.

Includes index.

Cover; Title Page; Copyright Page; Dedicated to R. Kent Nagle; Contents; Preface; Our Goal; New to This Edition; Prerequisites; Sample Syllabi; Retained Features; Technology and Supplements; Acknowledgments; Acknowledgments for the Global Edition; Chapter 1: Introduction; 1.1. Background; 1.2. Solutions and Initial Value Problems; 1.3. Direction Fields; 1.4. The Approximation Method of Euler; Chapter 1: Summary; Review Problems for Chapter 1; Technical Writing Exercises for Chapter 1; Projects for Chapter 1; A. Picard‘s Method; B. The Phase Line; C. Applications to Economics.

D. Taylor Series MethodChapter 2: First-Order Differential Equations; 2.1. Introduction: Motion of a Falling Body; 2.2. Separable Equations; 2.3. Linear Equations; 2.4. Exact Equations; 2.5. Special Integrating Factors; 2.6. Substitutions and Transformations; Chapter 2: Summary; Review Problems for Chapter 2; Technical Writing Exercises for Chapter 2; Projects for Chapter 2; A. Oil Spill in a Canal; B. Differential Equations in Clinical Medicine; C. Torricelli‘s Law of Fluid Flow; D. The Snowplow Problem; E. Two Snowplows; F. Clairaut Equations and Singular Solutions.

G. Multiple Solutions of a First-Order Initial Value ProblemH. Utility Functions and Risk Aversion; I. Designing a Solar Collector; J. Asymptotic Behavior of Solutions to Linear Equations; Chapter 3: Mathematical Models and Numerical Methods Involving First-Order Equations; 3.1. Mathematical Modeling; 3.2. Compartmental Analysis; 3.3. Heating and Cooling of Buildings; 3.4. Newtonian Mechanics; 3.5. Electrical Circuits; 3.6. Numerical Methods: A Closer Look At Euler‘s Algorithm; 3.7. Higher-Order Numerical Methods: Taylor and Runge-Kutta; Projects for Chapter 3; A. Dynamics of HIV Infection.

B. AquacultureC. Curve of Pursuit; D. Aircraft Guidance in a Crosswind; E. Market Equilibrium: Stability and Time Paths; F. Stability of Numerical Methods; G. Period Doubling and Chaos; Chapter 4: Linear Second-Order Equations; 4.1. Introduction: The Mass-Spring Oscillator; 4.2. Homogeneous Linear Equations: The General Solution; 4.3. Auxiliary Equations with Complex Roots; 4.4. Nonhomogeneous Equations: The Method of Undetermined Coefficients; 4.5. The Superposition Principle and Undetermined Coefficients Revisited; 4.6. Variation of Parameters; 4.7. Variable-Coefficient Equations.

4.8. Qualitative Considerations for Variable-Coefficient and Nonlinear Equations4.9. A Closer Look at Free Mechanical Vibrations; 4.10. A Closer Look at Forced Mechanical Vibrations; Chapter 4: Summary; Review Problems for Chapter 4; Technical Writing Exercises for Chapter 4; Projects for Chapter 4; A. Nonlinear Equations Solvable by First-Order Techniques; B. Apollo Reentry; C. Simple Pendulum; D. Linearization of Nonlinear Problems; E. Convolution Method; F. Undetermined Coefficients Using Complex Arithmetic; G. Asymptotic Behavior of Solutions; H. Gravity Train.

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