Name: Differential Equations: Theory, Technique, and Practice By George Simmons
SKU: 9780072863154
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Differential Equations: Theory, Technique, and Practice Summary

Differential Equations: Theory, Technique, and Practice by George Simmons

This traditional text is intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences. Written by two of the world's leading authorities on differential equations, Simmons/Krantz provides a cogent and accessible introduction to ordinary differential equations written in classical style. Its rich variety of modern applications in engineering, physics, and the applied sciences illuminate the concepts and techniques that students will use through practice to solve real-life problems in their careers.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.

About George Simmons

GEORGE F. SIMMONS has academic degree from the CAlifornia Institute of Technology, the university of chicago, and Yale University. He taught at several colleges and universities before joining the faculty of Colorado college in 1962, where he is a professor of mathematics. He is also the author of introduction to topology and Modern Analysis, Precalculus Mathematics in a Nutshell and calculus with Analytic Geometry. McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide

Preface1 What is a Differential Equation?1.1 Introductory Remarks1.2 The Nature of Solutions1.3 Separable Equations1.4 First-Order Linear Equations1.5 Exact Equations1.6 Orthogonal Trajectories and Families of Curves1.7 Homogeneous Equations1.8 Integrating Factors1.9 Reduction of Order1.9.1 Dependent Variable Missing1.9.2 Independent Variable Missing1.10 The Hanging Chain and Pursuit Curves1.10.1 The Hanging Chain1.10.2 Pursuit Curves1.11 Electrical CircuitsAnatomy of an Application: The Design of a Dialysis MachineProblems for Review and Discovery2 Second-Order Linear Equations2.1 Second-Order Linear Equations with Constant Coefficients2.2 The Method of Undetermined Coefficients2.3 The Method of Variation of Parameters2.4 The Use of a Known Solution to Find Another2.5 Vibrations and Oscillations2.5.1 Undamped Simple Harmonic Motion2.5.2 Damped Vibrations2.5.3 Forced Vibrations2.5.4 A Few Remarks About Electricity2.6 Newton's Law of Gravitation and Kepler's Laws2.6.1 Kepler's Second Law2.6.2 Kepler's First Law2.6.3 Kepler's Third Law2.7 Higher Order Linear Equations, Coupled Harmonic OscillatorsHistorical Note: EulerAnatomy of an Application: Bessel Functions and the Vibrating MembraneProblems for Review and Discovery3 Qualitative Properties and Theoretical Aspects3.1 Review of Linear Algebra3.1.1 Vector Spaces3.1.2 The Concept Linear Independence3.1.3 Bases3.1.4 Inner Product Spaces3.1.5 Linear Transformations and Matrices3.1.6 Eigenvalues and Eigenvectors3.2 A Bit of Theory3.3 Picard's Existence and Uniqueness Theorem3.3.1 The Form of a Differential Equation3.3.2 Picard's Iteration Technique3.3.3 Some Illustrative Examples3.3.4 Estimation of the Picard Iterates3.4 Oscillations and the Sturm Separation Theorem3.5 The Sturm Comparison TheoremAnatomy of an Application: The Green's FunctionProblems for Review and Discovery4 Power Series Solutions and Special Functions4.1 Introduction and Review of Power Series4.1.1 Review of Power Series4.2 Series Solutions of First-Order Differential Equations4.3 Second-Order Linear Equations: Ordinary Points4.4 Regular Singular Points4.5 More on Regular Singular Points4.6 Gauss's Hypergeometric EquationHistorical Note: GaussHistorical Note: AbelAnatomy of an Application: Steady-State Temperature in a BallProblems for Review and Discovery5 Fourier Series: Basic Concepts5.1 Fourier Coefficients5.2 Some Remarks about Convergence5.3 Even and Odd Functions: Cosine and Sine Series5.4 Fourier Series on Arbitrary Intervals5.5 Orthogonal FunctionsHistorical Note: RiemannAnatomy of an Application: Introduction to the Fourier TransformProblems for Review and Discovery6 Partial Differential Equations and Boundary Value Problems6.1 Introduction and Historical Remarks6.2 Eigenvalues, Eigenfunctions, and the Vibrating String6.2.1 Boundary Value Problems6.2.2 Derivation of the Wave Equation6.2.3 Solution of the Wave Equation6.3 The Heat Equation6.4 The Dirichlet Problem for a Disc6.4.1 The Poisson Integral6.5 Sturm-Liouville ProblemsHistorical Note: FourierHistorical Note: DirichletAnatomy of an Application: Some Ideas from Quantum MechanicsProblems for Review and Discovery7 Laplace Transforms7.1 Introduction7.2 Applications to Differential Equations7.3 Derivatives and Integrals of Laplace Transforms7.4 Convolutions7.3.1 Abel's Mechanical Problem7.5 The Unit Step and Impulse FunctionsHistorical Note: LaplaceAnatomy of an Application: Flow Initiated by an Impulsively-Started Flat PlateProblems for Review and Discovery8 The Calculus of Variations8.1 Introductory Remarks8.2 Euler's Equation8.3 Isoperimetric Problems and the Like8.3.1 Lagrange Multipliers8.3.2 Integral Side Conditions8.3.3 Finite Side ConditionsHistorical Note: NewtonAnatomy of an Application: Hamilton's Principle and its ImplicationsProblems for Review and Discovery9 Numerical Methods9.1 Introductory Remarks9.2 The Method of Euler9.3 The Error Term9.4 An Improved Euler Method9.5 The Runge-Kutta MethodAnatomy of an Application: A Constant Perturbation Method for Linear, Second-Order EquationsProblems for Review and Discovery10 Systems of First-Order Equations10.1 Introductory Remarks10.2 Linear Systems10.3 Homogeneous Linear Systems with Constant Coefficients10.4 Nonlinear Systems: Volterra's Predator-Prey EquationsAnatomy of an Application: Solution of Systems with Matrices and ExponentialsProblems for Review and Discovery11 The Nonlinear Theory11.1 Some Motivating Examples11.2 Specializing Down11.3 Types of Critical Points: Stability11.4 Critical Points and Stability for Linear Systems11.5 Stability by Liapunov's Direct Method11.6 Simple Critical Points of Nonlinear Systems11.7 Nonlinear Mechanics: Conservative Systems11.8 Periodic Solutions: The Poincare-Bendixson TheoremHistorical Note: PoincareAnatomy of an Application: Mechanical Analysis of a Block on a SpringProblems for Review and Discovery12 Dynamical Systems12.1 Flows12.1.1 Dynamical Systems12.1.2 Stable and Unstable Fixed Points12.1.3 Linear Dynamics in the Plane12.2 Some Ideas from Topology12.2.1 Open and Closed Sets12.2.2 The Idea of Connectedness12.2.3 Closed Curves in the Plane12.3 Planar Autonomous Systems12.3.1 Ingredients of the Proof of Poincare-BendixsonAnatomy of an Application: Lagrange's EquationsProblems for Review and DiscoveryBibliography

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Sku

CIN0072863153G

ISBN 13

9780072863154

ISBN 10

0072863153

Title

Differential Equations: Theory, Technique, and Practice by George Simmons

Author

George Simmons

Condition

Used - Good

Binding type

Hardback

Publisher

McGraw-Hill Education - Europe

Year published

2006-02-16

Number of pages

544

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Differential Equations: Theory, Technique, and Practice George Simmons

Differential Equations: Theory, Technique, and Practice by George Simmons

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Differential Equations: Theory, Technique, and Practice Summary

Differential Equations: Theory, Technique, and Practice by George Simmons

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