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Differential Equations with Boundary Value Problems  무료배송

 
지은이 : John Polking, Al Boggess, and David Arnold
출판사 : Prentice Hall
판수 : 2nd
페이지수 : 768
ISBN : 0131862367
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 176,000원 ( 무료배송 )
적립금 : 5,280 Point
     

 

Combining traditional material with a modern systems approach, this handbook provides a thorough introduction to differential equations, tempering its classic "pure math" approach with more practical applied aspects. Features up-to-date coverage of key topics such as first order equations, matrix algebra, systems, and phase plane portraits. Illustrates complex concepts through extensive detailed figures. Focuses on interpreting and solving problems through optional technology projects. For anyone interested in learning more about differential equations.


Chapter 1: Introduction to Differential Equations
Differential Equation Models. The Derivative. Integration.
Chapter 2:  First-Order Equations
Differential Equations and Solutions. Solutions to Separable Equations. Models of Motion. Linear Equations.
Mixing Problems. Exact Differential Equations. Existence and Uniqueness of Solutions. Dependence of Solutions on Initial Conditions. Autonomous Equations and Stability.
Project 2.10 The Daredevil Skydiver.

Chapter 3: Modeling and Applications
Modeling Population Growth. Models and the Real World. Personal Finance. Electrical Circuits. Project 3.5 The Spruce Budworm. Project 3.6 Social Security, Now or Later.
Chapter 4: Second-Order Equations
Definitions and Examples. Second-Order Equations and Systems. Linear, Homogeneous Equations with Constant Coefficients. Harmonic Motion. Inhomogeneous Equations; the Method of Undetermined Coefficients. Variation of Parameters. Forced Harmonic Motion. Project 4.8 Nonlinear Oscillators.
Chapter 5: The Laplace Transform
The Definition of the Laplace Transform. Basic Properties of the Laplace Transform 241. The Inverse Laplace Transform
Using the Laplace Transform to Solve Differential Equations. Discontinuous Forcing Terms. The Delta Function. Convolutions. Summary. Project 5.9 Forced Harmonic Oscillators.
Chapter 6: Numerical Methods
Euler뭩 Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale.
Project 6.6 Numerical Error Comparison.
Chapter 7: Matrix Algebra
Vectors and Matrices. Systems of Linear Equations with Two or Three Variables. Solving Systems of Equations. Homogeneous and Inhomogeneous Systems. Bases of a subspace. Square Matrices. Determinants.
Chapter 8:  An Introduction to Systems
Definitions and Examples. Geometric Interpretation of Solutions. Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8.6 Long-Term Behavior of Solutions.
Chapter 9:  Linear Systems with Constant Coefficients
Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules.
Chapter 10: Nonlinear Systems
The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator뾒rey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species.
Chapter 11: Series Solutions to Differential Equations
Review of Power Series. Series Solutions Near Ordinary Points. Legendre뭩 Equation. Types of Singular Points뺼uler뭩 Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points the General Case. Bessel뭩 Equation and Bessel Functions
Chapter 12: Fourier Series
Computation of Fourier Series. Convergence of Fourier Series. Fourier Cosine and Sine Series. The Complex Form of a Fourier Series. The Discrete Fourier Transform and the FFT.
Chapter 13: Partial Differential Equations
Derivation of the Heat Equation. Separation of Variables for the Heat Equation. The Wave Equation. Laplace뭩 Equation. Laplace뭩 Equation on a Disk. Sturm Liouville Problems. Orthogonality and Generalized Fourier Series. Temperature in a Ball뻃egendre Polynomials. Time Dependent PDEs in Higher Dimension. Domains with Circular Symmetry뺹essel Functions.
Appendix: Complex Numbers and Matrices
Answers to Odd-Numbered Problems
Index
"I used this book for a course in ODE's. The edition that was available for purchase at our school's bookstore also included a book by the authors for using MatLab for solving ODE's, The combination of the two were great. The book is logically structured and generally easy to read. The authors use many examples from a variety of fields. The MatLab book was a phenomenal help: it's the best intro to MatLab that I've found, and was very useful in helping to solve problems. My only beef with the book is that since this is a first edition, there are several errors in the odd numbered solutions at the end of the book, which caused many sleepless nights."


"I bought this book because it was a requirement to have for the class. Could rarely ever reference it or rely on it for understanding. I'm not sure what it is in particular but I wasn't a big fan of the presentation. I in all honestly used it primarily for assigned problems and that's it. good thing is as always, price on amazon beats the bookstore price."
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