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Introduction to Differential Equations written by
Jeffrey R. Chasnov .
This edition is based on four themes: methods of solution of initial-boundary value problems, properties and existence of solutions, applications of partial differential equations, and use of software to carry out computations and graphics.
The focus is on equations of diffusion processes and wave motion, and on Dirichlet and Neumann problems. Following an introductory chapter, we look at methods applied to these equations in bounded and unbounded media, and in one and several space dimensions. The topics are organized to make it easy to match problems in specific settings to methods for writing solutions. Methods include Fourier series and integrals, the use of characteristics, integral solutions, integral transforms, and special functions and eigenfunction expansions. Properties of solutions that are considered include existence and uniqueness issues, maximum and mean value principles, integral representations, and sensitivity of solutions to initial and boundary conditions.
In addition to standard material for an introductory course, topics include traveling-wave solutions of Burger
s equation, damped wave motion, heat and wave equations with forcing terms, a general treatment of eigenfunction expansions, a complete solution of the telegraph equation using the Fourier transform, the use of characteristics to solve Cauchy problems and vibrating string problems with moving ends, double Fourier series solutions, and the PoissonKirchhoff integral solution of the wave equation in two dimensions. There are also proofs of important theorems, including an existence theorem for a Dirichlet problem and a convergence theorem for Fourier series.
Finally, there is a section on the use of MAPLE™ to carry out computations and experiment with graphics. MATLAB @, MATHEMATICA ®, and other packages may also be used for these numerical aspects of partial differential equations.
Title: Introduction to Differential Equations
Edition:
Author(s): Jeffrey R. Chasnov
Publisher:
Series:
Year: 2021
Pages: 149
Type: PDF
Language: English
ISBN:
Country: US
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About Author :- The author Jeffrey R. Chasnov is a Professor of Mathematics at the Hong Kong University of Science and Technology, where he has been teaching since 1993. He is an expatriate American from New York and California, and earned his BA from UC Berkeley and PhD from Columbia University, with post-doctoral fellowships at NASA, Stanford, and Grenoble, France, and a sabbatical semester at Harvey Mudd College. He is the author of numerous research articles in fluid turbulence and mathematical biology, and has authored online textbooks and videos for his courses on differential equations, matrix algebra, mathematical biology and scientific computation. Before and after work, he enjoys family life, swimming and tennis, and takes great pleasure in his family’s annual camping and skiing vacations.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Matrix Algebra for Engineers by Jeffrey R Chasnov
• Download PDF Vector Calculus for Engineers by Jeffrey Chasnov
• Download PDF Introduction to Differential Equations by Jeffrey R. Chasnov
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Introduction to Differential Equations written by
Jeffrey R. Chasnov cover the following topics.
0. A short mathematical review
The trigonometric functions, The exponential function and the natural logarithm, Definition of the derivative, Differentiating a combination of functions (The sum or difference rule, The product rule, The quotient rule, The chain rule, Differentiating elementary functions (The power rule, Trigonometric functions, Exponential and natural logarithm functions, Definition of the integral, The fundamental theorem of calculus, Definite and indefinite integrals, Indefinite integrals of elementary functions, Substitution, Integration by parts, Taylor series, Functions of several variables, Complex numbers
1. Introduction to odes
The simplest type of differential equation
2. First-order odes
The Euler method, Separable equations, Linear equations, Applications (Compound interest, Chemical reactions, Terminal velocity, Escape velocity, RC circuit, The logistic equation)
3. Second-order odes, constant coefficients
The Euler method, The principle of superposition, The Wronskian, Homogeneous odes, Real, distinct roots
4. The Laplace transform
Definition and properties, Solution of initial value problems, Heaviside and Dirac delta functions (Heaviside function, Dirac delta function, Discontinuous or impulsive terms)
5. Series solutions
Ordinary points, Regular singular points: Cauchy-Euler equations (Real, distinct roots, Complex conjugate roots, Repeated roots)
6. Systems of equations
Matrices, determinants and the eigenvalue problem, Coupled first-order equations (Two distinct real eigenvalues, Complex conjugate eigenvalues, Repeated eigenvalues with one eigenvector, Normal modes)
7. Nonlinear differential equations
Fixed points and stability (One dimension, Two dimensions), One-dimensional bifurcations (Saddle-node bifurcation, Transcritical bifurcation, Supercritical pitchfork bifurcation, Subcritical pitchfork bifurcation, Application: a mathematical model of a fishery), Two-dimensional bifurcations (Supercritical Hopf bifurcation, Subcritical Hopf bifurcation)
8. Partial differential equations
Derivation of the diffusion equation, Derivation of the wave equation, Fourier series, Fourier cosine and sine series, Solution of the diffusion equation (Homogeneous boundary conditions, Inhomogeneous boundary conditions, Pipe with closed ends), Solution of the wave equation (Plucked string, Hammered string, General initial conditions), The Laplace equation (Dirichlet problem for a rectangle, Dirichlet problem for a circle), The Schrödinger equation (Heuristic derivation of the Schrödinger equation, The time-independent Schrödinger equation, Particle in a one-dimensional box, The simple harmonic oscillator, Particle in a three-dimensional box, The hydrogen atom)
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