Applied partial differential equations / J. David Logan.
By: Logan, J. David.
Series: Undergraduate texts in mathematics.Publisher: Switzerland : Springer, 2015Edition: 3rd ed.Description: x, 289 p. : illustrations ; 24 cm.ISBN: 9783319124926.Subject(s): Partial Differential EquationsDDC classification: 515.353Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

515.353 L831 (Browse shelf)  Available  136478 
Includes bibliographical references and index.
1: The Physical Origins of Partial Differential Equations 
1.1 PDE Models 
1.2 Conservation Laws 
1.3 Diffusion 
1.4 Diffusion and Randomness 
1.5 Vibrations and Acoustics 
1.6 Quantum Mechanics@* 
1.7 Heat Conduction in Higher Dimensions 
1.8 Laplace's Equation 
1.9 Classification of PDEs 
2. Partial Differential Equations on Unbounded Domains 
2.1 Cauchy Problem for the Heat Equation 
2.2 Cauchy Problem for the Wave Equation 
2.3 WellPosed Problems 
2.4 SemiInfinite Domains 
2.5 Sources and Duhamel's Principle 
2.6 Laplace Transforms 
2.7 Fourier Transforms 
3. Orthogonal Expansions 
3.1 The Fourier Method 
3.2 Orthogonal Expansions 
3.3 Classical Fourier Series.4. Partial Differential Equations on Bounded Domains 
4.1 Overview of Separation of Variables 
4.2 SturmLiouville Problems 
4.3 Generalization and Singular Problems 
4.4 Laplace's Equation 
4.5 Cooling of a Sphere 
4.6 Diffusion inb a Disk 
4.7 Sources on Bounded Domains 
4.8 Poisson's Equation@*.5. Applications in the Life Sciences.5.1 AgeStructured Models 
5.2 Traveling Waves Fronts 
5.3 Equilibria and Stability 
6. Numerical computation of solutions 
6.1 Finite Difference Approximation 
6.2 Explicit Scheme for the Heat Equation 
6.3 Laplace's Equation 
6.4 Implicit Scheme for the Heat Equation 
Appendix A. Differential Equations 
References 
Index.
This text presents the standard material usually covered in a onesemester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science.
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