Viser: Partial Differential Equations for Scientists and Engineers
Søgbar e-bog
Partial Differential Equations for Scientists and Engineers Vital Source e-bog
Stanley J. Farlow
(2012)
Dover Publications
199,00 kr.
Leveres umiddelbart efter køb
Partial Differential Equations for Scientists and Engineers
Stanley J. Farlow
(2003)
Sprog: Engelsk
Dover Publications, Incorporated
199,00 kr.
1 stk på lager
Hvor kan jeg afhente varen?Detaljer om varen
- Vital Source searchable e-book (Reflowable pages): 414 sider
- Udgiver: Dover Publications (Marts 2012)
- ISBN: 9780486134734
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations. This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.
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Bookshelf online: 5 år fra købsdato.
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Detaljer om varen
- Paperback: 414 sider
- Udgiver: Dover Publications, Incorporated (Marts 2003)
- ISBN: 9780486676203
This highly useful text for students and professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Suggestions for further reading. Solution guide available upon request. 1982 edition.
1. Introduction Lesson
1. Introduction to Partial Differential Equations2. Diffusion-Type Problems Lesson
2. Diffusion-Type Problems (Parabolic Equations) Lesson
3. Boundary Conditions for Diffusion-Type Problems Lesson
4. Derivation of the Heat Equation Lesson
5. Separation of Variables Lesson
6. Transforming Nonhomogeneous BCs into Homogeneous Ones Lesson
7. Solving More Complicated Problems by Separation of Variables Lesson
8. Transforming Hard Equations into Easier Ones Lesson
9. Solving Nonhomogeneous PDEs (Eigenfunction Expansions) Lesson
10. Integral Transforms (Sine and Cosine Transforms) Lesson
11. The Fourier Series and Transform Lesson
12. The Fourier Transform and its Application to PDEs Lesson
13. The Laplace Transform Lesson
14. Duhamel's Principle Lesson
15. The Convection Term u subscript x in Diffusion Problems3. Hyperbolic-Type Problems Lesson
16. The One Dimensional Wave Equation (Hyperbolic Equations) Lesson
17. The D'Alembert Solution of the Wave Equation Lesson
18. More on the D'Alembert Solution Lesson
19. Boundary Conditions Associated with the Wave Equation Lesson
20. The Finite Vibrating String (Standing Waves) Lesson
21. The Vibrating Beam (Fourth-Order PDE) Lesson
22. Dimensionless Problems Lesson
23. Classification of PDEs (Canonical Form of the Hyperbolic Equation) Lesson
24. The Wave Equation in Two and Three Dimensions (Free Space) Lesson
25. The Finite Fourier Transforms (Sine and Cosine Transforms) Lesson
26. Superposition (The Backbone of Linear Systems) Lesson
27. First-Order Equations (Method of Characteristics) Lesson
28. Nonlinear First-Order Equations (Conservation Equations) Lesson
29. Systems of PDEs Lesson
30. The Vibrating Drumhead (Wave Equation in Polar Coordinates)4. Elliptic-Type Problems Lesson
31. The Laplacian (an intuitive description) Lesson
32. General Nature of Boundary-Value Problems Lesson
33. Interior Dirichlet Problem for a Circle Lesson
34. The Dirichlet Problem in an Annulus Lesson
35. Laplace's Equation in Spherical Coordinates (Spherical Harmonics) Lesson
36. A Nonhomogeneous Dirichlet Problem (Green's Functions)5. Numerical and Approximate Methods Lesson
37. Numerical Solutions (Elliptic Problems) Lesson
38. An Explicit Finite-Difference Method Lesson
39. An Implicit Finite-Difference Method (Crank-Nicolson Method) Lesson
40. Analytic versus Numerical Solutions Lesson
41. Classification of PDEs (Parabolic and Elliptic Equations) Lesson
42. Monte Carlo Methods (An Introduction) Lesson
43. Monte Carlo Solutions of Partial Differential Equations) Lesson
44. Calculus of Variations (Euler-Lagrange Equations) Lesson
45. Variational Methods for Solving PDEs (Method of Ritz) Lesson
46. Perturbation method for Solving PDEs Lesson
47. Conformal-Mapping Solution of PDEs Answers to Selected ProblemsAppendix
1. Integral Transform TablesAppendix
2. PDE Crossword PuzzleAppendix
3. Laplacian in Different Coordinate SystemsAppendix
4. Types of Partial Differential Equations Index
1. Introduction to Partial Differential Equations2. Diffusion-Type Problems Lesson
2. Diffusion-Type Problems (Parabolic Equations) Lesson
3. Boundary Conditions for Diffusion-Type Problems Lesson
4. Derivation of the Heat Equation Lesson
5. Separation of Variables Lesson
6. Transforming Nonhomogeneous BCs into Homogeneous Ones Lesson
7. Solving More Complicated Problems by Separation of Variables Lesson
8. Transforming Hard Equations into Easier Ones Lesson
9. Solving Nonhomogeneous PDEs (Eigenfunction Expansions) Lesson
10. Integral Transforms (Sine and Cosine Transforms) Lesson
11. The Fourier Series and Transform Lesson
12. The Fourier Transform and its Application to PDEs Lesson
13. The Laplace Transform Lesson
14. Duhamel's Principle Lesson
15. The Convection Term u subscript x in Diffusion Problems3. Hyperbolic-Type Problems Lesson
16. The One Dimensional Wave Equation (Hyperbolic Equations) Lesson
17. The D'Alembert Solution of the Wave Equation Lesson
18. More on the D'Alembert Solution Lesson
19. Boundary Conditions Associated with the Wave Equation Lesson
20. The Finite Vibrating String (Standing Waves) Lesson
21. The Vibrating Beam (Fourth-Order PDE) Lesson
22. Dimensionless Problems Lesson
23. Classification of PDEs (Canonical Form of the Hyperbolic Equation) Lesson
24. The Wave Equation in Two and Three Dimensions (Free Space) Lesson
25. The Finite Fourier Transforms (Sine and Cosine Transforms) Lesson
26. Superposition (The Backbone of Linear Systems) Lesson
27. First-Order Equations (Method of Characteristics) Lesson
28. Nonlinear First-Order Equations (Conservation Equations) Lesson
29. Systems of PDEs Lesson
30. The Vibrating Drumhead (Wave Equation in Polar Coordinates)4. Elliptic-Type Problems Lesson
31. The Laplacian (an intuitive description) Lesson
32. General Nature of Boundary-Value Problems Lesson
33. Interior Dirichlet Problem for a Circle Lesson
34. The Dirichlet Problem in an Annulus Lesson
35. Laplace's Equation in Spherical Coordinates (Spherical Harmonics) Lesson
36. A Nonhomogeneous Dirichlet Problem (Green's Functions)5. Numerical and Approximate Methods Lesson
37. Numerical Solutions (Elliptic Problems) Lesson
38. An Explicit Finite-Difference Method Lesson
39. An Implicit Finite-Difference Method (Crank-Nicolson Method) Lesson
40. Analytic versus Numerical Solutions Lesson
41. Classification of PDEs (Parabolic and Elliptic Equations) Lesson
42. Monte Carlo Methods (An Introduction) Lesson
43. Monte Carlo Solutions of Partial Differential Equations) Lesson
44. Calculus of Variations (Euler-Lagrange Equations) Lesson
45. Variational Methods for Solving PDEs (Method of Ritz) Lesson
46. Perturbation method for Solving PDEs Lesson
47. Conformal-Mapping Solution of PDEs Answers to Selected ProblemsAppendix
1. Integral Transform TablesAppendix
2. PDE Crossword PuzzleAppendix
3. Laplacian in Different Coordinate SystemsAppendix
4. Types of Partial Differential Equations Index
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