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Advanced topics in applied mathematics : for engineering and the physical sciences

Author: Sudhakar Nair
Publisher: New York : Cambridge University Press, 2011, ©2011.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"This book is ideal for engineering, physical science, and applied mathematics students and professionals who want to enhance their mathematical knowledge. Advanced Topics in Applied Mathematics covers four essential applied mathematics topics: Green's functions, Integral equations, Fourier transforms, and Laplace transforms. Also included is a useful discussion of topics such as the Wiener-Hopf method, Finite  Read more...
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Document Type: Book
All Authors / Contributors: Sudhakar Nair
ISBN: 9781107006201 1107006201
OCLC Number: 690090214
Description: x, 222 pages : illustrations ; 24 cm
Contents: Machine generated contents note: 1. Green's Functions --
1.1. Heaviside Step Function --
1.2. Dirac Delta Function --
1.2.1. Macaulay Brackets --
1.2.2. Higher Dimensions --
1.2.3. Test Functions, Linear Functionals, and Distributions --
1.2.4. Examples: Delta Function --
1.3. Linear Differential Operators --
1.3.1. Example: Boundary Conditions --
1.4. Inner Product and Norm --
1.5. Green's Operator and Green's Function --
1.5.1. Examples: Direct Integrations --
1.6. Adjoint Operators --
1.6.1. Example: Adjoint Operator --
1.7. Green's Function and Adjoint Green's Function --
1.8. Green's Function for L --
1.9. Sturm-Liouville Operator --
1.9.1. Method of Variable Constants --
1.9.2. Example: Self-Adjoint Problem --
1.9.3. Example: Non-Self-Adjoint Problem --
1.10. Eigenfunctions and Green's Function --
1.10.1. Example: Eigenfunctions --
1.11. Higher-Dimensional Operators --
1.11.1. Example: Steady-State Heat Conduction in a Plate --
1.11.2. Example: Poisson's Equation in a Rectangle. 1.11.3. Steady-State Waves and the Helmholtz Equation --
1.12. Method of Images --
1.13. Complex Variables and the Laplace Equation --
1.13.1. Nonhomogeneous Boundary Conditions --
1.13.2. Example: Laplace Equation in a Semi-infinite Region --
1.13.3. Example: Laplace Equation in a Unit Circle --
1.14. Generalized Green's Function --
1.14.1. Examples: Generalized Green's Functions --
1.14.2. A Recipe for Generalized Green's Function --
1.15. Non-Self-Adjoint Operator --
1.16. More on Green's Functions --
2. Integral Equations --
2.1. Classification --
2.2. Integral Equation from Differential Equations --
2.3. Example: Converting Differential Equation --
2.4. Separable Kernel --
2.5. Eigenvalue Problem --
2.5.1. Example: Eigenvalues --
2.5.2. Nonhomogeneous Equation with a Parameter --
2.6. Hilbert-Schmidt Theory --
2.7. Iterations, Neumann Series, and Resolvent Kernel --
2.7.1. Example: Neumann Series --
2.7.2. Example: Direct Calculation of the Resolvent Kernel --
2.8. Quadratic Forms --
2.9. Expansion Theorems for Symmetric Kernels. 2.10. Eigenfunctions by Iteration --
2.11. Bound Relations --
2.12. Approximate Solution --
2.12.1. Approximate Kernel --
2.12.2. Approximate Solution --
2.12.3. Numerical Solution --
2.13. Volterra Equation --
2.13.1. Example: Volterra Equation --
2.14. Equations of the First Kind --
2.15. Dual Integral Equations --
2.16. Singular Integral Equations --
2.16.1. Examples: Singular Equations --
2.17. Abel Integral Equation --
2.18. Boundary Element Method --
2.18.1. Example: Laplace Operator --
2.19. Proper Orthogonal Decomposition --
3. Fourier Transforms --
3.1. Fourier Series --
3.2. Fourier Transform --
3.2.2. Riemann-Lebesgue Lemma --
3.2.2. Localization Lemma --
3.3. Fourier Integral Theorem --
3.4. Fourier Cosine and Sine Transforms --
3.5. Properties of Fourier Transforms --
3.5.1. Derivatives of F --
3.5.2. Scaling --
3.5.3. Phase Change --
3.5.4. Shift --
3.5.5. Derivatives of & fnof; --
3.6. Properties of Trigonometric Transforms --
3.6.1. Derivatives of Fc and Fs --
3.6.2. Scaling --
3.6.3. Derivatives of & fnof. 4.2. Properties of the Laplace Transform --
4.2.1. Linearity --
4.2.2. Scaling --
4.2.3. Shifting --
4.2.4. Phase Factor --
4.2.5. Derivative --
4.2.6. Integral --
4.2.7. Power Factors --
4.3. Transforms of Elementary Functions --
4.4. Convolution Integral --
4.5. Inversion Using Elementary Properties --
4.6. Inversion Using the Residue Theorem --
4.7. Inversion Requiring Branch Cuts --
4.8. Theorems of Tauber --
4.8.1. Behavior of f (t) as t ₂!0 --
4.8.2. Behavior of f (t) as t ₂! --
4.9. Applications of Laplace Transform --
4.9.1. Ordinary Differential Equations --
4.9.2. Boundary Value Problems --
4.9.3. Partial Differential Equations --
4.9.4. Integral Equations --
4.9.5. Cagniard-De Hoop Method --
4.10. Sequences and the Z-Transform --
4.10.1. Difference Equations --
4.10.2. First-Order Difference Equation --
4.10.3. Second-Order Difference Equation --
4.10.4. Brilluoin Approximation for Crystal Acoustics.
Responsibility: Sudhakar Nair.

Abstract:

This book covers four essential applied mathematics topics: Green's functions, integral equations, Fourier transforms and Laplace transforms.  Read more...

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