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LEADER 06952cam 2200529 i 4500

001 ocn690090214;

003 OCoLC;

005 20141212073928.0;

008 101210t20112011nyua b 001 0 eng ;

010 a| 2010052380;

020 a| 9781107006201 (hardback);

020 a| 1107006201 (hardback);

029 1 a| AU@b| 000046405605;

035 a| (Sirsi) o690090214;

035 a| (OCoLC)690090214;

042 a| pcc;

049 a| EREE;

050 00 a| TA347.D45b| N35 2011;

082 00 a| 620.001/512| 22;

084 a| TEC0090002| bisacsh;

100 1 a| Nair, Sudhakar,d| 1944-e| author.=| ^A1060588;

245 10 a| Advanced topics in applied mathematics :b| for engineering and the physical sciences /c| Sudhakar Nair.;

300 a| x, 222 pages :b| illustrations ;c| 24 cm;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

504 a| Includes bibliographical references and indexes.;

520 a| "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 Hilbert transforms, Cagniard-De Hoop method, and the proper orthogonal decomposition. This book reflects Sudhakar Nair's long classroom experience and includes numerous examples of differential and integral equations from engineering and physics to illustrate the solution procedures. The text includes exercise sets at the end of each chapter and a solutions manual, which is available for instructors"--c| Provided by publisher.;

505 00 g| Machine generated contents note:g| 1.t| Green's Functions --g| 1.1.t| Heaviside Step Function --g| 1.2.t| Dirac Delta Function --g| 1.2.1.t| Macaulay Brackets --g| 1.2.2.t| Higher Dimensions --g| 1.2.3.t| Test Functions, Linear Functionals, and Distributions --g| 1.2.4.t| Examples: Delta Function --g| 1.3.t| Linear Differential Operators --g| 1.3.1.t| Example: Boundary Conditions --g| 1.4.t| Inner Product and Norm --g| 1.5.t| Green's Operator and Green's Function --g| 1.5.1.t| Examples: Direct Integrations --g| 1.6.t| Adjoint Operators --g| 1.6.1.t| Example: Adjoint Operator --g| 1.7.t| Green's Function and Adjoint Green's Function --g| 1.8.t| Green's Function for L --g| 1.9.t| Sturm-Liouville Operator --g| 1.9.1.t| Method of Variable Constants --g| 1.9.2.t| Example: Self-Adjoint Problem --g| 1.9.3.t| Example: Non-Self-Adjoint Problem --g| 1.10.t| Eigenfunctions and Green's Function --g| 1.10.1.t| Example: Eigenfunctions --g| 1.11.t| Higher-Dimensional Operators --g| 1.11.1.t| Example: Steady-State Heat Conduction in a Plate --g| 1.11.2.t| Example: Poisson's Equation in a Rectangle;

505 00 g| 1.11.3.t| Steady-State Waves and the Helmholtz Equation --g| 1.12.t| Method of Images --g| 1.13.t| Complex Variables and the Laplace Equation --g| 1.13.1.t| Nonhomogeneous Boundary Conditions --g| 1.13.2.t| Example: Laplace Equation in a Semi-infinite Region --g| 1.13.3.t| Example: Laplace Equation in a Unit Circle --g| 1.14.t| Generalized Green's Function --g| 1.14.1.t| Examples: Generalized Green's Functions --g| 1.14.2.t| A Recipe for Generalized Green's Function --g| 1.15.t| Non-Self-Adjoint Operator --g| 1.16.t| More on Green's Functions --g| 2.t| Integral Equations --g| 2.1.t| Classification --g| 2.2.t| Integral Equation from Differential Equations --g| 2.3.t| Example: Converting Differential Equation --g| 2.4.t| Separable Kernel --g| 2.5.t| Eigenvalue Problem --g| 2.5.1.t| Example: Eigenvalues --g| 2.5.2.t| Nonhomogeneous Equation with a Parameter --g| 2.6.t| Hilbert-Schmidt Theory --g| 2.7.t| Iterations, Neumann Series, and Resolvent Kernel --g| 2.7.1.t| Example: Neumann Series --g| 2.7.2.t| Example: Direct Calculation of the Resolvent Kernel --g| 2.8.t| Quadratic Forms --g| 2.9.t| Expansion Theorems for Symmetric Kernels;

505 00 g| 2.10.t| Eigenfunctions by Iteration --g| 2.11.t| Bound Relations --g| 2.12.t| Approximate Solution --g| 2.12.1.t| Approximate Kernel --g| 2.12.2.t| Approximate Solution --g| 2.12.3.t| Numerical Solution --g| 2.13.t| Volterra Equation --g| 2.13.1.t| Example: Volterra Equation --g| 2.14.t| Equations of the First Kind --g| 2.15.t| Dual Integral Equations --g| 2.16.t| Singular Integral Equations --g| 2.16.1.t| Examples: Singular Equations --g| 2.17.t| Abel Integral Equation --g| 2.18.t| Boundary Element Method --g| 2.18.1.t| Example: Laplace Operator --g| 2.19.t| Proper Orthogonal Decomposition --g| 3.t| Fourier Transforms --g| 3.1.t| Fourier Series --g| 3.2.t| Fourier Transform --g| 3.2.2.t| Riemann-Lebesgue Lemma --g| 3.2.2.t| Localization Lemma --g| 3.3.t| Fourier Integral Theorem --g| 3.4.t| Fourier Cosine and Sine Transforms --g| 3.5.t| Properties of Fourier Transforms --g| 3.5.1.t| Derivatives of F --g| 3.5.2.t| Scaling --g| 3.5.3.t| Phase Change --g| 3.5.4.t| Shift --g| 3.5.5.t| Derivatives of &fnof; --g| 3.6.t| Properties of Trigonometric Transforms --g| 3.6.1.t| Derivatives of Fc and Fs --g| 3.6.2.t| Scaling --g| 3.6.3.t| Derivatives of &fnof;;

505 00 g| 4.2.t| Properties of the Laplace Transform --g| 4.2.1.t| Linearity --g| 4.2.2.t| Scaling --g| 4.2.3.t| Shifting --g| 4.2.4.t| Phase Factor --g| 4.2.5.t| Derivative --g| 4.2.6.t| Integral --g| 4.2.7.t| Power Factors --g| 4.3.t| Transforms of Elementary Functions --g| 4.4.t| Convolution Integral --g| 4.5.t| Inversion Using Elementary Properties --g| 4.6.t| Inversion Using the Residue Theorem --g| 4.7.t| Inversion Requiring Branch Cuts --g| 4.8.t| Theorems of Tauber --g| 4.8.1.t| Behavior of &fnof;(t) as t → 0 --g| 4.8.2.t| Behavior of &fnof;(t) as t → ∞ --g| 4.9.t| Applications of Laplace Transform --g| 4.9.1.t| Ordinary Differential Equations --g| 4.9.2.t| Boundary Value Problems --g| 4.9.3.t| Partial Differential Equations --g| 4.9.4.t| Integral Equations --g| 4.9.5.t| Cagniard-De Hoop Method --g| 4.10.t| Sequences and the Z-Transform --g| 4.10.1.t| Difference Equations --g| 4.10.2.t| First-Order Difference Equation --g| 4.10.3.t| Second-Order Difference Equation --g| 4.10.4.t| Brilluoin Approximation for Crystal Acoustics.;

650 0 a| Differential equations.=| ^A15524;

650 0 a| Engineering mathematics.=| ^A21880;

650 0 a| Mathematical physics.=| ^A15920;

949 a| TA347.D45 N35 2011h| JOYNER48o| jmpli| 30372015794859;

938 a| Baker and Taylorb| BTCPn| BK0009453437;

938 a| YBP Library Servicesb| YANKn| 3587402;

938 a| Coutts Information Servicesb| COUTn| 15029931;

938 a| Ingramb| INGRn| 9781107006201;

938 a| Midwest Library Servicesb| MWSTn| 02482322011;

994 a| C0b| ERE;

596 a| 1;

998 a| 2614378;

999 a| TA347.D45 N35 2011w| LCc| 1i| 30372015794859d| 10/22/2014e| 11/15/2011f| 12/6/2012g| 1l| JGESm| JOYNERq| 1r| Ys| Yt| JGESBKu| 11/10/2011x| BOOKz| JSTACKSo| .STAFF. jmpl;

Advanced topics in applied mathematics : for engineering and the physical sciences / Sudhakar Nair.

Author/creator	Nair, Sudhakar, 1944- author.
Format	Book
Publication Info	New York : Cambridge University Press, 2011, ©2011.
Description	x, 222 pages : illustrations ; 24 cm
Subjects	Differential equations. Engineering mathematics. Mathematical physics.

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
Contents	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
Contents	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;
Contents	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 &fnof;(t) as t → 0 -- 4.8.2. Behavior of &fnof;(t) as t → ∞ -- 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.
Abstract	"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 Hilbert transforms, Cagniard-De Hoop method, and the proper orthogonal decomposition. This book reflects Sudhakar Nair's long classroom experience and includes numerous examples of differential and integral equations from engineering and physics to illustrate the solution procedures. The text includes exercise sets at the end of each chapter and a solutions manual, which is available for instructors"-- Provided by publisher.
Bibliography note	Includes bibliographical references and indexes.
LCCN	2010052380
ISBN	9781107006201 (hardback)
ISBN	1107006201 (hardback)

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Advanced topics in applied mathematics : for engineering and the physical sciences / Sudhakar Nair.

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