Applied Mathematics

This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I r...

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Main Author: Mahan, Gerald D.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer US 2002, 2002
Edition:1st ed. 2002
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Applied Mathematics  |h Elektronische Ressource  |c by Gerald D. Mahan 
250 |a 1st ed. 2002 
260 |a New York, NY  |b Springer US  |c 2002, 2002 
300 |a XI, 368 p  |b online resource 
505 0 |a 1. Determinants -- 1.1. Cramer’s Rule -- 1.2. Gaussian Elimination -- 1.3. Special Determinants -- 2. Matrices -- 2.1. Several Theorems -- 2.2. Linear Equations -- 2.3. Inverse of a Matrix -- 2.4. Eigenvalues and Eigenvectors -- 2.5. Unitary Transformations -- 2.6. Hon-Hermitian Matrices -- 2.7. A Special Matrix -- 2.8. Gram-Schmidt -- 2.9. Chains -- 3. Group Theory -- 3.1. Basic Properties of Groups -- 3.2. Group Representations -- 3.3. Characters -- 3.4. Direct Product Groups -- 3.5. Basis Functions -- 3.6. Angular Momentum -- 3.7. Products of Representations -- 3.8. Quantum Mechanics -- 3.9. Double Groups -- 4. Complex Variables -- 4.1. Introduction -- 4.2. Analytic Functions -- 4.3. Multivalued Functions -- 4.4. Contour Integrals -- 4.5. Meromorphic Functions -- 4.6. Higher Poles -- 4.7. Integrals Involving Branch Cuts -- 4.8. Approximate Evaluation of Integrals -- 5. Series -- 5.1. Taylor Series -- 5.2. Convergence -- 5.3. Laurent Series -- 5.4. Meromorphic Functions --  
505 0 |a 5.5. Asymptotic Series -- 5.6. Summing Series -- 5.7. Padé Approximants -- 6. Conformal Mapping -- 6.1. Laplace’s Equation -- 6.2. Mapping -- 6.3. Examples -- 6.4. Schwartz-Christoffel Transformations -- 6.5. van der Pauw -- 7. Markov Averaging -- 7.1. Random Walk -- 7.2. Speckle -- 7.3. Inhomogeneous Broadening -- 8. Fourier Transforms -- 8.1. Fourier Transforms -- 8.2. Laplace Transforms -- 8.3. Wavelets -- 9. Equations of Physics -- 9.1. Boundary and Initial Conditions -- 9.2. Boltzmann Equation -- 9.3. Solving Differential Equations -- 9.4. Elliptic Integrals -- 10. One Dimension -- 10.1. Introduction -- 10.2. Diffusion Equation -- 10.3. Wave Equation -- 11. Two Dimensions -- 11.1. Rectangular Coordinates -- 11.2. Polar Coordinates -- 12. Three Dimensions -- 12.1. Cartesian Coordinates -- 12.2. Cylindrical Coordinates -- 12.3. Spherical Coordinates -- 12.4. Problems Inside a Sphere -- 12.5. Vector Wave Equation -- 13. Odds and Ends -- 13.1. Hypergeometric Functions --  
505 0 |a 13.2. Orthogonal Polynomials -- 13.3. Sturm-Liouville -- 13.4. Green’s Functions -- 13.5. Singular Integral Equations 
653 |a Applied mathematics 
653 |a Engineering 
653 |a Characterization and Evaluation of Materials 
653 |a Engineering mathematics 
653 |a Materials science 
653 |a Applications of Mathematics 
653 |a Mathematical physics 
653 |a Theoretical, Mathematical and Computational Physics 
653 |a Engineering, general 
710 2 |a SpringerLink (Online service) 
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082 0 |a 519 
520 |a This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I realized that my own research students did not learn much in this course at my university. Then I learned that the available textbooks were too introduc­ tory. While teaching this course without an assigned text, I wrote up my lecture notes and gave them to the students. This textbook is a result of that endeavor. When I took this course many, many, years ago, the primary references were the two volumes of P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953). The present text returns the contents to a similar level, although the syllabus is quite different than given in this venerable pair of books