Author	Mahan, Gerald Dennis. author
Title	Applied Mathematics [electronic resource] / by Gerald Dennis Mahan
Imprint	Boston, MA : Springer US : Imprint: Springer, 2002
Connect to	http://dx.doi.org/10.1007/978-1-4615-1315-5
Descript	XI, 368 p. online resource

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 introducยญ 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

1. Determinants -- 1.1. Cramerโs 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 -- 5.5. Asymptotic Series -- 5.6. Summing Series -- 5.7. Padรฉ Approximants -- 6. Conformal Mapping -- 6.1. Laplaceโs 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 -- 13.2. Orthogonal Polynomials -- 13.3. Sturm-Liouville -- 13.4. Greenโs Functions -- 13.5. Singular Integral Equations

1. Mathematics
2. Applied mathematics
3. Engineering mathematics
4. Physics
5. Engineering
6. Materials science
7. Mathematics
8. Applications of Mathematics
9. Theoretical
10. Mathematical and Computational Physics
11. Engineering
12. general
13. Characterization and Evaluation of Materials