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This book addresses the need for mathematical techniques to be introduced early on in the undergraduate program. Topics that are unique to the undergraduate curriculum, i.e. series, complex analysis, variational calculus, and integral transforms, do overlap in the advanced undergraduate-graduate curriculum and need to be introduced early on in the undergraduate program at the appropriate level. Topical coverage includes functional analysis; vector analysis; general coordinates and tensors; determinants and matrices; linear algebra; infinite series; complex numbers and functions; complex integrals and series; ordinary differential equations; second-order differential equations and special functions; Bessel's equation and Bessel's functions; partial differential equations and special functions; other useful functions of mathematical physics; Fourier series; integral transforms; variational analysis; probability theory; and information theory.
The book equips students with the necessary mathematical skills that are required by a majority of the physics and engineering undergraduate programs, and it also establishes the background needed to understand and appreciate more advanced topics.
Preface. Acknowledgments. 1. Functional Analysis. 2. Vector Analysis. 3. Generalized Coordinates and Tensors. 4. Determinants and Matrices. 5. Linear Algebra. 6. Sequences and Series. 7. Complex Numbers and Functions. 8. Complex Analysis. 9. Ordinary Differential Equations. 10. Second-Order Differential Equations and Special Functions. 11. Bessel's Equation and Bessel Functions. 12. Partial Differential Equations and Separation Variables. 13. Fourier Series. 14. Fourier and Laplace Transforms. 15. Calculus of Variations. 16. Probability Theory and Distributions. 17. Information Theory. References. Index.
S. Selcuk Bayin, PhD, is Professor in the Department of Physics at the Middle East Technical University in Ankara, Turkey. He has over twenty years of academic experience on the use of mathematical methods in physics courses, and his current research focuses on general relativity and cosmology. Dr. Bayin is the author of Mathematical Methods in Science and Engineering, also published by Wiley.