A First Course in Applied Mathematics

For courses in Engineering Mathematics and for all entering graduate students in applied fields needing a math review. Unique in both content and approach, this is the first text at this level to give a unified treatment of mathematical analysis and its applications to physical and modeling problems. It covers both modern and classical topics and features a wide range of significant applications.

Review of Calculus and ODE. 1. Sets, Numbers, Functions, R, C, Rn. 2. Linear Algebra. 3. Limits, Sequences, Series, Uniform Convergence Examples: Fractals. 4. Differentiation (Inverse, Implicit Functions, Divergence, Gradient). 5. Integration (Riemann, Gauss) and Integral Equations. 6. Classical Mechanics. 7. Ordinary Differential Equations. 8. Approximation and Numerical Methods. 9. Fourier Series and Orthogonal Series, Fast-Fourier Transform and Wavelets. 10. Sturm-Liouville Theory with Special Functions. 11. Integral Transforms. 12. Mathematical Models. 13. Partial Differential Equations. 14. Function Theory. 15. Probability Theory and Statistical Mechanics. 16. Image Processing.