This course discusses some of the analytical and numerical techniques used in solving engineering problems. Most of the topics in this course deal with problems in mathematical physics.

• Fourier Analysis
• Ordinary Differential Equations
• Partial Differential Equations
• Conformal Mapping
• Integral Equations
• Variational Techniques
• Finite Element Method
  • Solution of Laplace Equation
  • Example Code
• Numerical Solution of the Heat Equation
  • Talk in PDF Format
• Error Analysis in Science and Engineering
• Optimization using Simulated Annealing

Each topic has analytical and numerical parts. Almost all assignments will involve computer programming. But this course is not only about solving differential equations. One main objective is to understand the physics behind the equations.

• E. Kreyszig

  Advanced Engineering Mathematics

  John Wiley & Sons, Seventh Edition, 1993

• R. J. Schilling and S. L. Harris

  Applied Numerical Methods for Engineers

  Thomson, Singapore, 2000

• T. W. Koerner

  Fourier Analysis

  Cambridge University Press, 1988

• R. V. Churchill

  Fourier Series and Boundary Value Problems

  McGraw Hill, New York, 1941

• R. N. Bracewell

  The Fourier Transform and Its Applications

  McGraw Hill, New York, 1966

• W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery

  Numerical Recipes in C/FORTRAN

  Prentice Hall of India, New Delhi, 1994

• E. V. Krishnamurthy and S. K. Sen

  Numerical Algorithms

  Affiliated East West Press, New Delhi, 2001

• E. V. Krishnamurthy and S. K. Sen

  Programming in MATLAB

  Affiliated East West Press, New Delhi, 2003