Applied Numerical Methods

ABOUT THE COURSE:Objective: - To approximately solve problems of algebra and calculus, using repetitive calculations, implemented in a computerLearning Outcome: At the end of the course the students should be able to - write the algorithms for numerical solution of basic problems of algebra and calculus, such as solution of algebraic and differential equations, optimization using gradient descent, prediction using regression, - implement the above algorithms in a computer writing their own programs from scratch, - write the limitations of the above algorithms, and - solve complex problems combining multiple algorithms.INTENDED AUDIENCE: 3rd, 4th year UG students and PG students in any branch of engineeringPREREQUISITES: Undergraduate engineering mathematics Knowledge of a programming language (preferable)INDUSTRY SUPPORT: BARC, DRDO, GE, ANSYS, CSIR laboratories

Week 1: Course introduction, algorithm development, root finding, role/examples of numerical methods in practical problem solvingWeek 2:Minimalistic introduction to computer programmingWeek 3:System of linear/non-linear EquationsWeek 4:Eigenvalue problemWeek 5: Interpolation, finite difference, numerical differentiationWeek 6: Numerical integration, Ordinary differential equationsWeek 7:Ordinary differential equationsWeek 8:Partial differential equationsWeek 9: Case studies: modeling, nondimensionalization, solution, validationWeek 10:Regression and related techniquesWeek 11:Optimization methods, gradient descentWeek 12:Artificial neural network