The main goal of this course is to learn how to solve mathematical problems that require computational power. MATLAB/Mathematica will be the preferred platform for pursuing this goal. No prior experience with MATLAB is required. The labs are designed to introduce the student to MATLAB and how it can be used in solving mathematical problems.
At the end of this course the student should be able to: (1) Decide when and how much to rely on a computer in the process of solving a mathematical problem. (2) Develop the necessary code, test the code and analyze the outcome of the code. (3) Use the computer output to present the solution to the original problem and gain further insight in the problem and its solution.
- Vector and matrix operation, Building exploratory environments
- Floating point arithmetic, Error analysis
- The interpolating polynomial, Piecewise linear interpolation
- Piecewise cubic Hermite interpolation
- Different degree spline interpolations
- Shape-preserving interpolants, Bisection method
- Newton’s method, Second method
- Inverse quadratic interpolation
- Quasi-Newton’s method
- Basic quadrature rules, Adaptive quadrature,
- Least squares data fitting, Models and data curve fitting
- Norms, The QR factorization
- Pseudo inverse, Eigenvalues and singular values
- Symmetric and Hermitian matrices
- Eigenvalue and singular value decompositions
- Eigenvalue sensitivity and accuracy
- Singular sensitivity and accuracy
- Principle components
- Parallel computing, Matrix-matrix product
- Moler, D. (2004). Numerical computing with Matlab. Philadelphia: Society for Industrial and Applied Mathematics.
- Lindﬁeld, G. R. and Penny, J. E. T. (2012). Numerical methods using Matlab (3rd ed.). Massachusetts: Academic Press.
- Burdern, R. L. and Faires, J. D. (2004). Numerical analysis (8th ed.). New York: Brooks Cole.
- Hoffman, J. D. (1992). Numerical methods for engineers and scientists (2nd ed.). New York: Marcel Dekker, Inc.
- Ramin, S. E. (2017). Numerical methods for engineers and scientists using Matlab. Florida: CRC Press
- Recent research articles.
RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS
For your final project you are to demonstrate your ability to use the documentation for Matlab and/or octave to learn how to apply a package not covered in class, or to apply features of a package not covered in class.
Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04)
Mid-Term Exam: 30
Final-Term Exam: 50
Key Dates and Time of Class Meeting
Monday--Tuesday 3:30 pm-5: 00 pm (MPhil-II (SS))
Commencement of Classes 15-03-2021
Mid Term Examination 17-05-2021
Final Term Examination 12-07-2021
Result Decleration 27-07-2021