### Scientific Computation (MATH-7150)

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.

Learning Outcomes

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.

Prerequisites: Nill

Contents

1. Vector and matrix operation, Building exploratory environments
2. Floating point arithmetic, Error analysis
3. The interpolating polynomial, Piecewise linear interpolation
4. Piecewise cubic Hermite interpolation
5. Different degree spline interpolations
6. Shape-preserving interpolants, Bisection method
7. Newton’s method, Second method
9. Quasi-Newton’s method
11. Least squares data fitting, Models and data curve fitting
12.  Norms, The QR factorization
13. Pseudo inverse, Eigenvalues and singular values
14.  Symmetric and Hermitian matrices
15.  Eigenvalue and singular value decompositions
16.  Eigenvalue sensitivity and accuracy
17.  Singular sensitivity and accuracy
18.  Principle components
19. Parallel computing, Matrix-matrix product

Recommended Books

1. Moler, D. (2004). Numerical computing with Matlab. Philadelphia: Society for Industrial and Applied Mathematics.
2. Lindﬁeld, G. R. and Penny, J. E. T. (2012).  Numerical methods using Matlab (3rd ed.). Massachusetts: Academic Press.

Suggested Books

1. Burdern, R. L. and Faires, J. D. (2004). Numerical analysis (8th ed.). New York: Brooks Cole.
2. Hoffman, J.  D. (1992). Numerical methods for engineers and scientists (2nd ed.). New York: Marcel Dekker, Inc.
3. Ramin, S. E. (2017). Numerical methods for engineers and scientists using Matlab. Florida: CRC Press
4. 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.

ASSESSMENT CRITERIA

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