This course is designed to teach students about basics of scientific computing for solving problems which are generated by data using interpolation and approximation techniques and learn how to match numerical method to mathematical properties.

*Learning Outcomes*

This course gives the students the knowledge of problem classes, basic mathematical and numerical concepts and software for solution of engineering and scientific problems formulated as using data sets. After successful completion, students should be able to design, implement and use interpolations for computer solution of scientific problems involving problems generated by set of data.

*Prerequisites: Nill*

*Contents*

- Basic concepts of Euclidean geometry.
- Scalar and vector functions.
- Barycentric coordinates.
- Convex hull.
- Matrices of affine maps.
- Translation, rotation, scaling, reflection and shear.
- Curve fitting, least squares line fitting, least squares power fit.
- Data linearization method for exponential functions, nonlinear least-squares method for exponential functions, transformations for data linearization.
- linear least squares, Polynomial fitting.
- Basic concepts of interpolation, Lagrange’s method, error terms and error bounds of Lagrange’s method.
- Divided differences method.
- Newton polynomials, error terms and error bounds of Newton polynomials.
- Central difference interpolation formulae.
- Gauss’s forward interpolation formula
- Gauss’s backward interpolation formula.
- Hermite’s methods.

*Recommended Books*

- David S.,
*Curves and Surfaces for Computer Graphics*, (Springer Science + Business Media Inc, 2006) - John H. M., Kurtis, D. F.,
*Numerical methods using MATLAB*, (Prentice Hall, 1999).

*Suggested Books *

- Rao S.S
*. Optimization Theory and Applications*. 2nd ed. (Wiley Eastern Ltd, 1992) - Sudaran R.K. A first course in optimization theory. 3rd ed.( CUP, 1996)
- Chang E.K.P and Zak, S.I.I.
*An Introduction to Optimization*. 3nd ed. (Wiley, 2004).

**RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS**

It is applied on problems which are not discussed in the course using MATLAB/Mathematica. Design algorithms for numerical solutions of data using other types of Splines available in literature.

**ASSESSMENT CRITERIA**

Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04

Mid-Term Exam: 30

Final-Term Exam: 50

Monday--Tuesday 9:30am-11:00am (Ex-PPP sub-campuses)

Wednesday--Thursday 11:00am-12:30pm (Main Campus)

Commencement of Classes October 12, 2020

Mid Term Examination December 14 to 18, 2020

Final Term Examination February 08 to 12, 2020

Declaration of Result February 19, 2020