### Theory of Splines-I (MATH-425 & MATH-453)

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

1. Basic concepts of Euclidean geometry.
2. Scalar and vector functions.
3. Barycentric coordinates.
4. Convex hull.
5. Matrices of affine maps.
6. Translation, rotation, scaling, reflection and shear.
7. Curve fitting, least squares line fitting, least squares power fit.
8. Data linearization method for exponential functions, nonlinear least-squares method for exponential functions, transformations for data linearization.
9. linear least squares, Polynomial fitting.
10. Basic concepts of interpolation, Lagrange’s method, error terms and error bounds of Lagrange’s method.
11. Divided differences method.
12. Newton polynomials, error terms and error bounds of Newton polynomials.
13. Central difference interpolation formulae.
14. Gauss’s forward interpolation formula
15. Gauss’s backward interpolation formula.
16. Hermite’s methods.

Recommended Books

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

Suggested Books

1. Rao S.S. Optimization Theory and Applications. 2nd ed. (Wiley Eastern Ltd, 1992)
2. Sudaran R.K. A first course in optimization theory. 3rd ed.( CUP, 1996)
3. 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

### Key Dates and Time of Class Meeting

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