Mathematics I - Topics

Scope and objectives: 

At the end of the course the student would be able to

·         understand the fundamentals of linear and matrix algebra

·         solve systems of linear equations using analytical and numerical techniques

·         formulate and solve linear programming problems

Text Books :

T1: Erwin Kreyszig, Advanced Engineering Mathematics, Wiley India, 9^th Edition 2011.

      

T2: Hamdy A Taha, Operations Research: An Introduction, Pearson / PHI, 8^th Edition,2009.  

Mathematics Topics :

Topic		Chapter Reference
Operation on matrices and introduction to vector spaces.		TextBook - T1 Chap.- 7 Sec.- 7.1 – 7.4 and 7.9
Solution of linear system of equations, Determinants, Inverse of a matrix, Gauss Jordan elimination		TextBook - T1 Chap. 7 Sec.- 7.5 – 7.8
Eigen values, eigen vectors and their applications		TextBook - T1 Chap. 8 Sec. 8.1 – 8.3
Eigen bases, diagonalization and quadratic forms		TextBook - T1 Chap. 8 Sec 8.4 – 8.5
Linear systems: Gauss elimination with pivoting, LU decomposition		TextBook - T1 Chap. 20 Sec. 20.1 – 20.2
Iterative methods of solving linear systems		TextBook - T1 Chap. 20 Sec. 20.3 – 20.4
Matrix eigen value problems		TextBook - T1 Chap. 20 Sec. 20.6 – 20.8
Review and problem solving
Syllabus for Mid-Semester Test: Topics covered in the first 8 weeks
Modelling with Linear programming, Graphical approach	TextBook – T2 Chap. 2 Sec.  2.1 – 2.2. Subsec. 2.3.3
The simplex method	TextBook – T2 Chap. 3 Sec. 3.1 – 3.3
Big M and Two Phase Method	TextBook – T2 Chap. 3 Sec. 3.4
Special cases of the simplex method and sensitivity analysis	TextBook – T2 Chap. 3 Subsec. 3.6.1- 3.6.2
The Dual Simplex Method and the Generalized Simplex Algorithm	TextBook – T2 Chap. 4 Sec. 4.1 – 4.4
Post optimal analysis	TextBook – T2 Chap. 4 Sec. 4.5
Review and problem solving
Syllabus for Comprehensive  Exam (Open Book): All topics given in Plan

Source:- from my MS Prof.