MAL101, Mathematics-II

Instructors

Lecture: Dr. Pawan Kumar Mishra (pawan@iitbhilai.ac.in, +919118498909)

Tutorials: The students are distributed in 5 groups for tutorial classes.  

Timings

Lecture: Monday, Tuesday and Thursday, 10:30am-11:25 am

Tutorial:Thursday, 12:30pm-1:25pm 

Venue

Venue for lectures-L209

Course Content

• Systems of linear equations: Elementary operations-row-reduced echelon matrices-Gauss elimination LU factorization-linear independence-rank of a matrix-solutions of linear systems-existence and uniqueness; 

• Vector spaces: Vector space-subspaces-spanning space-bases and dimensions; 

• Linear transformations: Linear transformation-matrix representations of linear transformations-range space and rank-null space and nullity-the rank and nullity theorem-invertibility; Eigenvalues and eigenvectors: Eigen values-eigenvectors and some applications of eigenvalue problems-Hermitian, skew-Hermitian, unitary matrices and their eigenvalues-eigen bases; Diagonalization: Annihilating polynomial-the minimal polynomial and the characteristic polynomial-Cayley-Hamilton theorem-real quadratic form; Inner product spaces: Inner product spaces-orthonormal bases- Gram-Schmidt process;

• Differential Equations: Review of First Order ODE- Lipschitz condition-Picard`s theorem; Linear differential equations: Linear dependence and Wronskian-linear ODE with constant coefficients of higher ordercharacteristic equations- Cauchy-Euler equations-method of undetermined coefficients-method of variation of parameters- solutions methods using Laplace Transform. 

Evaluation

There will be two quizzes, each of 10 marks and  mid and end semester exams of 40 marks each.

        Reference Books

• Linear Algebra by Kenneth Hoffman and Ray Kunze (Pearson)

• Introduction to Linear Algebra by Gilbert Strang (South Asian Edition)

• Advanced Engineering Mathematics, E. Kreyszig ( John Wiley)

                                    Lectures and Tutorials                        

Lecture 1-5              Tutorial-1 ,        Tutorial-2           Lecture 6-8     Tutorial-3        Lecture 9-11      Lecture 12-14    Lecture 15-16      Lecture 17-18             Tutorial-4                  Quiz-I                Quiz-I Solution    Lecture 19-20     Lecture 21     MidSem_Answers    Tutorial-5     Lecture 22-23     Lecture 24-25   Tutorial-6      Lecture 26-27       Tutorial-7       Lecture 28-30    Tutorial-8         Lecture 31-35    Quiz-II           Lecture 36-39         Tutorial-9       Lecture 40-41   End Semester Marking Scheme 

     Suggestions

It is advised that students should try to solve tutorial sheet before coming to the tutorial class.  In case, you feel uncomfortable either in the lectures or in tutorials, you are advised to contact to the course instructor as soon as possible so that the issue can be resolved well within time. As the evaluation is continuous, you are not likely to get extra time to prepare for your exams. Therefore , you should learn in the classes in order to perform well. Avoid any malpractice in exams. These cases will be taken care as per the institute policy.  A minimimum attendance to pass the course is required as per the institute policy.