Linear Algebra

Semester 3

Institute of Engineering and Technology, AU

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Credit: 3-0-1-4

Class Contact Hours: Tuesday and Thursday 14.00 to 16.00.

Instructor: Ratnik Gandhi


Prerequisite: Discrete Mathematics


Objective and Outcomes

·         Learn basic linear algebraic techniques and utilize them for modeling and solving engineering problems.

Contents:

1          The geometry of linear equations     

2          Elimination with matrices     

3          Matrix operations and inverses         

4          LU and LDU factorization       

5          Transposes and permutations

6          Vector spaces and subspaces

7          The nullspace: Solving Ax = 0

8          Rectangular PA = LU and Ax = b

9          Row reduced echelon form   

10        Basis and dimension  

11        The four fundamental subspaces

12        Graphs and networks 

13        Orthogonality

14        Projections and subspaces     

15        Least squares approximations           

16        Gram-Schmidt and A = QR

17        Properties of determinants   

18        Formulas for determinants    

19        Applications of determinants

20        Eigenvalues and eigenvectors           

21        Diagonalization          

22        Markov matrices       

23        Differential equations

24        Symmetric matrices  

25        Positive definite matrices      

26        Matrices in engineering

27        Similar matrices        

28        Singular value decomposition

29        Fourier series, FFT, complex matrices          

30        Linear transformations          

31        Choice of basis

32        Linear programming 

33        Numerical linear algebra      

34        Computational science          

 

How?

We shall devote 2 weeks (roughly 6 to 8 hours) for a chapter of Gilbert Strang book.

-         Video Lectures.

 

4 Sessions a week:

  • -          2 hours of problem solving with the facilitator
  • -          1 hour of instructions
  • -          1 hour of problem solving/ working on projects(in team)

Activities:

  • -          Problem solving
  • -          Team project (3 weeks + 7 weeks)
  • -          Computer Programming
  • -          Competition

 

Evaluation:                                                                                                  

  • -          Exams-10% of questions will come from homework/tutorial assignment
  • -          Projects

 

Primary references:

  • 1.      Gilbert Strang (Chronology and content): Book and Video Lectures
  • 2.      David C Lay (Applications and Problems)