Linear algebra is the study of linear systems of equations, vector spaces, and linear transformations. Solving systems of linear equations is a basic tool of many mathematical procedures used for solving problems in science and engineering. 

Prerequisite 

To succeed in this course you will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems.

Learning Outcomes

At the end of this course the student will be able to:

• Solve linear systems of equations
• Comprehend vector spaces, subspaces and inner product spaces
• Understand fundamental properties of matrices including determinants, inverse matrices, matrix factorizations, eigenvalues, orthogonality and diagonalization
• Have an insight into the applicability of linear algebra
• Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra.

Contents

• Matrices: Addition, Multiplication, Transpose. 
• Matrices and Systems of Linear Equations. 
• Block Matrices. Polynomial in Matrices. 
• Invertible Matrices, Complex Matrices. 
• Elementary Matrices and Applications. 
• Quadratic Forms, Simlarity.
• Vector Spaces, Subspaces.
• Linear Combination, Linear Spans. 
• Basis and Dimension.
• Change of Basis.
• Orthogonality.
• Inner Product Spaces, Cauchy-Schwarz Inequality. 
• Applications, Porjections, Inner Products and Matrices. 
• Normed Vector Spaces.

Recommended Books

1. . Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill. 
2.  Mathematical Methods for Physicists by George Arfken and Hans J. Weber, (6th and onwards editions) Acad Press.
3. Advanced Engineering Mathematics, Erwin Kreyszig, (2007).
4.  Mathematical Physics by E. Butkov, Addison-Wesley London.

Suggested Books

1.  Elementary Linear Algebra and its Applications by Howard Anton and Chris Rorres, 11th Edition.
2. David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron
3. Linear Algebra and Its Applications by David C Lay and Steven R Lay. 

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

Key Dates and Time of Class Meeting

Wednesday-Thursday                                                             1:00pm-2:00pm

Firday                                                                                         2:00pm-3:00pm

Commencement of Classes                                                   January 13, 2020

Mid Term Examination                                                            March 09-13, 2020

Final Term Examination                                                          May 04-08, 2020

Declaration of Result                                                              May 19, 2020