The objectives of the course are to introduce students to the basic ideas and methods of linear algebra and enable them to understand the idea of matrix theory. Emphasis is given to topics that will be useful in other disciplines, including eigenvalues and eigenvectors, orthogonal polynomials, Gamma and Beta functions with applications.

**Prerequisite**

Elementary Algebra and Trigonometry.

**Learning Outcomes**

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

- Solve linear systems of equations
- Understand fundamental properties of matrices including determinants, inverse matrices, eigenvalues and eigenvectors.
- 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**

- Real Number System, Complex Numbers, Introduction to sets, set operations.
- Function and its types.
- Matrices: Introduction to matrices, types of matrices, matrix inverse, determinants.
- Systems of linear equations, Cramer's rule.
- Quadratic equations: Solution of quadratic equations, equations reducible to quadratic equations.
- Cube roots of unity, relation between roots and coefficients of quadratic equations, Solution of system of equations.
- Sequence and Series: Arithmetic Progression, Arithmetic Mean, Geometric Progression, Geometric Mean, Harmonic Progression, Harmonic Mean.
- Fourier Transform, Taylor series, Inverse Series, orthogonal polynomials,
- Binomial Theorem: Introduction to Mathematical Induction, Binomial Theorem with rational and irrational indices.
- Trigonometry,
- Gamma and Beta functions with applications.
- Eigenvalues and eigenvectors.

**Recommended Books**

- Dolciani, MP., Wooton, W., Beckonback, EF., Sharron, S., "Algebra and Trigonometry" 1978, Houghton Mifflin Company, College Algebra and Trigonometry, 1978, PWS-Kent Company, Boston.
- Swokowski, FW., "Fundamentals of Algebra and Trigonometry", 6th Edition, PWS-Kent Company, Boston.
- Hogg, R. M., and Craig, A. T., "Introduction to Mathematical Statistics" 1995, Prentice Hall.
- Kaplan, W. C. "Advance Calculus" 1984, Addison and Wiley.

**Suggested Book**

- Stewart, J., Redlin, L., Watson, S.,
*Algebra and Trigonometry,*4th edition, Cengage Learning (2015).

**ASSESSMENT CRITERIA**

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

Mid-Term Exam: 30

Final-Term Exam: 50

Tuesday 4:00pm-5:00pm

Thursday 2:00pm-3:00pm

Friday 3:00pm-4:00pm

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