### Mathematics I (URCM-5107)

Introduction:

Intoduce the students to solve the system of equation by an easy method (matrices evaluation), to familiar the students with binomial theorem and its applications, trignometry, to eigenvalues and eigen vectors.

Pre requisite:

Pre requisites for linear algebra include courses typically called Elementary Algebra and intermediate algebra as well as introductory to trigonometry

Learning Outcomes:

Students will able to solve the system of equations in the form of matrices, by various techniques and by column row operation of matrices

Course Content:

• Proliminaries: Real Number system, Complex Numbers, Introductíon to sets. set operation, lunction and its types
• Matrices: Introduction to matrices, types of matrices, Matrix inverse, deteminants,
• system of linear equations, Cramer's rule.
• Solution of quadratic equations, equalon reduces to quadratic equatíons, cube roots of unity,
• relation between roots and coefficients of quadratic equations.
• Qution of system of equations Sequences and Series: Arimetic Progression, Arithmetic Mean,
• geometrc Progression, Gcometric Mean, Harmonic Progression, Harmonic Mean,
• Fourier transforms, Taylor series, Inverse Series. Orthogonal Polynomials,
• Binomial Thcorem: Introduction to Mathematical Induction,Binomial theorem with rational and irrational indices. Trigonometry,
•  Eigenvalues and Eigen vectors, Gamma and Beta functions with applications

Text Book:

1. Doleiani MP, Wooton W, Becknback EF, Sharron S, "Algcbra and rignometry 1978, Houghuon and Mifrilin.Kaufimann JE. Coliege Algebra and trigonometry, 1978, PWS-Kent Company, Boston. dition), 1986, PWS-Kent Compahy, Boston. Hogg, R. M. & Craig, A. T. "Introduction to Mathematical Statistics
2. Swokowski EW, "Fundmentals of Algebra and Trignometry" (6 1995, Prentice llall. KKaplan, W.C. "Advance Calculus 1984, Addision and Wiley.21

PPT/Handout:

Samshad, M., Ghaury, M . S., Bhatti, Saleem, K. (2005) Algera and Trigonometry, Union Book Deport. Lahore.

Doleiani MP, Wooton W, Becknback EF, Sharron S, "Algcbra and rignometry 1978, Houghuon and Mifrilin.Kaufimann JE. Coliege Algebra and trigonometry, 1978, PWS-Kent Company, Boston. dition), 1986, PWS-Kent Compahy, Boston. Hogg, R. M. & Craig, A. T. "Introduction to Mathematical Statistics

Assesment Criteria:

Assignments 5%

Quiz 5%

Class Attendence /Class Participation/Presentation 10%

Mid Term 30%

Final Term 50 %

Key Dates and Time:

 Commencement of Classes: Monday 9AM to 10PM Tuesday 9AM to 10 PM Wednesday 9AM to 10 PM October 12, 2020 (Monday )   Mid-Term Examination: December 28, 2020 to January 01, 2021 (Monday to Friday) Final-Term Examination: March 01 to 05, 2021 (Monday to Friday) Declaration of Result: March 12, 2021 (Friday)