MATHEMATICS-I:

INTRODUCTION:

The goal of Mathematics-I is to prepare students for first-year calculus. Helping students gain proficiency in their understanding and ability to utilize real-valued functions, the primary tool in Calculus, accomplishes this goal. Students are presented a broad set of 'function tools', including a general understanding of function properties  together with 'library' of commonly used functions.

Learning Skills:  

It is intended that students become skills at recognizing the different families of functions and the primary properties  that set each apart, are able to apply the general function properties to each type of function, and are able to use the special set of algebraic skills associated with each. Students are also expected to become adept in utilizing and interpreting the results from graphing calculators, as an important investgative tool.

Pre-requisite:

 Mathematics-I.

Course Content:

1. Preliminaries.
2. Real-number system, complex numbers.
3. Introduction to sets, set operations, functions, types of functions.
4. Matrices Introduction to matrices, types, matrix inverse, determinants, system of linear equations, Cramer's rule.
5. Quadratic Equations.
6. Solution of quadratic equations, qualitative analysis of roots of a quadratic.
7. Equations reducible to quadratic equations.
8. Cube roots of unity, relation between roots and coefficients of quadratic.
9. Sequences and Series.
10. Arithmetic progression.
11. Geometric progression.
12. Harmonic progression.
13. Binomial Theorem.
14. Introduction to mathematical induction.
15. Binomial theorem with rational and irrational indices.
16. Trigonometry, Fundamentals of trigonometry, Trigonometry indentities.

​Recommended Texts:

1. Thomas, G, B., & Finney, A, R, (2005), Calculus Reading; Addison-Wesley
2. Anton, H., Bevens, I., & Davis, S. (2005), Calculus; A new Horizon (8th ed,) New York: John Wiley.

​Suggested Reading:

1. Srewart, J, (1995), Calculus, (3rd ed,), Pacific Grove, California: Brooks/Cole.
2. Swokowski, E, W, (1983), Calculus and analysis geometry, Boston: PWS-Kent company.
3. Thomas, G, B., & Finney, A, R, (2005), Calculus (11th ed.), Reading; Addison-Wesley.