Course Objectives

The objectives of this course are to:

1. Introduce students to the concepts of sets, subsets, and operations using Venn diagrams.

2. Develop an understanding of number systems and their classifications.

3. Equip students with problem-solving skills for quadratic equations.

4. Provide foundational knowledge of trigonometric functions and their applications.

5. Introduce students to the binomial theorem and its practical use in solving mathematical problems.

2.  Overall Learning Outcomes

By the end of this course, students should be able to:

  1. Explain basic definitions of sets, subsets, unions, intersections, complements, and represent them using Venn diagrams.
  2. Solve quadratic equations using various methods.
  3. Apply trigonometric functions to solve problems involving angles and their measurements.
  4. Identify and classify different types of numbers, including real, rational, and complex numbers.
  5. Apply the binomial theorem to expand algebraic expressions and solve relevant problems.

3.  Detailed Course Content

Module 1: Set Theory and Number Systems

1. Elementary Set Theory:

  • Definitions: Sets, subsets, union, intersection, complements.
  • Operations with sets using Venn diagrams.

2. Number Systems:

  • Real numbers, integers, rational and irrational numbers.

Module 2: Algebra

1. Quadratic Equations:

  • Roots and coefficients.
  • Methods of solving: factorization, completing the square, and the quadratic formula.

2. Binomial Theorem:

  • Expansion of (a + b)^n for positive integer values of n.
  • Applications in solving algebraic problems.

Module 3: Complex Numbers

1. Introduction to Complex Numbers:

  • Definitions and arithmetic of complex numbers.
  • Representation on the Argand diagram.

2. De Moivre’s Theorem:

  • Powers and roots of complex numbers.

3. Nth Roots of Unity:

  • Concept and computation.

Module 4: Trigonometry

1. Circular Measure:

  • Definition and conversion between degrees and radians.
  • Applications in geometry and physics.

2. Trigonometric Functions:

  • Definitions and values for angles of any magnitude.
  • Addition and factor formulae.

Module 5: Sequences and Series

1. Real Sequences and Series:

  • Definitions and examples.
  • Introduction to convergence and divergence (basic concepts only)

11. Teaching/Learning Methods

1. Lectures: Delivery of theoretical concepts and mathematical examples.

2. Tutorials: Problem-solving sessions to enhance understanding.

3. Assignments: Regular homework to apply learned concepts.

4. Group Discussions: Collaborative learning to solve complex problems.

12. Modes of Assessment

1. Continuous Assessment (40%):

a. Assignments (10%)

b. Quizzes (10%)

c. Midterm Test (20%)

2.  Final Examination (60%)

13. Reading List/References

Required Texts

  1. Kreyszig, E. (2019). Advanced Engineering Mathematics (10th ed.). Wiley.
  2. Stroud, K. A., & Booth, D. J. (2016). Engineering Mathematics (7th ed.). Palgrave Macmillan.

Additional Readings

  1. James, G. (2018). Modern Engineering Mathematics (6th ed.). Pearson.
  2. Lay, D. C., McDonald, S. R., & Lay, J. J. (2016). Linear Algebra and Its Applications (5th ed.). Pearson.