Elementary set theory, subsets, union, intersections complement, and Venn diagrams. Real numbers; integers, rational and irrational numbers, mathematical induction. Real sequences and series, theory of quadratic equations, binomial theorem, roots of unity. Circular measure, trigonometric functions of angles of any magnitude, addition and factor formulae
Function of a Real Variable: Definition of Functions of Real variable, Types of function. Graph of a function of real variables: Graphical representation. Limits and continuity of functions of real variables: Idea of limits of functions of real variable, the rate of change of a function, differentiation from first principle, the concept of continuity of function of real variable, Limits and limit location. Techniques of differentiation: Differentiation of the sum and difference of functions, differentiation of a product of functions, differentiation of a quotient of functions second and higher derivatives, differentiation of a function of a function, differentiation of inverse functions, differentiation of implicit functions, differentiation from parametric equations. Application of differentiation: Applications to kinematics, the tangent and normal to a curve, the maximum and minimum of a function. Extreme curve sketching: Turning points of a curve, minimum and maximum values of a curve. Integration: Integration of a constant, methods of integration , integration of rational algebraic fractions, integration by substitution, integration by partial fractions, integration of trigonometric functions . Applications of integration: Application of geometry and mechanics, areas of plane shapes, volume of plane shapes.
This course is a first course in Applied Mathematics designed primarily for students in Sciences and Engineering. However, it also meets the need of students in other fields, as a course that introduces students to theories, applications and solving problems in Vectors, Dynamics and Geometry. As a gateway into Applied Mathematics, the course focuses on operations with Vectors and Scalars, solving problems in Dynamics and Geometry. The course is to prepare the students for Applied Mathematics at higher levels. Some of the topics to cover include Geometric representation of vectors in 1 â€“ 3 dimensions, direction cosines, Two-dimensional coordinate geometry, Straight lines, circles, Kinetics of particles, components of velocity and acceleration of a particle moving in a plane.