At the end of the course, students should be able to:
Number systems. Indices, Surds and logarithms. Polynomials. Remainder and factor theorems. Polynomial equations. Rational functions. Partial fractions. Fields. Ordered fields. Inequalities. Mathematical Induction. Permutations and combinations. Binomial theorem. Sequences and series. The quadratic equation and function. Relation between the roots and the coefficients. Complex numbers. Addition. Subtraction, multiplication and division. Argand diagram. De-Moivre’s theorem, n-th roots of complex numbers. Elementary set theory. Venn diagrams and applications. De-Morgan’s laws. Trigonometry.
Elementary properties of basic trigonometric functions. Addition formulae and basic identities. Sine and cosine formulae. Half angle formulae. Area of a triangle. Solution of trigonometric equations. Inverse trigonometric functions. Functions. Concept and notation. Examples. Composition, exponential and logarithmic functions. Graphs and properties. Limits and continuity. Techniques for finding limits. The derivative. Calculation from first principles. Techniques of differentiation. Chain rule.
Higher order derivatives. Extremum problems. Mean-value theorem. Applications. Indeterminate forms and L’ Hospital’s rule. Taylor’s and MaClauren’s series. Curve sketching. Integrations as the reverse of differentiation, as area, as limit of finite sums. Definite integrals. Properties of definite integrals. Applications.
