This section of Calculus lays foundations for modern Analysis. The course emphasizes understanding of the basic ideas of Calculus and rigorous proofs will be given for all basic theorems.
Syllabus: Number systems. Sequences and series. Functions of a real variable. Graphs of functions. Limits and continuity. Differentiation. Mean value theorem. L’Hospital rule. Maclaurin and Taylor series. Curve tracing. Riemann integral. Definite and indefinite integrals. Fundamental theorem of calculus. Applications of differential and integral calculus in areas such as optimisation and mechanics.