Course overview
This course will develop concepts in calculus and apply them to problems using analytic and software techniques, along with elementary skills for proving mathematical statements. Contents include: A review of the topics in Calculus 1 with a viewpoint of mathematical analysis, i.e. in more depth: proof of facts in limits and continuity, differentiation, integration; Integration techniques: simple substitutions, integration by parts, rational functions and partial fractions, trigonometric substitutions; Polar coordinates, equations of simple curves and integration; L’Hopital’s rule; Improper integrals. Sequences, convergence of sequences; Infinite series, convergence tests for series, Maclaurin and Taylor series; Calculus in two and three variables: limits and continuity, partial differentiation, illustration of multivariable optimisation problems; Proofs of most theorems involved in the above topics.