Calculus

What it covers

• Functions, limits, continuity, asymptotes
• Differentiation: linearization, implicit differentiation, Newton's method, L'Hôpital's rule
• Integration: FTC, substitution, integration by parts, improper integrals
• Sequences and series: convergence tests, power series, Taylor/Maclaurin series
• Multivariable calculus: partial derivatives, gradients, tangent planes, critical-point optimization, double integrals
• Complex numbers: polar form, Euler's identity, De Moivre's formula

Assessment

Midterm (lectures 1-10, short-answer only, only the final answer graded, 2h) + Endterm (all material, short-answer + open questions, 3h). Final grade = (Midterm + 2×Endterm)/3; passing needs an average ≥5.75 and an endterm ≥5.0. One comprehensive resit, weighted 100%, replaces the final grade if higher. No calculators.

Resources

• Essence of Calculus – 3Blue1Brown, Differential Calculus – 3Blue1Brown — intuition, not technique.

Worth knowing

• Short-answer questions grade only the final answer — no partial credit, so algebraic precision matters more here than on the endterm's open questions.
• Common pitfalls flagged in the material: one-sided infinite limits ("does not exist," not ∞), factors that cancel into a removable hole rather than an asymptote, absolute vs conditional convergence, forgetting to check both endpoints of a power-series interval.
• No calculators on any exam.