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Covered so far
Lecture 1: Functions: definition, examples, some graphs, domain and range.
Lecture 2: Adding, multiplying functions and so on, composing functions, inverting functions.
Lecture 3: Cancelled due to a one-off scheduling difficulty with the lecture theatre.
Lecture 4: Inverses again, the limit and the one-sided limit.
Lecture 5: Calculating limits, infinite limits.
Lecture 6: More infinite limits, limits at infinity.
Lecture 7: Limits at infinity, calculating limits at infinity.
Lecture 8: Messing with square roots, limit of expressions with square roots. The epsilon-delta definition of limits.
Lecture 9: More on the epsilon-delta limit. Start of differentiation, motivation, the definition. Simple examples of working out the rate of change from the limit definition.
Lecture 10: Differenciation; tangents, examples, x^n.
Lecture 11: Differenciation of sums, products and quotients.
Lecture 12: Higher derivatives, revising trigonometry.
Lecture 13: Differciating trignometric functions, chain rule.
Lecture 14: More chain rule, start of max and min.
Lecture 15: More max and min, points of inflection and so on.
Lecture 16: Max and min, points of inflection. Start of Taylor series.
Lecture 17: Taylor series (Note 1), start of the growth equation.
Lecture 18: The Christmas quiz.
Lecture 19: Solving the growth equation, the exponential.
Lecture 20: The exponential, compound interest.
Lecture 21: The natural log.
Lecture 22: Implicite differentiation (Note 2), differentiating the log.
Lecture 23: Differenciating inverse sine.
Lecture 24: The method of l'Hopital.