Calculus I These notes are based off Prof. Pilkington‘s lecture materials. All the general course info can be found here. Survey List of Symbols The notes from the “board” can be found here. Lecture 1 – Review of Functions Lecture 2 – Tangents and Velocity Lecture 3 – Limits of Functions Lecture 4 – Laws of Limits Lecture 5 – Continuity of Functions Lecture 6 – Derivatives and Rates of Change Lecture 7 – The Derivative as a Function Lecture 8 – Differentiation formulas Lecture 9 – Derivatives of Trigonometric Functions Lecture 10 – Chain Rule Lecture 11 – Implicit Differentiation Lecture 12 – Rates of change in natural and social sciences Lecture 13 – Related rates Lecture 14 – Linear approximations and differentials Lecture 15 – Maxima and minima Lecture 16 – The Mean Value Theorem Lecture 17 & 18 – Derivatives and graphs Lecture 19 – Limits at infinity Lecture 20 – Summary of curve sketching Lecture 21 – Optimisation problems Lecture 22 – Newton’s method Lecture 23 – Antiderivatives Lecture 24 – Areas and distance Lecture 25 – The definite integral Lecture 26 – The Fundamental Theorem of Calculus Lecture 27 – The Indefinite Integral and Applications of FTC Lecture 28 – Integration by Substitution Lecture 29 – Area between curves Lecture 30 – Volumes Lecture 31 – Volumes Lecture 32 – Work Lecture 33 – Average value of a function