University of Portsmouth (UOP)

This document contains everything you need to know about multiple integration. This is very useful to any student studying calculus.

This document contains everything you need to know to fully grasp the concept and usefulness of multivariable differentiation. This contains proof of the chain rule, informal and formal definitions of limits, level sets, level curves and tangent planes. It also includes information about critical points, derivatives, directional derivatives and much more. This is very useful for any student studying Calculus

This document contains the definitions and everything you need to know on Hyperbolic Functions. This mainly focuses on the definitions of the functions and the differentiated and integrated versions. This is very useful for any student studying Calculus

This document contains everything you need to know on the tougher aspects of integration. It focuses mainly on reduction formulae of sin , cos and tan and their proofs. However, it does also include integrals using partial fractions, Product powers of sin and cos and Pythagorean Substitutions. This document is very useful for any student studying calculus.

This document provides the basics of Taylor Approximation and how to calculate how many iterations are required for a certain remainder. It also focuses on the numbers e and pi and on logarithmic differentiation

This document contains everything you need to know on Integration and the different types, focusing on proofs and the use of these methods (eg By Parts). It also includes a practical summary for these methods. This document is very useful for any student studying Calculus.

This document explains exactly how to plot graphs using Calculus (Differentiation). It includes the different tests that can be used to determine critical points and the importance and relevance of these critical points. This is very useful for any student studying calculus.

This document contains everything you need to know on the tougher parts of differentiation and limits, mainly focusing on the proofs of the chain, product and quotient rules. This is colourfully laid out and includes many more definitions and is very useful for any student studying Calculus.

This document is laid out colourfully, containing everything you need to know on Continuity and Differentiability in Calculus. This is very useful for any student studying Calculus. It includes: Continuity, Differentiation, Proofs of Rules, Explanations of Big O and Little o notations and much more.

This document contains everything to do with limits in one variable functions in Calculus. This is very useful for any university student studying calculus at any level. This document contains: Limits, Theorems, Proofs and diagrams and lots of very useful information.