May 22, 2019






Chapter 1





































































































































































Vertical line test

Composite functions

Secant line

Transformation

Inverse functions

Onetoone function

How to find inverse function

Chapter 2

Definition of a limit

Concept of a limit

Onesided/Twosided limits

Understand and be able to use limit laws

Squeeze theorem

Definition of infinite limits

Limits at infinity

Continuity

Theorems of continuity

Continuity on an interval

Chapter 3

Geometric meaning of tangent line and derivatives

Definition of derivatives

Relation between differentiable and continuous functions

Rules of differentiation

Chain rule

Implicit differentiation

Chapter 4

Absolute maximum and minimum

Local max and min

Local extreme point theorem

Definition of critical points and how to find them

Test for intervals of increase and decrease

First derivative test

Concavity and inflection point

Test for concavity

Second derivative test used to identify local max and min

Be able to solve optimisation problem

Definition of linear approximation to f at 0

Mean value theorem

L\'Hopital\'s rule

Antiderivative

Chapter 5

Geometric meaning of integration

Regular partition, grid points

Riermann sum and all variants

Definite integral

Net area

Reversing limit and identical limit

Be able to use fundamental theorems of calculus to compute definite integral

Integrals of even and odd functions

Substitution rule

Chapter 6

Area of a region between functions

Length of a curve

Chapter 7

Integration by parts

Definition of improper integrals