Course outline

TopicsCLP TextActive CalculusApex CalculusMooculusStewart
Week 1 Tangents and velocity
Introduction to limits
Using limit laws
1.1-1.4 1.1-1.2 1.1 & 1.3-1.4 1.1-1.3 2.1-2.3
Week 2 Limits at infinity
Continuity
A first look at derivatives
1.5-1.6 & 2.1-2.3 1.7
2.8
1.3
1.5-1.6 & 2.1-2.2 2.1-2.3 & 3.1 2.5-2.7
Week 3 A second look at derivatives
Derivatives of sums, products and ratios
Derivatives of exponentials
2.3-2.4 & 2.6-2.7 1.4, 2.1, 2.3 2.3-2.4 3.1-3.2 & 5.1-5.2 2.8 & 3.1-3.2
Week 4 Derivatives of trig functions
The chain rule
Inverse functions
2.8-2.9 & 0.6 2.2,2.4-2.6 2.3-2.4
2.5
7.1 & 6.1 & 0.2 3.3-3.4 & 1.6
Week 5 Logarithms (and their derivatives)
Implicit differentiation
Inverse trig functions
2.10-2.12 2.6-2.7 2.6-2.7 6.2-6.3 & 7.2 3.5-3.6
Week 6 Rates of change
Exponential growth and decay
3.1
3.3
8.2 & 11.2 3.7-3.8
Week 7 Related rates
Linear approximations
Taylor polynomials
3.2
3.4
3.5
1.8
8.5
4.2
4.4
8.7
8.3 & 10.1
no Taylor
3.9-3.10
no Taylor
Week 8 Taylor's formula and remainders
Finding maxima and minima
3.4
3.5
8.5
3.3
8.7
3.1
no Taylor
4.1 & 9.1
no Taylor
4.1
Week 9 Mean value theorem
Curve sketching
2.13
3.6
no MVT
3.2
3.2, 3.3-3.5 10.3 & 4.1 4.2-4.3 & 4.5
Week 10 More curve sketching
3.6 3.2 3.3-3.5 4.2-4.5 4.3 & 4.5
Week 11 Optimisation problems
L'Hopital's rule
3.5
3.7
3.4 & 2.8 4.3
9.2 & 8.1 4.4 & 4.7
Week 12 Antiderivatives
Review (if time)
4.1 4.4 11.1 4.9