Course outline

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