- Week 1 Introduction, precalculus review (lines, functions, and trigonometry), two dimensional vectors. Chapter 0 and section 1.1
The precalculus chapter will be reviewed very rapidly
- Week 2 Dot product, parameterized curves, (qualitative) definition of limit. Sections
1.2, 1.3, 2.1, 2.2. Section 2.1 on tangent and velocity, will
be done rapidly and only to motivate limits. The concepts
of tangents and velocity will be revisited in later sections.
- Week 3 Calculation of limits, limits at infinity,
continuity, velocity. Sections 2.3, 2.5, 2.6, 2.7. Limits at infinity
will be covered rapidly. Note that the epsilon-delta definition
(section 2.4)
is skipped.
- Week 4 Differentiation and rates of change. Sections
3.1, 3.2, 3.3.
- Week 5 Derivatives of the trigonometric functions,
the chain rule and EXAM I (Covering thru 3.2). Sections 3.4, 3.5.
- Week 6 Implicit differentiation, higher derivatives, derivatives
of vector-valued functions and parameterized curves. Sections 3.6, 3.7, 3.8, 3.9. The section on higher derivatives
is very short and will be covered rapidly.
- Week 7 Related rates, exponential functions and inverse functions.
Sections 3.10, 4.1, 4.2 (skip 3.11 and Newton's method (3.12) will
be done in lab).
- Week 8 Logarithmic functions and exponential growth and decay.
Sections 4.3, 4.4, 4.5.
- Week 9 Inverse trigonometric functions, L'Hospital's rule
and EXAM II (Covering 3.3 - 4.4).
Sections 4.6, 4.8.
- Week 10 Mean value theorem, critical points and first
derivative test.
Sections 5.1, 5.2, 5.3.
- Week 11 Second derivative test
and applied max/min. Sections 5.4, 5.7 (parts of 5.5, 5.6
on curve sketching will be done in lab).
- Week 12 Antiderivatives
and Riemann sums and the definitive integral.
Sections 5.9, 6.1, 6.2, 6.3
- Week 13 The Fundamental Theorem of Calculus.
(in the fall, Thanksgiving falls this week.)Section 6.4.
- Week 14 Substitution rule and EXAM III
(Covering 4.5 - 6.4).
Section 6.5.
- Week 15 Review for FINAL. Note that the last week of class has
redefined day(s). See Important Dates for details.