Math 8: Calculus of Functions of One and Several Variables

Daily Schedule

The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.

Date Sections in Text Description Practice Problems
(M) Mar 25 Vol. 2
5.1, 5.2
Sequences, infinite series, the harmonic series
Sequences and series handout
§5.1: #6, 8
§5.2: #69, 75
(W) Mar 27 Vol. 2
5.2, 5.3
Geometric series, telescoping series §5.2: #105, 137
Write 2.15 as a fraction
(F) Mar 29 Vol. 2
5.3, 5.4
Divergence test, integral test, comparison test §5.3: #153, 163
§5.4: #198, 200
(M) Apr 1 Vol. 2
5.5, 5.6
Alternating series test, ratio test
Alternating series and ratio test worksheet
§5.5: #262, 263
§5.6: #321, 323
(Tu) Apr 2 Section 2 x-hour
Chapter 5 problem session
Series tests flowchart
(W) Apr 3 Vol. 2
6.1
Power series, radius and interval of convergence
Power series worksheet
PowerSeries.nb
§6.1: #13, 15, 23
(Th) Apr 4 Section 1 x-hour
Review alternating series and ratio test worksheet
Series tests flowchart
(F) Apr 5 Vol. 2
6.2
Properties of Power Series
Power series properties handout, Section 1
Power series properties handout, Section 2
HW 1 due 4 pm
§6.2: #65, 95
(M) Apr 8 Vol. 2
6.3
Taylor polynomials, Taylor and Maclaurin Series
Taylor series worksheet
Taylor series video
(W) Apr 10 Vol. 2
6.3
Remainder estimates §6.3: #132, 146
(Th) Apr 11 Section 1 x-hour
Exam 1 review
Practice Exam
More past exams
(F) Apr 12 Vol. 2
6.4
Applications of Taylor series
Non-elementary integrals worksheet
HW 2 due 4 pm
(M) Apr 15 Vol. 3
2.1, 2.2
Coordinates, distance formula, simple surfaces
Properties of vector operations handout
§2.1: #25
§2.2: #88, 97
(Tu) Apr 16 Exam 1: 4:30 - 6:30 pm, Silsby 028
Solutions
(W) Apr 17 Vol. 3
2.3
Dot products and projections I
Dot product and projections worksheet
§2.3: #135, 145
(F) Apr 19 Vol. 3
2.3
Dot products and projections II
HW 3 due 4 pm
(M) Apr 22 Vol. 3
2.4
Cross products and geometry; relation to volume and area
Cross product animation
Cross product worksheet
Cross product video
§2.4: #183, 224(a)
(W) Apr 24 Vol. 3
2.5
Equations of lines and planes
Lines and planes worksheet
(Th) Apr 25
x-hour
Section 1 x-hour
Discussion of solutions to Exam 1
(F) Apr 26 Vol. 3
3.1
Vector-valued functions and space curves
VectorValuedFunctionPlot.nb
HW 4 due 4 pm
§3.1: #4, 16, 23, 25
(M) Apr 29 Vol. 3
3.2, 3.3
Derivatives and integrals along curves, arc length
Calculus of vector-valued functions handout
§3.2: #42, 45, 55, 73
(W) May 1 Vol. 3
4.1
Functions of 2 and 3 variables; level curves and contour maps
Arc length handout
(Th) May 2 Section 1 x-hour
Exam 2 review
Practice Exam, Solutions
More past exams
(F) May 3 Vol. 3
4.2
Limits and continuity in dimensions 2 and 3
Limits and continuity handout
HW 5 due 4 pm
(M) May 6 Vol. 3
4.3
Partial derivatives
Partial derivatives handout
PartialDerivativePlot.nb
(Tu) May 7 Exam 2: 4:30 - 6:30 pm, Silsby 028
Solutions
More past exams
(W) May 8 Vol. 3
4.4
Tangent planes and linear approximations
Tangent planes handout
(F) May 10 Vol. 3
4.5
Chain rule
Chain rule handout
HW 6 due 4 pm
(M) May 13 Vol. 3
4.6
(W) May 15 Vol. 3
4.6
(F) May 17 Vol. 3
4.7
Extreme values I
Local extrema handout
HW 7 due 4 pm
(M) May 20 Vol. 3
4.7
Extreme values II
Global extrema handout
(W) May 22 Vol. 3
4.8
Lagrange multipliers I
Lagrange multipliers handout
(F) May 24 Vol. 3
4.8
Lagrange multipliers II
Lagrange multipliers II handout
HW 8 due 4 pm
Lagrange multipliers practice
Solutions
(M) May 27 Memorial Day: no class
(W) May 29 Review
(Sat) Jun 1
Final Exam: 11:30 am - 2:30 pm, Carpenter 013
Review sheet
Practice Exam A, Solutions
Practice Exam B, Solutions