Math 8: Calculus of Functions of One and Several Variables

Math 8: Calculus of Functions of One and Several Variables
Spring 2019

Daily Schedule

The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.
Numbered practice problems are from the pdf versions of the text.

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 		Gradient and directional derivatives I
Gradient handout
(W) May 15 Vol. 3
4.6 		Gradient and directional derivatives II
(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

Mathematics Department ∈ Dartmouth College