Jen Paulhus, Ph.D.

Calculus III

email: jpaulhus@mtholyoke.edu
Office Hours:
     Mondays 4:30-5:30 PM
     Wednesdays 10:30-11:30 AM
     Thursdays 2:30-3:30 PM
     Fridays 9:30-10:30 AM
     or by appointment

Class Meeting: Monday, Wednesday, Friday 3:15-4:30 PM

Text: APEX Calculus 3, Version 4.0, Hartman
Material Covered: Chapters 10-14, parts of 9

Syllabus

Homework Assignments     Quiz Topics

Daily Topics

Class Date Section Topics Desmos Link
Sept. 4 10.1 (pgs. 559-562) coordinate planes, distance in space, standard equation of a sphere Day 1
Sept. 6 10.2, 10.3 (pgs. 574-582, 588-589) vector, initial point, terminal point, magnitude, component form, vector algebra properties of vector operation, unit vector, dot product Day 2
Sept. 9 10.3 (pgs. 589-595) dot product and angles, orthogonal vectors, orthogonal projection,
Sept. 11 10.4, 11.1 (pgs. 601-605, 631-635) cross product, right hand rule, vector-valued functions, vector Vector Valued Functions
Sept. 13 10.5, 10.6 (pgs. 612-617, 623-624) parametric and symmetric equations of a line, skew lines, normal vectors, standard and general form for planes Lines and Planes
Sept. 16 10.6, 12.1 (pgs. 625-627, 683-684) parallel planes, multivariable functions Slices
Sept. 18 12.1, 12.2 (pgs.685-688, 690-698) level curve, open disk, boundary point, interior point, open, closed, bounded sets, limits, continuity More Level Curves
Sept. 20 12.3 (pgs. 700-707) partial derivative with respect to x and with respect to y Partial Derivatives
Sept. 23 12.3(pgs. 708-710) second partial derivatives, Clairaut's Theorem (Theorem 12.3.1) 2nd Partials
Sept. 25 12.7 (pgs.739-740, 745-746) tangent plane Tangent Plane
Sept. 27 Exam 1
Sept. 30 12.5 (pgs. 721-725) multivariable chain rule
Oct. 2 12.6 (pgs. 729-730) directional derivatives Directional Derivatives
Oct. 4 12.6, 12.7 (pgs. 731-737, 746-747) gradient
Oct. 7 12.8 (pgs. 749-751) critical point, saddle point Maximum and Minimums
Oct. 9 12.8 (pgs. 752-754) 2nd Derivative Test
Oct. 11 12.8 (pgs. 754-757) Extreme Value Theorem, absolute maximum, absolute minimum Optimization
Oct. 16 see Moodle for notes Lagrange multiplier, method of Lagrange multipliers Lagrange Multipliers
Oct. 18 13.2 (pgs. 769-770) Riemann sums, double integrals Single Variable Example
Oct. 21 9.4 (pgs. 533-543) polar coordinates, polar functions
Oct. 23 Exam 2
Oct. 25 no class LEAP Symposium
Oct. 28 13.1 (pgs. 759-766) iterated integrals Iterated Integrals
Oct. 30 13.2 (pgs. 771-778) Fubini's Theorem, properties of double integrals, changing order of integration Double Integral Regions
Nov. 1 13.3 (pgs. 780-781) double integrals and polar coordinates 3d Integral Pictures
Nov. 4 13.3 (pgs. 782-785) more polar coordinates and procedure for triple integrals
Nov. 6 13.6, 13.7 (pgs. 808, 828, 831-832) motivation for triple integral, cylindrical and spherical coordinates
Nov. 8 13.6 (pgs. 809-818, 829-830, 833) setting up triple integrals First Example
Nov. 11 13.6, 13.7 (pgs. 809-818, 829-830, 833) more triple integrals Examples
Nov. 13 9.2, 9.3 (pgs. 511-515, 527-528) brief recap of parametric equations and arc length
Nov. 15 14.1, 14.2 (pgs. 840-846, 850-851) line integrals, vector fields Line Integral
Nov. 18 14.2 (pg. 857) gradient vector field Vector Field Generator (not my own!)
Nov. 20 Exam 2
Nov. 22 14.3 (pgs. 859-864) line integrals over vector fields
Nov. 25 14.3 (pgs. 865-868) fundmental theorm of line integrals
Dec. 2 14.3, 14.4 (pgs. 868, 874-876) conservative vector fields, Green's Theorem
  Dec. 4/td> 14.4 (pgs. 870-873, 877-878) Divergence Theorem
  Dec. 6 14.7 (pgs. 900-908) Overview of Stoke's Theorem
  Dec. 9 final exam review

Homework Assignments

Homework assignments are due on Gradescope at 3:00 PM on the date listed below. See the syllabus for more information about submitting homework.

Show your work on the homework. Answers with no work will receive zero points.

Due date Problem Set
Sept. 6 Homework 1
Sept. 10 Homework 2
Sept. 13 Homework 3
Sept. 17 Homework 4
Sept. 20 Homework 5
Sept. 24 Homework 6
Oct. 1 Homework 7
Oct. 4 Homework 8
Oct. 8 Homework 9
Oct. 11 Homework 10
Oct. 18 Homework 11
Oct. 29 Homework 12
Nov. 1 Homework 13
Nov. 5 Homework 14
Nov. 8 Homework 15
Nov. 12 Homework 16
Nov. 15 Homework 17
Nov. 22 Homework 18
Nov. 26 Homework 19
Dec. 3 Homework 20
Dec. 6 Homework 21
Dec. 10 Homework 22 (TBA)

Quiz Topics

Quizzes will be posted on Gradescope at 10 AM on the day listed under "Posting Date". They are due by 10 PM on the day listed under "Due Date" (36 hours after they are posted). You will have 30 minutes from the time you first access the quiz to complete it.

Quiz Posting Date Due Date Section(s)
# 1 Sept. 10 Sept. 11 10.1 and 10.2 (testing your knowledge of definitions and basic properties)
# 2 Sept. 17 Sept. 18 10.3-10.5
# 3 Oct. 1 Oct. 2 12.3, 12.7
# 4 Oct. 8 Oct. 9 12.3, 12.5, 12.6
# 5 Oct. 29 Oct. 30 9.4, Lagrange multipliers
# 6 Nov. 4 Nov. 7 13.1, 13.2
# 7 Nov. 12 Nov. 13 13.3, basic triple integrals, cylindrical and spherical coordinates
# 8 Dec. 3 Dec. 4 14.1-14.3