MTH 212 Multivariate Calculus (Spring 2021):

This course studies differential and integral calculus of real and vector-valued functions. Topics include vectors and vector-valued functions; functions of several variables, limits, continuity, partial differentiation, gradient; line, surface, and multiple integrals; vector fields and theorems of Green and Stokes.
Week | Sections to Read and
| Suggested Problems for Practice
| Class Materials and Assignments

2/1 § 11.1: exer. 1,5,11,13,17,21,25,31,33,35,39,45,47,
51,59,61,65,69

§ 11.2: exer. 1,5,9,13,15,17,21,23,25,29,31,33,35,39,41,
43,45,49,51
Find 2 videos on syllabus and beginning of section 11.1
on live.wilkes.edu

§11.1 notes
§11.2 notes

Read Mathematica tutorials (see links above)

Common Math Errors

Some trig integrals review

Demo on 3-space: Mathematica notebook

2/8 § 11.3: exer. 1,5,7,9,13,15,19,23,25,29,31,43,45

§ 11.4: exer. 3,7,9,13,17,21,23,27,29,31,33,37,39,43,47
§11.3 notes
§11.4 notes

Summary: Dot Product vs. Cross Product

Demo on vectors: Mathematica notebook

WeBWorK Orientation due 2/10
WeBWorK1 due 2/12

2/15 § 11.5: exer. 1,3,7,9,13,19,21,23,25,27,29,31,35,41,
45,47,49,57,61,63-71 odd

A4 (conics): exer. 1,3,5,7,17,21,27,33,51,53,55,57

§ 11.6: exer. 1-12,13,19,23,27,31,33,37,41

§ 12.1: exer. 1,5,9,13,15,16,19,21,23,25,27-34

§ 10.1: exer. 1,5,13,19,23,36,38,39

§11.5 notes
Demo on lines and planes: Mathematica notebook

Quadrics (slides)
Demo on quadrics: Mathematica notebook

§12.1 notes (also see examples in §10.1)
Demo on parametric curves: notebook

WeBWorK2 due 2/19

2/22 Exam I on 2/26 (Friday)

§ 12.2: exer. 1,5,9,11,15,17

§ 12.3: exer. 1,3,5,9,11,13,18
§12.2 notes
§12.3 notes

Exam I: study guide and formula sheet
practice problems for Exam I
(Exam I solutions: Section A and Section B )

Project 1: due 2/24; Project 1 Help file

WeBWorK3 due 3/1

3/1 § 12.4: exer. 1,3,7,9,13,17,19

§ 12.5: exer. 1,3,5,7,9,13,15

§ 10.3: exer. 1,3,5,7,9,13,17,21,25,27,31,33,37,41,47,53,59,63
§12.4 notes
§12.5 notes

Demo on TNB-frame and acceleration: notebook

§10.3 notes
Demo on polar curves: notebook

WeBWorK4 due 3/6

3/8 § 10.4: exer. 1,5,9,13,27,29,31

§ 10.5: exer. 1,5,9,13,15,21,23,25

§ 13.1: exer. 1-29 odd,31-36,43,49,55,59,61,63

§ 13.2: exer. 1,7,11,13,17,21,31,33,35,59,61,65,67
§§10.4,10.5 notes

§13.1 notes
Demo on level curves and surfaces: notebook

§13.2 notes
Demo on limits: notebook

Project 2: due 3/10; Project 2 Help file

WeBWorK5 due 3/12

3/15 § 13.3: exer. 1,5,9,17,19,23,29,31,35,37,39,41,47,51,53,
55,59,61,69,70

§ 13.4: exer. 1,5,7,9,11,25,29,33,37,39,41,43

§ 13.5: exer. 1,5,7,11,15,19,23,27,29,31,33
§13.3 notes
Demo on partial derivatives: notebook

§13.4 notes

§13.5 notes
Demo on directional derivatives: notebook

WeBWorK6 due 3/21

3/22 Exam II on 3/26 (Friday)

§ 13.6: exer. 1,5,9,13,17,25,27,39,55

§ 13.7: exer. 1-30 odd
§13.6 notes
Demo on gradients and tangent planes: notebook

§13.7 notes
Demo on max/min/saddle points: notebook

Exam II study guide and formula sheet
practice problems for Exam II
(Exam II solutions: Section A and Section B )

Project 3: due 3/24
Project help: see Demo on polar curves and
Demo on level curves and surfaces

WeBWorK7 due 3/28

3/29 § 13.8: exer. 1,5,9,13,17,21,23,29,31,33

No classes 4/1-4/2
§13.8 notes

WeBWorK8 due 4/5

4/5 § 14.1: exer. 1,5,9,13,15,19,21,25

§ 14.2: exer. 1-11 odd,15,19,23,27,29,33,37,41,45,47,
51,53,57,59,61

§ 14.3: exer. 1,5,9,13,17,19,21

§ 14.4: exer. 1,3,5,7,9,13,15,17,21,23,25,29,31,33
§14.1 notes
§14.2 notes
Demo on double integrals: notebook

§ 14.3 notes

§ 14.4 notes
Demo on double integrals in polar form: notebook

Project 4: due 4/8
Project help:
see Demo on gradients and tangent planes
and Demo on min/max/saddle points

WeBWorK9 due 4/11

4/12 Exam III on 4/16 (Friday)

§ 14.5: exer. 3,5,9,13,17,21,25,27,37,41

§ 14.6: exer. 1,5,9,11,15,19,21,25,29,31
§ 14.5 notes
Demo on triple integrals: notebook

§ 14.6 notes

Exam III study guide and formula sheet
practice problems for Exam III

WeBWorK10 due 4/18

4/19 § 14.7: exer. 1,5,7,11,13,17,19,21,25,27,29,31,33,
37,41,43,47,51,55,57,63,67,71,75,85,86

§ 14.8: exer. 1,3,5,7,9,11,15,21

§ 15.1: exer. 1-9,13,15,19,21,25,33,35

4/26 No class on 4/28 (Wednesday) Project 5: due 4/26
Project help: Demo notebooks on triple integrals