MTH 212 Multivariate Calculus (Fall 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 for Reading and
| Suggested Problems for Practice
| Class Materials and Assignments

8/30 § 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
Lecture notes §11.1
Lecture notes §11.2

Read Mathematica tutorials (find links above)

Common Math Errors

Some trig integrals review

Demo on 3-space: Mathematica notebook

9/6 No class on Monday (Labor Day)

§ 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
Lecture notes §11.3
Lecture notes §11.4

Summary: Dot Product vs. Cross Product

Demo on vectors: Mathematica notebook

WeBWorK Orientation due 9/7
WeBWorK1 due 9/11

9/13 § 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
Lecture notes §11.5
Demo on lines and planes: Mathematica notebook

Conic sections

Quadrics (slides)
Demo on quadrics: Mathematica notebook

WeBWorK2 due 9/18

9/20 Exam I on 9/24 (Friday)

§ 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

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

Lecture Notes §12.2

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

Project 1: due 9/21; Project 1 Help file

9/27 § 12.2: exer. 1,5,9,11,15,17

§ 12.3: exer. 1,3,5,9,11,13,18

§ 12.4: exer. 1,3,7,9,13,17,19

§ 12.5: exer. 1,3,5,7,9,13,15

Lecture notes §12.3
Lecture notes §12.4
Lecture notes §12.5

Demo on TNB-frame and acceleration: notebook

WeBWorK3 due 9/29 (new deadline!)
WeBWorK4 due 10/4

10/4 § 10.3: exer. 1,3,5,7,9,13,17,21,25,27,31,33,37,
41,47,53,59,63

§ 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
Lecture notes §10.3
Lecture notes §§10.4,10.5
Demo on polar curves: notebook

Lecture notes §13.1
Demo on level curves and surfaces: notebook

Project 2: due 10/7; Project 2 Help file

WeBWorK5 due 10/11

10/11 No class on Friday (Fall Break)

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

§ 13.3: exer. 1,5,9,17,19,23,29,31,35,37,39,41,47,51,53,
55,59,61,69,70
Lecture notes §13.2
Demo on limits: notebook

Lecture notes §13.3
Demo on partial derivatives: notebook

WeBWorK6 due 10/19 (new deadline!)

10/18 Exam II on 10/22 (Friday)

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

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

Project 3: due 10/20
Project help:
see Demo on polar curves and
Demo on level curves and surfaces

10/25 § 13.5: exer. 1,5,7,11,15,19,23,27,29,31,33

§ 13.6: exer. 1,5,9,13,17,25,27,39,55

§ 13.7: exer. 1-30 odd
Lecture notes §13.5
Demo on directional derivatives: notebook

Lecture notes §13.6
Demo on gradients and tangent planes: notebook

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

WeBWorK7 due 10/27

11/1 § 13.8: exer. 1,5,9,13,17,21,23,29,31,33

§ 14.1: exer. 1,5,9,13,15,19,21,25

Lecture notes §13.8

Demo on volume partition: notebook

Project 4: due 11/4
Project help:
see Demo on gradients and tangent planes
and Demo on min/max/saddle points

WeBWorK8 due 11/2

11/8 Exam III on 11/12 (Friday)

§ 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
Lecture notes §14.1
Lecture notes §14.2

Demo on double integrals: notebook

Lecture notes §14.3

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

WeBWorK9 due 11/9

11/15 § 14.4: exer. 1,3,5,7,9,13,15,17,21,23,25,29,31,33

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

Lecture notes § 14.5
Demo on triple integrals: notebook

Lecture notes § 14.6

WeBWorK10 due 11/16

11/22 § 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

Tuesday (11/23) follows Thursday schedule - no class!

Thanksgiving Break: 11/24-11/28
Lecture notes § 14.7
Demo on triple integrals in cylindrical coord's: notebook
Demo on triple integrals in spherical coord's: notebook

WeBWorK11 due 11/23

11/29 § 14.8: exer. 1,3,5,7,9,11,15,21

§ 15.1: exer. 1-9,13,15,19,21,25,33,35
Lecture notes § 14.8

Project 5: due 12/3
Project help: Demo notebooks on triple integrals

12/6 Exam IV on 12/10 (Friday) Exam IV study guide and formula sheet
practice problems for Exam IV

WeBWorK12 due 12/7

12/13