MTH 212 Multivariate Calculus (Fall 2023):

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

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
Lecture notes §11.1
Lecture notes §11.2

Demo on 3-space: Mathematica notebook

Read Mathematica tutorials (links above)

Common Math Errors

Some trig integrals review

WeBWorK Orientation due 9/1

2. 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 HW1 due 9/8

3. §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

WeBWorK HW2 due 9/19

4. Exam I is on 9/22 (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

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

WeBWorK HW3 due 10/2

5. §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
Lecture notes §12.2

Lecture notes §12.3

Lecture notes §12.4

6. §12.5: exer. 1,3,5,7,9,13,15

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

Lecture notes §12.5
Demo on TNB-frame and acceleration: notebook

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

Project 1: due 10/17
Project 1 Help file

WeBWorK HW4 due 10/6

7. No class on Friday (Fall Recess)

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

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

§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 §10.3

Lecture notes §13.3
Demo on partial derivatives: notebook

WeBWorK HW5 due 10/17

8. Exam II is on 10/20 (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)

WeBWorK HW6 due 10/20

9. §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
Lecture notes §13.5
Demo on directional derivatives: notebook

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

Project 2: due 11/7

WeBWorK HW7 due 10/27

10. §13.7: exer. 1-30 odd

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

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

Lecture notes §13.8

WeBWorK HW8 due 11/3 and HW9 due 11/7

11. §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

Lecture notes §14.1

Demo on volume partition: notebook

Lecture notes §14.2
Lecture notes §14.3

Demo on double integrals: notebook

WeBWorK HW10 due 11/14 (new deadline)

12. Exam III is on 11/17 (Friday)

§10.4: exer. 1,5,9,13,27,29,31

§10.5: exer. 1,5,9,13,15,21,23,25

§14.4: exer. 1,3,5,7,9,13,15,17,21,23,25,29,31,33
Lecture notes §§10.4,10.5
Demo on polar curves: notebook

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

Exam III study guide and formula sheet
practice problems for Exam III
(Exam III solutions )

WeBWorK HW11 due 11/29 (new deadline!)

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

Tuesday follows Thursday schedule: no class on 11/21

Thanksgiving Break: 11/22-11/26
Lecture notes §14.5
Demo on triple integrals: notebook


14. §14.6: exer. 1,5,9,11,15,19,21,25,29,31

§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

Lecture notes §14.6
Lecture notes §14.7

Demo on triple integrals in cylindrical coord's: notebook
Demo on triple integrals in spherical coord's: notebook

Project 3: due 12/1 (new deadline!)
Project help:
use demo notebooks on triple integrals

WeBWorK HW12 due 12/8

15. Exam IV on 12/8 (Friday)

§14.8 exer. 1,3,5,7,9,11,15,21

§15.1: exer. 1-9,13,15,19,21,25,33,35

§15.2: exer. 1,3,7,11,19,25,27,29,31,35,39,41,47

Lecture notes §14.8

Lecture notes §15.1

Lecture notes §15.2

Demo on vector fields: notebook

Exam IV study guide and formula sheet
practice problems for Exam IV
(Exam IV solutions)

16. Monday follows Friday schedule!

§15.4: exer. 5,9,13,15,19-25 odd,37

Final Exam: 12/13, 1:00-4:00 pm, SLC 411

Office hours during the finals week:
Tuesday, Wednesday 10:00 - 11:00 am
Lecture notes §15.4

Final Exam study guide and formula sheet
practice problems for the final

WeBWorK13 (last!) due 12/15