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.- Make sure to read the course SYLLABUS.
- Instructor: Dr. Sofya Chepushtanova, office SLC 408, email: sofya.chepushtanova@wilkes.edu.
- Meeting Times: MTWF 09:00-09:50 am in SLC 403.
- Office Hours: MTWF 10:00-10:50 am and W 11:00-11:50 am or by appointment.
- Textbook: University Calculus, Early Transcendentals, 4th ed., by Hass, Heil, Weir, Thomas, and Bogacki (Pearson); paperback ISBN-13: 9780134995540.
- WeBWorK is an open-source online homework system for math and science courses supported by the MAA and the NSF. We will use it for our homework. The name of the WeBWorK course is
MTH_212_FALL_2023.
Expect the email with login info from webwork@mathcs.wilkes.edu. As you get it, you should log in and change your password once the account is active.
Note: never call the help desk for anything to do with WeBWorK. Report all the WeBWorK issues to your instructor. - Mathematica is a Wolfram's original product - primarily aimed at technical computing for R&D and education. We will use it for
demonstrations and projects. To start with Mathematica, use the following links and tutorials:
- Download instructions: Mathematica at Wilkes
- Video tutorials: hands-on Start to Mathematica
- Wolfram's Getting Started with Mathematica
- Mathematica manual
from the publisher of your textbook
- Another Mathematica tutorial
Important: you will use Wilkes LIVE (D2L) to submit Mathematica projects.
- Download instructions: Mathematica at Wilkes
- Tutoring TBA
- Schedule (updated as the semester progresses):
| 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 |