MTH 212 Multivariate Calculus (Fall 2022):
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 405.
- Office Hours: MTR 10:00-10:50 am and MW 12:00-12:50 pm or by appointment.
- Textbook: University Calculus, Early Transcendentals, 4th ed., by Hass, Heil, Weir, Thomas, and Bogacki (Pearson); paperback ISBN-13: 9780134995540.
OR
University Calculus, Early Transcendentals, Multivariable Calculus, 4th ed., by Hass, Heil, Weir, Thomas, and Bogacki (Pearson); chapters 9-17 only, ISBN-13: 9780135165119.
OR
if you have an access to MyLab Math from your previously taken math courses, you can use an electronic version of the textbook available online: make sure to get the student registration instructions from me. - 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_2022.
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 information.
- Schedule (updated as the semester progresses):
Week | | Sections for Reading and | Suggested Problems for Practice |
| Class Materials and Assignments |
8/29 | §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 |
9/5 | 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 9/6 WeBWorK1 due 9/9 |
9/12 |
§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 9/19 |
9/19 | Exam I is on 9/23 (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) Project 1: due 9/20; Project 1 Help file WeBWorK3 due 9/28 (new deadline!) |
9/26 |
§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 §12.2 Lecture notes §12.3 Lecture notes §12.4 Lecture notes §12.5 Demo on TNB-frame and acceleration: notebook WeBWorK4 due 10/3 |
10/3 |
§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 10/4; Project 2 Help file WeBWorK5 due 10/10 |
10/10 | No class on Friday (Fall Recess) §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 10/18 |
10/17 | Exam II is on 10/21 (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) Project 3: due 10/19 Project help: see Demo on polar curves and Demo on level curves and surfaces |
10/24 |
§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 10/26 |
10/31 | §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 Lecture notes §14.1 Project 4: due 11/4 Project help: see Demo on gradients and tangent planes and Demo on min/max/saddle points WeBWorK8 due 11/1 |
11/7 | Exam III on 11/11 (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 §14.4: exer. 1,3,5,7,9,13,15,17,21,23,25,29,31,33 |
Lecture notes §14.2 Lecture notes §14.3 Demo on double integrals: 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 ) WeBWorK9 due 11/8 |
11/14 |
§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 §14.5 Demo on triple integrals: notebook Lecture notes §14.6 WeBWorK10 due 11/17 (new deadline!) |
11/21 |
§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 follows Thursday schedule - no class! Thanksgiving Break: 11/23-11/27 | Lecture notes §14.7 Demo on triple integrals in cylindrical coord's: notebook Demo on triple integrals in spherical coord's: notebook WeBWorK11 due 11/28 |
11/28 | §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 §15.1 Lecture notes §15.2 Demo on vector fields: notebook Project 5: due 11/30 Project help: Demo notebooks on triple integrals WeBWorK12 due 12/2 |
12/5 | Exam IV on 12/09 (Friday) §15.3: exer. 1,3,5,7,9,19,21 §15.4: exer. 5,9,13,15,19-25 odd,37 §15.5: exer. 3,5,9,13,17,21,23,25 |
Lecture notes §15.3 Lecture notes §15.4 Lecture notes §15.5 Demo on surface parametrization and area: notebook Exam IV study guide and formula sheet practice problems for Exam IV (ignore exercises 11-13) (Exam IV solutions) |
12/12 | Final Exam: 12/13, 1:00-4:00 pm, SLC 223 | Final Exam study guide and formula sheet practice problems for the final (ignore problems 10 and 11 - "flux across surface") WeBWorK13 (last!) due 12/14 Project 6: due 12/15 Project help: Demo notebooks on vector fields and surface area |