Math 215: Multivariable and Vector Calculus

Syllabus

The syllabus is available on Canvas.

Important dates

  • Last day to add/drop without “W”: [2022-09-19 Mon]
  • Midterm 1: [2022-10-06 Thu] 6pm–8pm
  • Midterm 2: [2022-11-10 Thu] 6pm–8pm
  • Final Exam: [2022-12-14 Wed] 8am–10am

Office Hours

  • Monday’s 9a–10a (Math Atrium in East Hall)
  • Wednesday’s 1p–2p (Math Lab)
  • Friday’s 9a–10a (Math Atrium in East Hall)
  • You may also attend any instructor’s office hours (see Canvas syllabus) or go to the Math Lab when they are open.

Homework Schedule

  • Written HW due every Tuesday
  • WebHW due every Saturday
  • Prelab assignments due the day of your lab meeting

Resources

  • For practice problems, look at examples and exercises in the corresponding textbook sections; answers to odd numbered questions are in the back of the book.
  • For more challenging problems, look at old exams.

Class Schedule, Notes, and Recordings

Note, recordings will be available for 7 10 days after the lecture, and will then be unpublished.

Date Topics Book Sections Notes and Recording (Section 10) Notes and Recording (Section 50) Additional Notes
[2022-08-29 Mon] Coordinates and vectors 12.1 & 12.2 Notes & Recording Notes & Recording Gateway Exam practice is available on WebHW
[2022-08-31 Wed] Dot product and cross product 12.3 & 12.4 Notes & Recording Notes & Recording  
[2022-09-02 Fri] Cross product and lines 12.4 & 12.5 Notes & Recording Notes & Recording  
[2022-09-05 Mon] No class (Labor Day)        
[2022-09-07 Wed] Equations of planes 12.5 Notes & Recording Notes & Recording Gateway Exam is open until [2022-09-15 Thu]
[2022-09-09 Fri] Equations of planes, cylinders, and quadric surfaces 12.5 & 12.6 Notes & Recording Notes & Recording  
[2022-09-12 Mon] Vector functions and space curves 13.1 & 13.2 Notes & Recording Notes & Recording  
[2022-09-14 Wed] Arc length and curvature 13.3 Notes & Recording Notes & Recording  
[2022-09-16 Fri] Velocity and acceleration 13.4 Notes & Recording Notes & Recording  
[2022-09-19 Mon] Functions of several variables 14.1 Notes & Recording Notes & Recording  
[2022-09-21 Wed] Partial derivatives 14.3 & 14.4 Notes & Recording Notes & Recording  
[2022-09-23 Fri] Tangent plane, linear approximation, and chain rule 14.4 & 14.5 Notes & Recording Notes & Recording  
[2022-09-26 Mon] Chain rule, directional derivative, and gradient 14.5 & 14.6 Notes & Recording Notes & Recording  
[2022-09-28 Wed] More gradient and local extrema 14.6 & 14.7 Notes & Recording Notes & Recording Written HW 4 due [2022-10-03 Mon] instead of Tuesday!
[2022-09-30 Fri] Local extrema continued and review 14.7 Notes & Recording Notes & Recording  
[2022-10-03 Mon] Review   Notes & Recording Notes & Recording Lecture had a substitute teacher; provided notes differ from lecture.
[2022-10-05 Wed] Review   Notes & Recording Notes & Recording Note, I made a few mistakes in lecture, but notes are corrected.
[2022-10-07 Fri] Global extrema 14.7 Notes & Recording Notes & Recording  
[2022-10-10 Mon] Lagrange multipliers 14.8 Notes & Recording Notes & Recording  
[2022-10-12 Wed] Double integrals on rectangular regions 15.1 Notes & Recording Notes & Recording  
[2022-10-14 Fri] Double integrals on general regions 15.2 Notes & Recording Notes & Recording  
[2022-10-17 Mon] No class (Fall Break)        
[2022-10-19 Wed] Double integrals on general regions continued & polar regions 15.2 & 15.3 Notes & Recording Notes & Recording Lecture had a substitute teacher; provided notes differ from lecture.
[2022-10-21 Fri] Double integrals in polar coordinates 15.3 Notes & Recording Notes & Recording Lecture had a substitute teacher; provided notes differ from lecture.
[2022-10-24 Mon] Applications of double integrals 15.4 & 15.5 Notes & Recording Notes & Recording  
[2022-10-26 Wed] Triple integrals 15.6 Notes & Recording Notes & Recording  
[2022-10-28 Fri] Triple integrals continued 15.6 Notes & Recording Notes & Recording  
[2022-10-31 Mon] Triple integrals in cylindrical and spherical coordinates 15.7 & 15.8 Notes & Recording Notes & Recording Written HW 7 due [2022-11-07 Mon] instead of Tuesday!
[2022-11-02 Wed] More triple integrals, comparisons, and vector fields 15.8 & 16.1 Notes & Recording Notes & Recording  
[2022-11-04 Fri] Line integrals 16.2 Notes & Recording Notes & Recording  
[2022-11-07 Mon] Midterm 2 Review   Notes & Recording Notes & Recording  
[2022-11-09 Wed] Midterm 2 Review   Notes & Recording Notes & Recording  
[2022-11-11 Fri] Fundamental theorem for line integrals 16.3 Notes & Recording Notes & Recording  
[2022-11-14 Mon] Green’s theorem 16.4 Notes & Recording Notes & Recording  
[2022-11-16 Wed] Green’s theorem (cont), divergence, and curl 16.4 & 16.5 Notes & Recording Notes & Recording  
[2022-11-18 Fri] Parametric surfaces 16.6 Notes & Recording Notes & Recording  
[2022-11-21 Mon] Surface integrals of scalar functions 16.7 Notes & Recording Notes & Recording  
[2022-11-23 Wed] No class        
[2022-11-25 Fri] No class        
[2022-11-28 Mon] Surface integrals of vector fields 16.7 Notes & Recording Notes & Recording  
[2022-11-30 Wed] Stokes’ theorem 16.8 Notes & Recording Notes & Recording  
[2022-12-02 Fri] Divergence theorem 16.9 Notes & Recording Notes & Recording  
[2022-12-05 Mon] Divergence theorem continued 16.9 Notes & Recording Notes & Recording  
[2022-12-07 Wed] Final review   Notes & Recording Notes & Recording  
[2022-12-09 Fri] Final review   Notes & Recording Notes & Recording  

In response to questions about similarities between Stokes’ theorem and Divergence theorem, I have made some BONUS and OPTIONAL notes on differential forms and generalized Stokes’ theorem: Optional Bonus notes on differential forms. See also the Wikipedia article on differential forms.

Date published: Monday, August 29, 2022