MATH_V 317 201 2024W2 Calculus IV

MATH 317  Multivariable and Vector Calculus

Contact info:

Course Structure:

Lectures will be in person:

  • Monday, Wednesday, Friday, 2:00 pm to 2:50 pm in LSK 200.
  • Office hours: Fridays 3:00pm - 4:00pm in Math 226.
  • TA Office hours: Mukul: Wednesdays 1:00pm-2:00pm, AUDX132.  Ray:  Thursdays 2:30pm-3:30pm, AUDX 133.
  • Math Learning Centre (MLC). MLC runs every weekday from 12 pm to 7 pm. From 12 pm to 5 pm, MLC is in person and primarily located in MATH 102. On some days, additional space is available in case MATH 102 reaches capacity. From 5 pm to 7 pm, MLC operates online. MLC Canvas page

Learning Materials:

  • Main  Text:  CLP-4 Vector Calculus Textbook by Joel Feldman, Andrew Rechnitzer, and Elyse Yeager.  This locally developed text is available here. The companion Problem Books (draft versions) to this text, available at the same site, will also be useful.
  • I will post my lecture notes under "pages"-->"notes"
  • I will post practice midterms and finals before each midterm and final.
  • Piazza: Access our course Piazza page from Canvas. The TA and I will answer questions there. 

Webwork

Weekly webwork assignments will appear on the Assignments tab in Canvas. Assignments are due on Monday at 3am. Always access the webwork assignment through the link in Canvas (otherwise the grades don't sync correctly). I will drop the lowest Webwork grade for each student at the end of the term.

Assessment of Learning:

There will be weekly webwork assigned as well as two midterms.  The course grade will normally be given by the better of the following two schemes: 

  • 50% Final Exam + 40% Midterm grades + 10% WebWork Grade, or
  • Scaled Final Exam grade - 10 

Please note that grades may be scaled.  

Midterm 1: In class, Wednesday, February 12th.

Midterm 2: In class, Friday,  March 14th. 

Final Exam:  April 22nd, 3:30pm--6:30pm, location TBD

Course Policies:

  • There will be two midterms during the term. There are no make-up midterms. Missing a midterm for a valid reason normally results in the weight of that midterm being re-distributed to the remaining midterm and final exam. Any student who misses a midterm is to present the Department of Mathematics self-declaration form for reporting a missed assessment to their instructor within 72 hours of the midterm date. This policy conforms with the UBC Vancouver Senate’s Academic Concession Policy V-135 and students are advised to read this policy carefully.

Course Topics: 

The topics fall broadly under two categories:

Vector valued functions of one variable:

We will study parameterize curves, velocity, acceleration, arclength, curvature, normal and binormal vectors, tangential and normal components of acceleration, planetary motion.   

Vector valued functions of several variables:

We will study vector fields, line integrals, conservative vector fields, and the fundamental theorem of line integrals. We will discuss necessary and sufficient conditions for a vector field to be conservative and learn how to find a potential function. We will study various forms of derivatives in vector calculus: Gradient, Curl, and Divergence. We will learn to parameterize surfaces and study integrals of functions over surfaces and flux integrals over surfaces. We will learn integral theorems: Green's theorem, Stoke's Theorem, and the Divergence theorem. Time permitting, we will use differential forms to translate vector calculus into a unified language that works in any dimension.

Schedule of Topics:

This is a tentative schedule. As the semester plays out, it will be adjusted accordingly.  

Week 1:  Introduction, parameterized curves, velocity, arclength. Chapters 1.0, 1.1 of CLP4

Week 2:    Parameterization by arclength, curvature of a curve, unit tangent vector and principle normal vector.  Chapters 1.2 and 1.3, some of 1.4 and 1.5

Week 3:  Motion, Velocity, Acceration, Newton's law, planetary motion. CLP4 1.3, some of 1.4 and 1.5, 1.10

Week 4:  Vector Fields, conservative vector fields, potential functions. CLP 2.1, 2.3

Week 5:  Line integrals, fundamental theorem of line integrals. Path independence, curl test, simply connected domains.  CLP 2.4, 4.5

Week 6:  Midterm 1. Parameterized surfaces,  CLP 3.1

Week 7:  Tangent planes, surface area. Integrals of functions on surfaces, integrals of vector fields (flux).  CLP  3.2, 3.3, 3.4, 3.5

Week 8: More flux, Divergence, CLP 4.1,

Week 9:  Interpretations of Grad, Curl, Div. . CLP 4.1

Week 10:  Midterm 2.  Divergence theorem. CLP 4.2

Week 11: Green's theorem, Stoke's theorem CLP 4.3, CLP 4.4

Week 12: Differential forms, generalized Stoke's theorem. CLP 4.7