## Math 314 - Calculus of Several Variables - Winter 2021

### Class Information

Instructor: Tuan Pham
Section 7
Class meetings: MWF 3:00 - 3:50 PM at TMCB 159.
Those unable to join in-person can join online at this link.
[Syllabus]   [Class Schedule]   [Learning Suite]   [WebAssign]

### Office Hours

MWF 4:00 - 5:00 PM and TTh 3:30 - 4:45 PM on Zoom at this link (not the same link at class meetings!)

### Assignments

• The schedule of written homework is here. It is to be submitted on Learning Suite.
• The schedule of online homework is on WebAssign or Learning Suite.
• ### Lecture notes

• Lecture 39 (Apr 14): review
• Lecture 38 - draft (Apr 12): Stokes theorem
• Lecture 37 - draft (Apr 9): surface integral
• Lecture 36 - draft (Apr 7): surface parametrization and surface area
• Lecture 35 - draft (Apr 5): divergence and curl
• Lecture 34 - draft (Apr 2): divergence of a vector field
• Lecture 33 - draft (Mar 31): Green's theorem
• Lecture 32 - draft (Mar 29): fundamental theorem of calculus for line integral
• Lecture 31 - draft (Mar 26): line integral of a vector field
• Lecture 30 - draft (Mar 24): line integral
• Lecture 29 - draft (Mar 22): vector fields
• Lecture 28 - draft (Mar 17): spherical coordinates
• Lecture 27 (Mar 15): review
• Lecture 26 - draft (Mar 12): change of variables
• Lecture 25 - draft (Mar 10): cylindrical coordinates, geometric transformation
• Lecture 24 - draft (Mar 8): more examples on triple integral
• Lecture 23 - draft (Mar 5): integral over a polar region, triple integral
• Lecture 22 - draft (Mar 3): integral over polar rectangle
• Lecture 21 - draft (Mar 1): average value, integral over a general region
• Lecture 20 - draft (Feb 26): double integral, iterated integral
• Lecture 19 - draft (Feb 24): extrema of a function (with constraints)
• Lecture 18 - draft (Feb 22): extrema of a function (without constraints)
• Lecture 17 - draft (Feb 19): geometric interpretation of the gradient vector
• Lecture 16 - draft (Feb 17): directional derivatives, the gradient
• Lecture 15 - draft (Feb 16): chain rule
• Lecture 14 - draft (Feb 12): tangent plane, linear approximation, differential
• Lecture 13 - draft (Feb 10): partial derivatives, Clairaut's theorem
• Lecture 12 - draft (Feb 08): review
• Lecture 11 - draft (Feb 05): limit of a function
• Lecture 10 - draft (Feb 03): functions of several variables, domain, level sets
• Lecture 9 - draft (Feb 01): motion, velocity, speed, acceleration
• Lecture 8 - draft (Jan 29): length and curvature of a curve
• Lecture 7 - draft (Jan 27): integral of vector functions, tangent vectors, length of a curve
• Lecture 6 - draft (Jan 25): intersection of surfaces, limits and derivative of a vector function
• Lecture 5 - draft (Jan 22): intersection of planes, surfaces and curves
• Lecture 4 - draft (Jan 20): cross product, triple product, equation of lines
• Lecture 3 - draft (Jan 15): dot product, projection, cross product
• Lecture 2 - draft (Jan 13): vector addition, scaling, length
• Lecture 1 - draft (Jan 11): introduction, 3D coordinate system
• ### Remarks before / after class

• Some review problems for Final exam, answer key
• Examples of surface integral (supplement to Lecture 37): video (code: 67@rs6^k), notes
• Finding surface area (supplement to Lecture 35): video (code: eN3#8..M), notes
• Check if a vector field is conservative (supplement to Lecture 32): video (code: +*b5Fp7k), notes
• Some review problems for Midterm II, answer key
• Evaluating double and triple integrals using Mathematica
• Integral over a polar rectangle (supplement to Lecture 22): video (code: 9&J=5eHY), notes
• Finding extrema of a function (supplement to Lecture 18): video (code: %C4x4PdC), notes
• Extrema of a function (supplement to Lecture 17): video (code: 28.9P.A1), notes
• Tangent plane of ellipsoid (supplement to Lecture 14): video (code: 2ak3^H6p), notes
• Some review problems for Midterm I
• Plotting regions and level sets on Mathematica
• Why do I get wrong answers in Webassign?
• Plotting surfaces and curves on Mathematica
• Equation of planes (supplement to Lecture 4): video (code: WU!E9%p!), notes
• Finishing an example given in class on Jan 15, 2021
• Practice plotting functions on Mathematica