MA261 Multivariate Calculus (Fall 2022)

Instructor: Folk Narongrit
Class Time: Tuesday/Thursday, 1:30-2:20, 2:30-3:20, and 3:30-4:20
Course Coordinator: Dr. Andrey Glubokov (

Learning outcomes (my version)
  • Understanding equations for lines, planes, quadric surfaces in 3D
  • Creating vector functions and parametrized vector functions
  • Be able to calculate velocity, acceleration, arc length, curvature
  • Be able to calculate partial derivatives and using the multivariable chain rule
  • Understanding the gradient, and using it to compute the directional derivatives and extremas.
  • Computing and applying double and triple integrals in 2D/3D
  • Computing vector fields, line integrals, and surface integrals.
  • Applying Green’s theorem, Stoke’s theorem, the fundamental theorem for line integrals, along with the direct method, to compute different integrals



Fall 2022 Exam 1 Solutions

Exam Review

Exam 1 – things you should be able to do
Exam 2 – things you should be able to do
Professor Johnny Brown’s Study Guide Exam 1 / Exam 2 / Final
Line and Surface Integral Flowcharts
Select Past Exam Solutions
Supplmental Instruction Study Session One-Page Notes Fall 2022

01 Vectors, Lines, Planes
02 Quadric Surfaces, Vector-Valued Functions
03 Calculus of Vector Functions, Motions in Space, Length of Curve
04 Curvature, Functions of Several Variables, Level Curves
05 Limits, Partial Derivatives
06 Tangent Plane, Linear Approximation, Max-Min Problems
07 Lagrange Multipliers
09 Double and Triple Integrals
10 Polar, Cylindrical, Spherical Coordinates
11 Spherical, Line Integral, Vector Fields
13 Conservation, Green’s Theorem, Fundamental Theorem, Gradients
14 Surface Integral
15 Stokes and Divergence Theorem

Exam 1: October 4, 8pm
Exam 2: November 8, 8pm

Course contents is under copyright protections of the instructor and licensed to you through CC BY-NC-ND 4.0 DEED.