Math 2E – Multivariable Calculus

Welcome to Math 2E, even more fun in several variables! In this course, we will pick up where Math 2D left off, and finish the material on integration. Then, we will delve into the beautiful world of vector calculus. Enjoy the ride! On this page you can find the syllabus and info about the exams, including practice exams.


Syllabus

Here is the syllabus for the course: Syllabus


Lecture Notes and Videos

Lecture Notes Title YouTube Videos
Lecture 1 15.2, 15.3 Review: Double and Triple Integrals Order of Integration
Important Surfaces Polar Integral
Multivariable Integral
Integral over a ring
Volume of Ice Cream Cone
Lecture 2 15.6 Review: Triple Integrals (I) Gaussian Integral
Triple Integrals
Integral sin(x^2)
Golden Integral
Lecture 3 15.6 Review: Triple Integrals (II) Intersection of 2 cylinders
Lecture 4 15.7 Cylindrical Coordinates Cylindrical Coordinates
Intersection of 3 cylinders (optional)
Lecture 5 15.8 Spherical Coordinates (I) Derivation of Spherical Coordinates
Lecture 6 15.8 Spherical Coordinates (II) Mass of the sun
Spherical Coordinates Example
Volume of Ice Cream Cone
Lecture 7 15.9 Change of Variables (I) The Jacobian
Lecture 8 15.9 Change of Variables (II) The Jacobian (II)
Change of Variables
r dr dtheta
Hyperbolic Coordinates
Lecture 9 16.1 Vector Fields Vector Calculus Overview
Lecture 10 16.2 Line Integrals (I) Parametric Equations
Line Integral
Line Integral Example
Line Integral Derivation
Integral over a Helix
Line Integral Another Example
Line Integral of a function
Lecture 11 16.2 Line Integrals (II) Line Integral with respect to x
Line Integral of a Vector Field
Lecture 12 16.3 FTC of Line Integrals (I) FTC of Line Integrals
Lecture 13 16.3 FTC of Line Integrals (II) FTC Example
FTC 3D Example
Path Independence
FTC Pitfalls
Lecture 14 Midterm
Lecture 15 16.4 Green’s Theorem (I) Green’s Theorem
Lecture 16 16.4 Green’s Theorem (II) Area of Ellipse
Area of Polygon
Winding Number (optional)
Lecture 17 16.6 Parametric Surfaces (I) Tangent Plane to Surface
Lecture 18 16.6 Parametric Surfaces (II) Surface Area of Sphere
Lecture 19 16.7 Surface Integrals (I) Surface Integral of Function
Lecture 20 16.7 Surface Integrals (II) Surface Integral of Vector Field
Lecture 21 16.5, 16.9 Divergence Theorem (I) Divergence Theorem
Lecture 22 16.9 Divergence Theorem (II) Derivative of Volume
Volume of Polyhedron (optional)
Lecture 23 16.5 Curl
Lecture 24 16.8 Stokes’ Theorem (I) Integral over a barrel
Lecture 25 16.8 Stokes’ Theorem (II) Stokes’ Theorem
Lecture 26 Review: Surface Integrals
Lecture 27 Review: Line Integrals
Lecture 28 Review: Parametric Surfaces Surface Area of Donut

Suggested Homework

Suggested homework is not to be turned in, but important for the quizzes and the exams.

Here are solutions to all the problems in Stewart:

Chapter 15 – Solutions

Chapter 16 – Solutions

Suggested Homework “Due” Date Comments
Homework 1 Thursday, January 9 AP Solution
Homework 2 Thursday, January 16
Homework 3 Thursday, January 23 AP Solutions
Homework 4 Thursday, January 30
Homework 5 Thursday, February 6
Homework 6 Thursday, February 13 AP Solution
Homework 7 Thursday, February 20 AP Solutions +
16.6.64(a) Solutions
Homework 8 Thursday, February 27
Homework 9 Thursday, March 5 AP Solutions
Homework 10 Thursday, March 12 AP Solutions

 


Useful links

Canvas Course Site (mainly to check your quiz and exam scores)

My Youtube Channel

Chapter 15 – Playlist

Chapter 16 – Playlist


Exams

Here you can find information about the exams, as well as other goodies such as study guides and practice exams.

 

Midterm Exam: Covers everything up to and including 16.3 (FTC of line integrals)

Lecture A: Friday, February 7, 11-11:50 AM in 104 Rowland Hall

Lecture F: Friday, February 7, 10-10:50 AM in 1600 Donald Bren Hall

 

Study Guide: Study Guide

Mock Midterm: Mock Midterm (Solutions)

Winter 2020 Midterm (10 am lecture): Midterm (Solutions)

Winter 2020 Midterm (11 am lecture): Midterm (Solutions)

Fall 2018 Midterm: Midterm (Solutions)

Review Problems: Midterm Review

More practice: More practice (courtesy Sho Seto)

Important Surfaces: Surfaces

Chapter 15 – Playlist

Chapter 16 – Playlist

 

Final Exam: Covers everything in this course

Lecture A: Friday, March 20, 8-10 AM, on Canvas

Lecture F: Monday, March 16, 10:30-12:30 PM on Canvas

 

Final Exam Instructions: Instructions (important, please read)

Study Guide: Study Guide

Mock Final: Mock Final (Solutions)

Winter 2020 Final Exam (10 am lecture): Final Exam (Solutions)

Winter 2020 Final Exam (11 am lecture): Final Exam (Solutions)

Fall 2018 Final Exam: Final Exam (Solutions)

More practice: More practice (Solutions; courtesy Sho Seto)

Vector Calculus Overview: Vector Calculus Overview

Line Integral Roadmap: Line Integrals

Surface Integral Roadmap: Surface Integrals

Line vs. Surface Integrals: Line vs. Surface Integrals

Five FTC: Five FTC

Chapter 15 – Playlist

Chapter 16 – Playlist