Absences
Danial:
Iftikhar:

# Detailed schedule for Math 241.

## Math 241: Week 1

Aug 24
Introduction (§12.1). Notes.
HW 1 (Due Fri Aug 28)
Aug 25
Review of parts of Calc I and II. Worksheet. Solutions.
Videos: Review of Taylor Series and Worksheet 8/25 problem 4
Aug 26
Vectors (§12.2) and the dot product (§12.3). Notes.
HW 2 (Due Mon Aug 31)
Aug 27
Parametric curves via vector arithmetic. Worksheet. Solutions.
Videos: Worksheet 8/27 problem 4 and Worksheet 8/27 problem 5
Aug 28
Dot product applications (§12.3) and equations for planes (§12.5). Notes.
HW 3 (due Wed, Sept 2)
Notes:
Class website: https://learn.illinois.edu (Moodle)

## Math 241: Week 2

Aug 31
Cross product (§12.4). Notes.
HW 4 (Due Fri, Sept 4)
Sept 1
Projections, distances, and planes. Worksheet. Solutions.
Videos: Worksheet 09/01 problem 2 and Worksheet 09/01 problem 5
Sept 2
Functions of several variables (§14.1). Notes.
Lecture Videos: Functions of Several Variables, and Level Curves and Surfaces.
Hopf fibration video.
HW 5 (Due Tue, Sep 08 due to labor day.)
Sept 3
Open Discussion (No worksheet): Vectors and the geometry of 3-space discussion.
Videos on Practice Exams: Practice Exam Problem 1 , Practice Exam Problem 2 , Practice Exam Problem 3 , and Practice Exam Problem 4 .
Sept 4
Level sets in 3d (§14.1); quadric surfaces (§12.6); intro to limits (§14.2). Notes.
More on limits.
HW 6 (Due Wed, Sept 09)
Notes:
No class on Monday, Sept 7 (Labor Day).
Class website: https://learn.illinois.edu (Moodle).
If you have a laptop or tablet, please bring it to section next week on Tuesday.

## Week 3

Sept 7
Labor Day, no class and HW 5 is due tomorrow not today.
Sept 8
If you have a laptop or tablet, please be prepared to use it during section today.
Sept 9
Limits in several variables (§14.2). Notes.
Lecture Videos: Limit of functions of two variables, Limit Examples, and Limit Laws.
Extras: Limit pictures;
HW 7 (Due Mon, Sept 14)
Sept 10
Quiz 1 during discussion section.
Functions of several variables; Limits. Worksheet. Solutions.
Videos: Worksheet Problem 2, Worksheet Problem 3, Past exam problem on limits,
Past exam Graph matching problem, and HW 6 # 13.
Sept 11
Limit laws (§14.2); Continuity in several variables (§14.2); partial derivatives (§14.3). Notes.
HW 8 (Due Wed, Sept 16)
Notes:
Midterm Exam 1 is next week on Tuesday, Sept 15 at 7pm (Illinois Time). Last date to apply for conflict exam is Friday, Sept 11, at 11:59 pm.

## Week 4

Sept 14
Applications of partial derivatives (§14.3 and §14.4). Notes.
Lecture Videos: Application of Partial Derivatives, Tangent Planes, and Differentiability.
Visualization: Heat equation.
HW 9 (Due Fri, Sept 18)
Sept 15
Review of Midterm 1.
Exam 1 at 7pm (Illinois time) tonight.
Videos: 2018 Practice Problem 1, 2018 Practice Problem 2, 2018 Practice Problem 3,
2018 Practice Problem 4, and 2018 Practice Problem 5.
Sept 16
No Class due to evening exam. However, HW 8 is due today.
Sept 17
Partial derivatives and differentiability. Worksheet. Solutions.
Sept 18
Chain rule (§14.5). Notes.
Lecture Videos: Chain Rule, and Derivation of Chain Rule.
HW 10 (Due Wed, Sept 23)
Notes:
Midterm 1 on Tuesday evening at 7pm (Illinois time). No class on Wednesday, Sept 16, due to evening exam.

## Week 5

Sept 21
More on the chain rule (§14.5), directional derivatives and the gradient (§14.6). Notes.
Lecture Videos: More Chain Rule, Directional Derivatives, and Visualization of Gradient vector.
HW 11 (Due Friday, Sept 25)
Sept 22
Open Discussion on Chain rule and directional derivatives.
Sept 23
More on the gradient (§14.6) and overview of optimization (§14.7–14.8). Notes.
Lecture Videos: More on gradient, and Overview of Optimization.
HW 12 (Due Mon, Sept 28)
Sept 24
Quiz 2 time window starts on Thursday, Sept 24, at 8am (Illinois Time) and ends on Friday, Sept 25 at 8am (Illinois Time).
Sept 25
Local min and max (§14.7). Notes.
Lecture Video: Local Min/Max, HW 13 (Due Wed, Sept 30)
Notes:
Midterm Exam 2 is next week on Tuesday, Sept 29.

## Week 6

Sept 28
Absolute min and max (§14.7). Notes.
Lecture Videos: Finding Min distance, Extreme Value Theorem (EVT) and Example, and distance Example.
Visualization: Min/max example.
HW 14 (Due Friday, Oct 2)
Sep 29
Review of Midterm 2.
Midterm 2 is tonight at 7pm (Illinois time)
Videos: 2019 midterm 1 Problem 5, 2019 midterm 1 Problem 6, 2019 midterm 1 Problem 10,
2019 midterm 2 Problem 6, and 2012 midterm 2 Problem 2.
Sep 30
No Class due to evening Midterm 2. However, HW 13 is due today.
Oct 1
Taylor series, the second derivative test, and changing coordinates. Worksheet. Solutions.
Oct 2
Constrained min/max (§14.8). Notes.
Video Lecture: Method of Lagrange Multipliers.
HW 15 (Due Wed, Oct 7)
Notes:
Midterm 2 on Tuesday evening at 7pm (Illinois time). No class on Wednesday, Sept 30, due to evening exam.

## Week 7

Oct 5
Introduction to space curves (§13.1–4). Notes.
Visualization: Cycloid.
HW 16 (Due Fri, Oct 9)
Oct 6
Constrained min/max via Lagrange multipliers. Worksheet. Solutions.
Oct 7
More on arc length (§13.3) and integrating functions on curves (§16.2, pages 1063–1065). Notes.
HW 17 (Due Mon, Oct 12)
Oct 8
Curves and integration. Worksheet. Solutions.
Quiz 3 time window starts on Thursday, Oct 08, at 8am (Illinois Time) and ends on Friday, Oct 09 at 8am (Illinois Time).
Oct 9
Vector fields (§16.1) and integrating them along curves (§16.2). Notes.
Example vector field: Live wind map
HW 18 (Due Wed, Oct 14)
Notes:
Midterm Exam 3 is next week on Tuesday, Oct 13.

## Week 8

Oct 12
More on integrating vector fields along curves; the Fundamental Theorem of Line Integrals (§16.2 and §16.3). Notes.
HW 19 (Due Fri, Oct 16 )
Oct 13
Review of Midterm 3.
Midterm 3 is tonight at 7pm (Illinois time).
Oct 14
No class due to evening exam. However, HW 18 is due today.
Oct 15
Integrating vector fields. Worksheet. Solutions.
Oct 16
Conservative vector fields (§16.3). NotesA and NotesB.
HW 20 (Due Wed, Oct 21)
Notes:
Midterm 3 on Tuesday, Oct 13, at 7pm (Illinois time). No class on Wednesday, Oct 14, due to evening exam.

## Week 9

Oct 19
Intro to multiple integrals (§15.1). Notes.
HW 21 (Due Fri, Oct 23)
Oct 20
Open discussion on Line integral problems.
Oct 21
Integrating over more complicated regions (§15.2 and §15.3). Notes.
HW 22 (Due Mon, Oct 26)
Oct 22
Multivariable integrals. Worksheet. Solutions.
Quiz 4 time window starts on Thursday, Oct 22, at 8am (Illinois Time) and ends on Friday, Oct 23 at 8am (Illinois Time).
Oct 23
Polar coordinates (§15.3) and applications (§15.4). Notes.
HW 23 (Due Wed, Oct 28)
Notes:
Midterm Exam 4 is next week on Tuesday, Oct 27.

## Week 10

Oct 26
Triple integrals (§15.6). Notes.
HW 24 (Due Fri, Oct 30)
Oct 27
Review of Midterm 4.
Midterm 4 is tonight at 7pm (Illinois time).
Oct 28
No class due to evening Exam. However, HW 23 is due today.
Oct 29
Transformations of the plane. Worksheet. Solutions.
Oct 30
Integrating in cylindrical and spherical coordinates (§15.7 and §15.8). Notes.
HW 25 (Due Wed, Nov 4)
Notes:
Midterm 4 on Tuesday, Oct 27, at 7pm (Illinois time). No class on Wednesday, Oct 28, due to evening exam.

## Week 11

Nov 2
Changing coordinates I (§15.9). Notes.
HW 26 (Due Fri, Nov 6)
Nov 3
No Discussion due to Election Holiday.
Nov 4
Changing coordinates II (§15.9). Notes.
HW 27 (Due Mon, Nov 9)
Nov 5
Integrating by changing coordinates. Worksheet. Solutions.
Nov 6
Surfaces in R3 (§16.6). Notes.
HW 28 (Due Wed, Nov 11)
Notes:

## Week 12

Nov 9
Area and integration on surfaces (§16.6 and §16.7). Notes.
Visualization: Cones.
HW 29 (Due Fri, Nov 13)
Nov 10
Surface Parametrizations Worksheet. Solutions.
Nov 11
Green’s Theorem (§16.4). Notes.
HW 30 (Due Mon, Nov 16)
Nov 12
Parametrizations and integrals. Worksheet. Solutions.
Quiz 5 time window starts on Thursday, Nov 12, at 8am (Illinois Time) and ends on Friday, Nov 13 at 8am (Illinois Time).
Nov 13
Green’s Theorem and conservative vector fields in 2D (§16.4), but mostly flux in 2D (§16.5). Notes.
HW 31 (Due Wed, Nov 18)
Notes:
Midterm Exam 5 is next week on Tuesday, Nov 17.

## Week 13

Nov 16
The Divergence Theorem in 2D (§16.5-16.9). Notes.
HW 32 (Due Fri, Nov 20)
Nov 17
Review of midterm 5.
Midterm 5 is tonight at 7pm (Illinois time).
Nov 18
No class due to evening exam. However, HW 31 is due today.
Nov 19
Green's Theorem. Worksheet. Solutions.
Nov 20
Surface integrals of vector fields and the divergence theorem in 3D (§16.7 and §16.9). Notes.
HW 33 (Due Wed, Dec 2)
Notes:
Midterm 5 is on Tuesday, Nov 17, at 7pm. No class on Wednesday, Nov 18, due to evening exam.

## Week 14

Nov 30
Stokes Theorem (§16.8), including the definition of the curl (§16.5). Notes.
HW 34 (Due Fri, Dec 4).
Dec 1
Surface integrals of vector fields. Worksheet. Solutions.
Dec 2
More on Stokes Theorem (§16.8), including understanding the curl (§16.5). Review of conservative vector fields. Notes.
HW 35 (Due Mon, Dec 7)
Dec 3
Stokes’ Theorem. Worksheet. Solutions.
Dec 4
Conservative vector fields in R3 (§16.8); Topology 101. Notes.
HW 36 (Due Wed, Dec 9)

## Week 15

Dec 7
Electrostatics and Gauss’s Law. (§16.9) Notes.
Dec 8
More on Stokes’ Theorem. Worksheet. Solutions.
Dec 9
Maxwell’s equations. Notes.
Dec 10