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)
HW: http://www.webassign.net/uiuc/login.html
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 3space 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.
Lecture Videos: Quadric Surfaces,
Visualizing Quadric Surfaces, and
Intro to Limit.
Interactive guide to quadric surfaces.
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

Visualizing Quadratic Surfaces.
Worksheet.
Solutions.
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.
Visualization: Gradient and level sets.
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

Open discussion on Gradient.
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 R^{3} (§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 (§16.516.9).
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 R^{3} (§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

Reading day.
 Dec 11

Finals begin.
 Dec 18

Finals end.
 Notes:
