MATH 2X03

(Fall 2019)

Dr. Madnick's Lectures: Mon & Wed & Thu. 1:30 pm - 2:20 pm. Location: JHE 264

Main Course Webpage: https://ms.mcmaster.ca/andy/courses/math2x03/

Logistical information about the course is on the "Main Course Webpage" listed above.

Logistical issues should be directed to Professor Nicas (not to Dr. Madnick).

Instructors:

Dr. Madnick (madnickj [at] mcmaster [dot] ca)
Prof. Nicas (nicas [at] mcmaster [dot] ca)

Teaching Assistants:

Anthony Tan (tana4 [at] mcmaster [dot] ca)
Pip Mathrau (mathap1 [at] mcmaster [dot] ca)

Tutorials:

For tutorial info, see the Main Course Webpage

Office Hours: HH = Hamilton Hall

Tuesday
- 3:35 pm - 4:25 pm (Prof. Nicas) (HH 310)
- 6:30 pm - 8:00 pm (Dr. Madnick) (HH 319)
Thursday
- 11:00 am - 2:00 pm (Pip & Anthony) (HH 104)
- 2:00 pm - 3:20 pm (Dr. Madnick) (HH 319)
Friday
- 11:30 am - 12:20 pm (Prof. Nicas) (HH 310)

The course will cover Chapter 15 (Lectures 1-13) and Chapter 16 (Lectures 14-35).

Important prerequisite knowledge from the textbook:

Sections 5.1 - 5.3 and 6.1
Sections 7.1 - 7.3
Chapter 12 (esp. 12.5 and 12.6)
Sections 14.1 - 14.3

Dr. Madnick's Lecture Notes

Lecture 1 (Wed 9/4)

Lecture 2 (Thu 9/5)

Lecture 3 (Mon 9/9) (Prof. Nicas)

Lecture 4 (Wed 9/11) (Dr. Rushworth)

Lecture 5 (Thu 9/12) (Dr. Rushworth)

Lecture 6 (Mon 9/16)

Lecture 7 (Wed 9/18)

Lecture 8 (Thu 9/19)

Lecture 9 (Mon 9/23)

Lecture 10 (Wed 9/25)

Lecture 11 (Thu 9/26)

Lecture 12 (Mon 9/30)

Lecture 13 (Wed 10/2)

Midterm 1: Thu 10/3 (Lectures 1 - 8)

Lecture 14 (Mon 10/7)

Lecture 15 (Wed 10/9)

Lecture 16 (Thu 10/10)

Lecture 17 (Mon 10/21)

Lecture 18 (Wed 10/23)

Lecture 19 (Thu 10/24)

Lecture 20 (Mon 10/28)

Lecture 21 (Wed 10/30)

Lecture 22 (Thu 10/31)

Lecture 23 (Mon 11/4)

Lecture 24 (Wed 11/6)

Lecture 25 (Thu 11/7)

Lecture 26 (Mon 11/11)

Lecture 27 (Wed 11/13)

Midterm 2: Thu 11/14 (Lectures 10 - 22)

Lecture 28 (Mon 11/18)

Lecture 29 (Wed 11/20)

Lecture 30 (Thu 11/21) (optional lecture)

Stokes' Theorem explanation

Lecture 31 (Mon 11/25)

Lecture 32 (Wed 11/27)

Notes on Maxwell's Equations (optional)

Lecture 33 (Thu 11/28) (optional lecture)

Lecture 34 (Mon 12/2) (optional lecture)

Final Exam: Sat 12/7

Review Problems for Final Exam:

Here is a set of 14 practice problems

These problems are excellent practice for the final exam. (Maybe one of them will reappear on the final exam, who knows?) Solutions will not be posted. However, you are welcome to discuss the problems with others, or to discuss them in office hours.

Helpful things to know for the exam: Stokes' Theorem; The Divergence Theorem in R^3; The conversion formula for spherical coordinates; Exact values of sine and cosine of common angles (0, pi/6, pi/4, pi/3, pi/2, etc.); How to compute the mass of an object given its density.

Don't worry about Section 15.9 (Change of Variables): it won't be covered. Don't worry about moments of inertia or centroids. Material in the lectures marked "optional lecture" also won't be covered.

More information about the final exam: https://ms.mcmaster.ca/andy/courses/math2x03/2X03finalexaminfo.html

Review Problems for Midterm 2. Here are 24 practice problems from the textbook. Answers are in the back of the book.

15.8 (Triple Integrals in Spherical): 21, 23, 25, 27
16.2 (Line Integrals): 9, 13, 19, 21
16.3 (Fundamental Theorem for Line Integrals): 5, 7, 9, 11, 13, 15, 17
16.4 (Green's Theorem): 5, 7, 9, 11, 13
16.5 (Curl and Divergence): 3, 13, 15, 19

Don't worry about Section 15.9 (Change of Variables). Don't worry about surface area. Don't worry about moments of inertia or centroids.

Make sure you're comfortable with: Spherical Coordinates; Line Integrals; Fundamental Theorem for Line Integrals; Conservative Vector Fields; Green's Theorem; Curl and Divergence.

More information about Midterm 2: https://ms.mcmaster.ca/andy/courses/math2x03/2X03test2info.html

Review Problems for Midterm 1. Here are 21 practice problems from the textbook. Answers are in the back of the book.

15.2 (Double Integrals in Cartesian): 17, 23, 27, 29, 31, 45
15.3 (Double Integrals in Polar): 7, 11, 13, 19, 21, 25, 27
15.4 (Mass & Center-of-Mass): 5, 7, 11, 13
15.6 (Triple Integrals in Cartesian): 13, 17, 21, 29

Make sure you know: Density / mass / moments for lamina. You should be very comfortable with: Double integrals in polar coordinates. Triple integrals (Cartesian coordinates only). Don't worry about surface area.

For additional practice -- especially with u-substitution -- you might also try:

15.1 (Integration practice): 29, 31, 33, 35, 39, 41.

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