Math 100: Differential Calculus with Applications
Section V02

Winter Term 2024

Lior Silberman

General Information

Office: MATX 1112, 604-827-3031
Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
Office hours (Fall 2024): after class (W 10:00-10:30 at the ESB atrium, W 14:00-14:30 at WW IRC Atrium), M 10:30-11:30 in my office, and by appointment.

Classes: TTh 8:00-9:30 ORCH 3018.
Tutorial: T 14:00-15:00 at ORCH 3062, Th 11-12 at ORCH 4062
Syllabus.
The default textbooks for pre-class reading and after-class practice are [1,4]. That said, there are many good textbooks in the field – see the References section below for a small selection of free and commercial textbooks. If you choose one of references [3,5,6,10] you may consult the old comparison table detailing how section numbers in those books correspond to the course topics.
The Lecture-by-lecture schedule below contains pre-class reading information, worksheets and more.

Additional resources

General questions (rule of thumb: any question that can be answered without knowing your name or student number) should be asked on the Piazza discussion forum. This includes both mathematical questions and questions about the syllabus or course policies.
Questions or requests concerining your personal case (grading issues, exemptions, etc) should be made to the instructor by email.
The Math Learning Centre is open Monday through Friday.
Here are some Common Errors in Undergraduate Mathematics. Avoiding these common pitfalls will improve your grade measurably.

Exams

Final

The final exam will be held on Sunday, April 21st between 12:00-14:30.
The department has lots of past final exams posted online that you can use for practice. Here are some tips regarding past exams.
- Until 2021 what is now MATH 100A,B,C used to be called MATH 100,102,104, so exams from all three courses are relevant. Science-flavoured questions are more likely to be found in past MATH 100 exams, DE questions are more likely to be found in past MATH 102 exams; Multivariable optimization questions may be found in past exams from MATH 105.
- The topics covered in our course are not identical year-to-year (with a big change in 2022WT1), so past exams include problems on topics we haven't covered, and may not include problems on topics we have covered.
- After some revising, it is essential to do at least one or two such exams under exam conditions: reserve 2.5 hours and work on the exam in a quiet room without using prohibited resources (notes/textbooks/calculators/friends/internet).
- We don't post solution to past exams in general, but some solutions (and hints!) are available on the Math Exam Resources Wiki. Also, the Undergraduate Math Society sells solutions to some past exams – both through their website and at their office in the Math Annex building.
Additional resources for preparing for the final exam include:
- Problems from the CLP problem book, which has many problems beyond the recommended problems for each week, as well as the Schaum's Outline textbook (reference [1] below).
- The worksheets and midterms.
I will hold review sessions ahead of the exam.
- For fairness reasons I cannot prepare my own material for such sessions — Instead the session will be entirely based on questions proposed by participants. You can submit problems in advance by email or ask them on the spot.

Midterm II

There will be a midterm exam in-class on Thursday, March 26.
Midterm information (also avilable as PDF)
Here are the test and the solutions

Midterm I

There will be a midterm exam in-class on Thursday, Feburary 15.
Midterm information (also avilable as PDF)
Here are the test and the solutions (files hosted on Canvas).
Here are the test and the solutions for retake 1.
Here are the test and the solutions for retake 2.

There will be two problem sets, due on Friday April 12th. Please submit typeset solutions by uploading a PDF file to the relevant Canvas assignment. The instructor recommends LyX for typesetting. If you need help with the mathematics or the typesetting don't hesitate to ask on Piazza or come to office hours.

Problem Set 1: PDF, LyX, LaTeX.
Problem Set 2: PDF, LyX, LaTeX.

Course Schedule

Ahead of each class you must read the relevant section from a textbook of your choice. Suggested problems for each lecture are from the same book as the suggested reading (CLP and OIL have a separate problem book but it is available at the same link).

Warning: the following information is tentative and subject to change at any time

Week	Date	Material	Reading	In-class	Suggested practice	Notes
1	T 9/1	Welcome & Motivation Asymptotics		Slides WS 1, Soln, Scan
1	Th 11/1	(continued)	Keshet Ch. 1	Scan
2	T 16/1	Limits	§§1.3-1.4	WS 2, Soln, Scan	§1.3 Q1-17 §1.5 Q1-8,13-15,17-19,27 §3.6.1 Q1,4,6	Evaluate limits in suggested problems using asymptotic thinking
2	Th 18/1	Derivatives Linear approximation	§§2.2-2.3 §3.4.2	WS 3, Soln, Scan	§2.2 Q1-5,9,10,12,18,26 §2.3 Q1-7 §3.4.2 Q1,5
3	T 23/1	Calculating derivatives	§2.4	WS 5, Soln, Scan	§2.4 Q7-10,13,15,16
3	Th 25/1	Exponential growth and decay Trig functions	§2.7 §3.3 §2.8	WS 6 Soln Scan
4	T 30/1	The Chain Rule	§2.9	WS 7, Soln Scan	§2.9 Q1-30
4	Th 1/2	Implicit Differentiation Related Rates Partial differentiation	CLP §2.10 CLP §2.11 OIL §§2.1	WS 8, Soln Scan	CLP §2.10 Q2,4-6,8-19,21-31 CLP §2.11 Q4-15 OIL §2.1 Q1-4
5	T 2/6	Curve sketching	§3.6	WS 9, Soln, Scan	§3.6.3 Q1-4; §3.6.6 Q1-10	Curve Sketching Notes
5	Th 2/8	Taylor expansion I	§§3.4.1-8	WS 10, Soln, Scan	§3.4.4 Q1-3; §3.4.5 Q1,2,5,6,9,10
6	T 2/13	Taylor expansion II	(same)	(same WS), Scan, Review
6	Th 2/15	Midterm I
2/19-23		Winter break
7	T 27/2	Inverse Trig Logarithmic differentiation	§2.12	WS 11, Soln, Scan	§2.12 Q6,7,9
7	Th 29/2	Differential Equations	CLP §3.3 Keshet §12.1, Ch. 13	WS 12, Soln, Scan	§3.3.1 Q1-5; §3.3.2: Q1,4,9 §3.3.3 Q1-6; §3.3.4: Q1,2,4-8
8	T 5/3	(continued)		WS 13, Soln, Scan
8	Th 7/3	Related Rates	§3.2	WS 14, Soln, Scan	§3.2	Related rates/Optimization Advice
9	T 12/3	Optimization	§3.5	WS 15, Soln, Scan	§3.5.1 Q1-7 §3.5.2 Q2,4,5 §3.5.2 Q1-15	Related rates/Optimization Advice
9	Th 14/3	(continued)	(same)	(same WS) Scan
10	T 19/3	Numerical computation: Euler Scheme	Keshet §12.3	Scan		Python code
10	Th 21/3	(continued)		(same WS) Scan
11	T 26/3	Review of Basics	N/A	WS 16, Scan
11	Th 28/3	Midterm II
12	T 2/4	Discussion of Midterm 2
12	Th 4/4	Multivariable sketching Multivariable differentiation	OIL §§1.1-3 OIL §§2.1-3	WS 17, Soln, Scan	OIL §1.1 Q1; §1.2 Q4-5 OIL §2.1 Q1-4; §2.2 1-6 OIL § 2.3 4-17 (do not classify critical points)
13	T 9/4	Multivariable optimization	OIL §§2.3-4	WS 18, Soln, Scan	OIL §2.4 Q1-11,13
13	Th 11/4	Review	Scan
	F 19/4	Review	Scan
	Su 21/4	12:00-14:30 Final Exam	Good luck!

References

Ayers, Schaum's Outline of Theory and Problems of Differential and Integral Calculus (all editions and versions are fine).
Belevan, Hamidi, Malhotra, and Yaeger, Optimal, Integral, Likely.
Boelkins, Austin and Schlicker, Active Calculus.
Feldman, Rechnitzer, and Yaeger, CLP-1 Differential Calculus textbook (see also the associated problem book)
Fowler and Snapp, Mooculus.
Hartman et al, APEX Calculus.
Keshet, Differential Calculus for the Life Sciences.
Mendelson, Schaum's Outline of Calculus.
Spiegel and Moyer, Schaum's Outline of College Algebra (all editions and versions are fine).
Stewart, Calculus: Early Transcendentals.

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Math 100: Differential Calculus with Applications Section V02