Math 125: Calculus I
USC Fall 2022

Instructors.

Time and location.

About.

This course is an introduction to calculus. Our main topics will be:

  1. functions, limits, and continuity
  2. derivatives and applications
  3. integrals and the fundamental theorem of calculus
  4. exponential and logarithmic functions.
We will follow sections 1.1-5.5 (inclusive) in the textbook by Stewart rather closely, with some exceptions.

I highly encourage (and expect) you to follow along concurrently with the relevant sections in the textbook. There may be some important material in the textbook that we do not cover in lectures (and vice versa). I recommend periodically re-reading the previous textbook sections in order to strengthen your understanding.

Mailing list.

If for some reason you aren't currently registered for this course on Blackboard please email Kyler to make sure you receive class emails.

Prerequisites.

Math 108 or placement exam.

Text.

The primary textbook is Essential Calculus (2nd edition) by James Stewart.

Problem sets.

In addition to the lectures, there will be weekly problem sets. These will be listed on this website (see the schedule below) and handed in via Gradescope. Late homeworks will not be accepted. However, we will drop the lowest problem set score.

Much of the course material will be developed in the problem sets. It is very important to do all of the problem sets to the best of your ability and to challenge yourself to solve the problems on your own, as this is the most effective way to absorb the material. We expect students to devote a significant amount of time to the problem sets.

While working on the problem sets, you are allowed to consult or collaborate with your peers, as well as textbooks and the internet (apart from cheating websites such as Chegg or Cramster). However, you must write down attributions for any peer, textbook, website etc from which you took any significant ideas. Moreover, you must attempt all problems on your own and your submitted solutions must be written out originally and individually. Submissions which are copied or suspiciously similar are subject to being rejected and potential disciplinary action.

Quizzes.

There will be quizzes every week (with some exceptions) assigned during the discussion sections.

Exams.

There will be two midterms (most likely during regular class time) and one final exam (scheduled by the registrar). All exams are graded on a curve, so please don't stress too much about the raw score. Note that the final exam will be shared with the other sections of Math 125.

Grading scheme.

Problem sets: 15%, quizzes: 10%, midterm exams: 40%, final exam: 35%. We will drop the lowest problem set grade and the lowest quiz grade.

Office hours.

Additional resources.

Tentative schedule.

Note: this schedule is tentative and will be continuously updated to adapt to the pace of the course. Please check back regularly for updates and problem set assignments. z
$\#$ Date Material References Problem set
1 Monday 8/22/22 Course introduction. Basics on sets and examples (reals, rationals, intervals, etc). Unions of sets. Functions between sets. Different ways of representing functions (symbolic, verbal, graphical, etc). Vertical line test. §1.1
2 Wednesday 8/24/22 More on functions. Domain, codomain, and range. Catalogue of functions. §1.1,§1.2 Pset 1 (due Weds 8/31/22 by 11:59pm) Pset 1 (due Weds 8/31/22 by 11:59pm):
§1.1: 2,4,5,6,7,8,28,30,36,60,62, §1.2: 5,17,18,19,43,50
3 Friday 8/26/22 Catalogue of functions continued. More practice with domain and range. Polynomials and their typical graphs. Power functions. Rational functions. Sine and cosine. §1.2
4 Monday 8/29/22 Introduction to limits. Left and right sided limits. Various examples and computational techniques. Computer graphs. §1.3,§1.4,§1.5
5 Wednesday 8/31/22 More on limits. Continuity and limit laws. The precise $\epsilon,\delta$ definition. §1.3,§1.4,§1.5 Pset 2 (due Weds 9/7/22 by 11:59pm) Pset 2 (due Weds 9/7/22 by 11:59pm):
§1.3: 4,8,10,12,24,34,46, §1.4: 1,2,4,6,10,22,24,32,34,42,50,54, §1.5: 6,12,20,27,34
6 Friday 9/2/22 More on continuity. The intermediate value theorem. The squeeze theorem and examples. Limits involving infinity. §1.5,§1.6
Monday 9/5/22: Labor day - no class
7 Wednesday 9/7/22 More examples of limits involving infinity. Tangent lines and derivatives of functions. §2.1 Pset 3 (due Weds 9/14/22 by 11:59pm) Pset 3 (due Weds 9/14/22 by 11:59pm):
§1.6: 3,9,13,18,22,24,28,31,42, §2.1: 1,3,11,17,20, §2.2: 3,5,23,43,45
8 Friday 9/9/22 Computing derivatives from the definition. Various examples such as polynomials, square root function, the absolute value function, etc. Three situations where differentiability fails. Deriving the sum rule and constant multiple rule. The "naive product rule" fails. §2.2,§2.3
9 Monday 9/12/22 Rules for computing derivatives and examples. Derivatives of trigonometric functions. The power rule, product rule and quotient rule. §2.3,§2.4
10 Wednesday 9/14/22 More practice with derivative rules. The chain rule. Examples. §2.5 Pset 4 (due Weds 9/21/22 by 11:59pm) Pset 4 (due Weds 9/21/22 by 11:59pm):
§2.3: 10,16,20,24,27,30,35,41,45 (feel free to use Desmos or any other plotting software for graphing problems) §2.4: 3,6,9,28,36,41 §2.5: 1,7,13,30,35,42
11 Friday 9/16/22 Equations of tangent lines and normal lines. Examples involving velocity, acceleration, and maxima. §2.1,§2.2,§2.3
12 Monday 9/19/22 Implicit differentiation and related rates. Some examples. §2.6,§2.7
13 Wednesday 9/21/22 Proof that $\lim\limits_{x \rightarrow 0}\tfrac{\sin(x)}{x} = 1$ using squeeze theorem and some trigonometry. More related rates examples. §1.4 (see page 42), §2.7 Pset 5 (due Weds 9/28/22 by 11:59pm) Pset 5 (due Weds 9/28/22 by 11:59pm):
§2.6: 2,5,8,16,22,23,28,34,37, §2.7: 2,5,11,14,16,25,41, §2.8: 1,6,11,15
14 Friday 9/23/22 More related rates examples. Linear approximations. §2.7, §2.8
15 Monday 9/26/22 Another linear approximation example. Absolute and local extreme of fuctions. The extreme value theorem and Fermat's theorem. Critical numbers. The closed interval method. §2.8,§3.1
16 Wednesday 9/28/22 Midterm review
17 Friday 9/30/22 midterm 1 during class Pset 6 (due Friday 10/7/22 by 11:59pm) Pset 6 (due Friday 10/7/22 by 11:59pm):
§3.1: 3,4,5,6,13,27,37,41,43,45, §3.2: 2,3,5,10,14,17
18 Monday 10/3/22
19 Wednesday 10/5/22
20 Friday 10/7/22
21 Monday 10/10/22
22 Wednesday 10/12/22
Friday 10/14/22: Fall recess - no class
23 Monday 10/17/22
24 Wednesday 10/19/22
25 Friday 10/21/22
26 Monday 10/24/22
27 Wednesday 10/26/22
28 Friday 10/28/22
29 Monday 10/31/22
30 Wednesday 11/2/22
31 Friday 11/4/22 midterm 2 during class (tentative date)
32 Monday 11/7/22
33 Wednesday 11/9/22
Friday 11/11/22: Veterans day - no class
34 Monday 11/14/22
35 Wednesday 11/16/22
36 Friday 11/18/22
37 Monday 11/21/22
Wednesday 11/23/22: Thanksgiving break - no class
Friday 11/25/22: Thanksgiving break - no class
38 Monday 11/28/22
39 Wednesday 11/30/22
40 Friday 12/2/22 (last day of class)
Wednesday 12/7/22: 2-4pm final exam (check schedule)
Image sources: here.