This is a copy of the original website for this course, which I taught at Columbia in Fall 2010. All of the contact information below is out-of-date.

Calculus I, Fall 2010, Section 12

General information
Day/Time: Tuesday, Thursday 6:10pm-7:25pm.
Location: 304 Hamilton.
Instructor
Kristen Hendricks
Office: 408 Mathematics.
Office Hours: Tuesday & Thursday 3-4 in Mathematics 528 , Monday 6-7 in Mathematics 528. Please let me know by e-mail if you are coming to the Monday session.
E-mail: hendricks@math.columbia.edu.
Please let me know if the course is too fast or too slow, if you'd like more examples, or if you have any other feedback.
Teaching Assistant
There is no TA for the class. However, you can get help in the Barnard help room (333 Milbank). See schedule.
Basics
This is a standard first course in calculus. In the first third of the course (roughly up to the first midterm) we will define limits, continuity, and derivatives. We will also learn techniques for calculating derivatives. In the second third of the class (roughly before the second midterm) we will learn to use derivatives for applications like related rates, optmization, and linear approximation. In the last third of the class, we will introduce integration, some of its applications, and the fundamental theorem of calculus.
Textbook
The text is James Stewart, Calculus (Early Transcendentals), 6th edition published by Thomson Brooks/Cole. It is available at the Columbia bookstore. It is also available online, probably at lower prices. Many of Stewart's other books look similar, so check carefully that you have chosen the correct text if you order online. This class will cover chapters 1 through 6; reading will be posted below. You are encouraged to do the reading before coming to class, to prepare you to get the most out of lecture.
Homework
Homework is extremely important! You can't understand calculus without doing problems -- a lot of them. Write up your solutions clearly and in detail. Homework will be assigned weekly from Stewart. It will be posted on the course website every Tuesday and Thursday and will usually be due the following Tuesday before the lecture begins. Homework is to be submitted in the mailbox on the 4th floor of the Math building. Graded homework will be returned in class, and homework solutions will be posted on courseworks. Late homework will not be graded, but your lowest two homework scores will be dropped.
Recommended Problems
The homework assignments are designed to be representative of the work you do to understand the material (otherwise they would be much longer...). For the typical student, just doing the homework probably won't be sufficient to really understand calculus. Some concepts might make sense to you right away, but others will require more time and practice. Which concepts are easy and which are hard will be different for each student, so learn to judge for yourself when you really understand something. I strongly encourage you to do as many problems as you need to feel like you understand the material. To facilitate this process for you, I will suggest two types of "recommended problems" each week: "for practice" and "for challenge." These will not be graded and should not be turned in. In the table below, the "for practice" problems are matched to the homework problems using little arrows. For example, 4.1.14-->7-13 means that if you had trouble with homework problem 14 in section 4.1, you should try problems 7-13 as practice. The "for challenge" problems are to push your understanding beyond the basics. Some of them are quite difficult, so don't be discouraged if you cannot solve them.

WebAssign is an online system for doing calculus problems. It will be completely optional in this class and will not affect your grade. Any book purchased through the university bookstore will have an access code for www.webassign.com; you can also purchase one at the site. When you log on, there will be a tutorial available to teach you how to enter your answers in a way that WebAssign understands. Each student does essentially the same WebAssign problems, but with slight variations. WebAssign is graded by a computer; it will allow you to submit answers to the same problems as many times as you wish before the deadline. There is no penalty for trying the same problem several times.
Getting Help
If you are having trouble with the homework, ask for help! There is a calculus help room in 333 Milbank. The schedule can be found here. Private tutors are also available. Email tutoring2009@math.columbia.edu to look for a tutor.
Collaboration Policy
You are encouraged to discuss the homework and course material with other students. However, you are must make an effort to first solve all problems on your own and you are not permitted to exchange written work. Suspiciously similar write-ups will not receive credit.


Exams
There will be two midterm exams and one final exam. The midterms will be taken in class on October 7 and November 9. The first midterm will be graded and returned before the Columbia and Barnard drop date, October 12. Make-up exams will be scheduled only with a note from the doctor or your dean.

The final exam will be outside of class. It has been provisionally scheduled by the university for 7:10--10:00pm, December 21. The university requires that all students take the final exam at its scheduled time. The only exceptions are for students who have final exams scheduled at the same time or three exams scheduled on the same day. If you find yourself in that situation, please inform all instructors involved as soon as possible and at least one week before the exam.

Notes and calculators will not be allowed on exams.
Grading
Grades will be calculated approximately as follows:
These percentages will be used as guidelines in determining your final grade. The lowest two homework scores will be dropped. Significant improvement on the final exam will also be taken into consideration.

Schedule

Day

Topic

Section

Homework

Recommmended Problems

9/14/10
spacer

09/07/10

Motivation

Review of Functions

Preview of Calculus, 1.1-1.3

1.1.19, 1.1.24, 1.1.32

1.2.4, 1.2.8

1.3.20, 1.3.43

Do the diagnostic tests at the start of your textbook. Get help if you don't understand any of the problems.

1.1.19 → 1.1.20, 1.1.10, 1.1.13

1.1.24 → 1.1.1, 1.1.2, 1.1.21, 1.1.25, 1.1.26, 1.1.23

1.1.32 → 1.1.33-40

1.2.4 → 1.2.1-3

1.2.8 → 1.2.5-7, 1.2.9

1.3.20 → 1.3.5, 1.3.9, 1.3.11, 1.3.14, 1.3.19, 1.3.21, 1.3.23

1.3.35 → 1.3.29, 1.3.31-34, 1.3.37-40, 1.3.44-46

09/09/10

Finish Review

1.5-1.6

1.5.19, 1.5.25

1.6.29, 1.6.38, 1.6.63

1.5.19 → 1.5.13-18

1.5.25 → 1.5.20, 1.5.21, 1.5.26

1.6.29 → 1.6.15-19, 1.6.21-26

1.6.38 → 1.6.33-37, 1.6.47-50

1.6.63 → 1.6.59-62, 1.6.66-68

For challenge: 1.5.29, 1.6.58

09/14/10

Tangent and Velocity
The Limit of a Function

2.1
2.2

2.1.3, 2.1.7

2.2.6, 2.2.14, 2.2.18, 2.2.29

2.1.3 → 2.1.4-6, 2.1.8, 2.1.9

2.1.7 → 2.1.1, 2.1.2

2.2.6 → 2.2.4, 2.2.5, 2.2.7-9

2.2.14 → 2.2.13, 2.2.16, 2.2.17

2.2.18 → 2.2.17, 2.2.19, 2.2.20

2.2.29 → 2.2.25-28, 2.2.30-32

For challenge: 2.2.40

9/21/10
spacer

09/16/10

Calculating Limits

2.3

2.3.6, 2.3.14, 2.3.30, 2.3.37, 2.3.46

2.3.6 → 2.3.1-5, 2.3.7-9

2.3.14 → 2.3.11-13, 2.3.14-20

2.3.30 → 2.3.10, 2.3.21-29

2.3.37 → 2.3.33-36

2.3.46 → 2.3.39-45

For challenge: 2.3.61, 2.3.62

09/21/10

Epsilon-Delta Definition of Limits

2.4

2.4.5, 2.4.18, 2.4.29, 2.4.36

2.4.5 → 2.4.1-4, 2.2.6-9

2.4.18 → 2.4.13-17

2.4.29, 2.4.36 -> 2.2.19-28, 2.2.30-32

2.4.44 → 2.4.41-43

For challenge: 2.4.40, 2.4.37, 2.4.44

9/28/10
spacer

09/23/10


Continuity


2.5

2.5.19, 2.5.34, 2.5.38, 2.5.42, 2.5.47

2.5.27 → 2.5.3-18

2.5.34 → 2.5.21-33

2.5.38 → 35-37, 2.5.39-40

2.5.42 → 2.5.41

2.5.47 → 2.5.44-46, 2.5.48-54

For challenge: 2.5.57, 2.5.64, 2.5.65

09/28/10

Limits at Infinity
Introduction to Derivatives

2.6 pgs. 130-137
2.7, 2.8

2.6.21

2.7.15, 2.7.27, 2.7.35

2.8.24, 2.8.38, 2.8.43

2.6.21 → 2.6.13-20, 2.6.22-38

2.7.15 → 2.7.9-14, 2.7.16

2.7.27 → 2.7.17-26, 2.7.28-30

2.7.35 → 2.7.31-34, 2.7.36

2.7.44-48

2.8.24 → 2.8.3-12, 2.8.19-23, 2.8.25-29

2.8.38 → 2.8.35-37

2.8.43 → 2.8.41-42, 2.8.44

For challenge: write down a proof of the constant multiples rule and difference rule.


10/05/10

(Homework submitted
by 5 pm on Oct 3
will be returned
before the midterm.)

09/30/10

Derivatives of Polynomials and Exponential Functions
Product and Quotient Rules

2.7, 2.8 continued
3.1
3.2

3.1.23, 3.1.28, 3.1.51, 3.1.64

3.2.12, 3.2.24, 3.2.35,.

3.1.23, 3.1.28 → 3.1.3-42

3.1.51 → 3.1.52-58

3.1.64 → 3.1.63, 3.1.65-68

3.2.12, 3.2.24 → 3.2.3-34

3.2.35 → 3.2.36-48

For challenge: 3.2.58

10/05/10

Derivatives of Trig Functions
Review

3.3

3.3.10, 3.3.27, 3.3.41

Practice midterm on courseworks

3.3.10, 3.3.27 → 3.3.1-30

3.3.41 → 3.3.39-48

For challenge: 3.3.50, 3.3.51

10/12/10

10/07/10

FIRST MIDTERM

Chapters 1-2, 3.1-3.2

Come look over your exam in office hours Monday or Tuesday. Talk to me if you have any concerns. Remember the drop date is Tuesday Oct. 12.

10/12/10

Chain Rule

3.4

3.4.17, 3.4.36, 3.4.41, 3.4.65, 3.4.82

Practice with any of the rest of the problems in this section – we'll use the chain rule constantly from now on.

10/19/10
spacer

10/14/10

Implicit Differentiation
Derivatives of Logarithmic Functions

3.5
3.6

3.5.14, 3.5.30, 3.5.46, 3.5.59

3.6.9, 3.6.18, 3.6.39

Extra Credit: 3.6.54

3.5.14 → 3.5.5-20

3.5.30 → 3.25-29

3.5.46 → 3.5.45-54

3.5.59 → 3.5.43, 3.5.60-62

3.6.9 → 3.6.2-8, 3.6.10-16

3.6.18 → 3.6.17-22

3.6.39 → 3.6.37-48, 3.6.50

For challenge: 3.5.44

10/19/10

Related Rates
Linear Approximations and Differentials

3.9
3.10

3.9.18, 3.9.26, 3.9.28

3.10.22, 3.10.27, 3.10.34

[You'll find all of the questions in the related rates section about equally useful. If you're having trouble with the assigned questions, start with the easier ones at the beginning of the section.]

3.10.22 → 3.10.11-21

3.10.27 → 3.10.6, 3.10.23-26, 3.10.28

3.10.34 → 3.10.33, 3.10.35-38

For challenge: 3.10.41

10/26/10

10/21/10

More on Linear Approximations
Maximum and Minimum Values

3.10
4.1

4.1.9, 4.1.54, 4.1.59, 4.1.70,

4.1.9 → 4.1.3-8

4.1.54, 4.1.59 → 4.1.47-62

4.1.70 → 4.1.69, 4.1.71, 4.1.73

For challenge: 4.1.78

10/26/10

Mean Value Theorem
Derivatives and the Shape of a Graph

4.2
4.3

4.2.16, 4.2.27, 4.2.33

4.3.39, 4.3.42, 4.3.64

4.2.16 → 4.2.11-15

4.2.27 → 4.2.17-26

4.2.33 → 4.2.31, 4.2.32

4.3.39, 4.3.42 → other curve-sketching problems in 4.3.33-52

4.3.64 → 4.3.61-63

11/04/10

10/28/10

L'Hospital's Rule
Curve Sketching

4.4
4.5

4.4.11, 4.4.14, 4.4.45

4.5.36

4.4.11, 4.4.14 → 4.4.5-38

4.4.45 → 4.4.39-46

4.4.49 → 4.4.47-52

4.4.60 → 4.4.55-64

4.5.36 → Do one or two other curve sketches from this section. Interchangeable with 4.3 recommended problems.

11/02/10

No Class




11/04/10

Review for Second Midterm




11/09/10

SECOND MIDTERM

3.4-3.6, 3.9, 3.10, 4.1-4.5



11/11/10

More L'Hospital's Rule
Optimization
Antiderivatives

4.4
4.7
4.9

4.4.49, 4.4.60

4.7.14, 4.7.19, 4.7.24, 4.7.30, 4.7.55, 4.7.63

4.4.49 → 4.4.47-52

4.4.60 → 4.4.55-64

4.7.14 → 4.7.10-13

4.7.19 → 4.7.17-8, 4.7.21

4.7.24, 4.7.30 → 4.7.22-29

4.7.55 → 4.7.56-58. Similar example also worked out carefully in text.

11/18/10

11/16/10

More antiderivatives
Areas and Distances

4.9
5.1

4.9.13, 4.9.36, 4.9.60

5.1.4, 5.1.11, 5.1.21

4.9.13 → Do one or two of 4.9.1-20

4.9.36 → Do one or two of 4.9.23-46.

4.9.60 → 4.9.57-62

5.1.4 → 5.1.3, 5.1.5, 5.1.6

5.1.11 → 5.1.12-15

5.1.21 → 5.1.17-20

11/23/10

(Solutions will be accepted by e-mail if you are out of town)

11/18/10

Definite Integrals
The Fundamental Theorem of Calculus

5.2
5.3

5.2.11, 5.2.28, 5.2.33

5.3.21, 5.3.26, 5.3.38, 5.3.39,

5.2: Primarily practice setting up and interpreting Riemann sums.

5.3: Practice taking definite integrals. A lot.

11/23/10

Indefinite Integrals and more FTC
Substitution Rule

5.4
5.5

5.4.18, 5.4.58

5.5.11, 5.5.32, 5.5.35, 5.5.42, 5.5.57,

5.5: If you feel confused about substitution, start by working through problems 1-6, which tell you the correct substitution and are therefore much easier. Then practice with the other problems in this section to learn how to find an appropriate u.

11/30/10

11/25/10

No Class





11/30/10

More Substitution
Area Between Curves

5.5
6.1

6.1.10, 6.1.15, 6.1.28, 6.1.31, 6.1.51

Do several of 6.1.5-28

12/09/10

12/02/01

Volume
Work

6.2
6.4

6.2.3, 6.2.6, 6.2.11, 6.2.52, 6.2.55

6.4.7, 6.4.14, 6.4.21

6.2.3, 6.2.6, 6.2.11 → 6.2.1-18

6.2.52, 6.2.55 → 6.2.49-65

6.4.7 → 6.4.8-12

6.4.14 → 6.4.13, 6.4.15-18

6.4.21 → 6.4.22-24

12/07/10

Final Review I

everything

spacer


spacer

12/09/10

Final Review II

everything

spacer


spacer

Dec 21
7:10 pm to 10:00 pm

FINAL EXAM
University Exam Schedule

everything!