Mathematics V1101
Calculus I
Spring 2007

T, Th, 6:10 - 7:25 PM, 417 Mathematics Building

Announcements

5/7 - Here is a practice final exam.

4/4 - I will hold extended pre-exam office hours today from 1:00pm-6:00pm.

4/4 - Solutions for the problems on the Midterm Review that we didn't go over in class are available here.

4/3 - Since the Stewart text contains no proof that any continuous function can be integrated on a closed interval, I have provided a self-contained (mostly...) proof of this fact here. There is a typo near the end: where it says something like "A_P_N^- - e/3 < A_P_N^- <= L <= A_P_N^+ < A_P_N^+ + e/3", you should replace that with "L - e/3 < A_P_N^- <= L <= A_P_N^+ < L + e/3". I don't really expect that anyone is reading this through, but if you do attempt to do so, and would like help, then come by my office and I will be happy to explain it to you.

4/2 - The Midterm Review is now available online. We will go over it in class on Tuesday 4/3. There are some typos: in the second part of problem 1, replace "1/(1-x^2)" with "(x^2-1)^(-1/2)"; consequently you may disregard problem 2(c).

2/18 - The homework for sections 3.2-3.6 is due Tuesday 2/27 by the start of class. This will count as two homework assignments (roughly 4% of your grade).

1/18 - The homework for sections 1.1-1.3 is due Tuesday 1/23 by the start of class. There is now a mailbox outside room 408.

1/16 - Here is J. Baldwin's sample midterm. Here is a review sheet which is (probably) a fairly good guide for this midterm. Note that implicit and logarithmic differentiation will not be tested, so ignore that part.

1/16 - One, Two, Three actual final exams from years past. You should use these as sample exams. If it is the case that some of the material tested in these was not covered in our course, you can ignore it.

Course Details

Call Number: 85280
Instructor: William (Danny) Gillam
Teaching Assistant: Shreyans Khema
Instructor's Office: 408 Mathematics
Instructor's Email: wgillam@math.columbia.edu
Office Hours: Tuesday and Thursday, 3pm - 4pm in 408 Mathematics
Text: J. Stewart, Essential Calculus: Early Transcendentals
This book has not been used before at Columbia.

Course description: We will cover the first seven chapters of the text. We begin with a review of the elementary functions studied in precalculus and discuss their basic properties. Next we cover limits and continuity, the foundations of calculus. Then we discuss derivatives, with applications and computational methods. Finally we cover integration, culminating in the Fundamental Theorem of Calculus and various applications. For more details, see the course schedule below.

Policies: Students are required to hand in homework every week, take the midterms and the final. Students are also expected to attend every class. For all written work, solve the problems in an organized fashion, with clear explanations. The grader can't read your mind. Ask questions if something is not clear, both in class and outside of class. Help is always available from me or the Barnard Help Room (333 Milbank Hall).

Calculators: Calculators are not required for this course, nor do I particularly encourage you to use one. If you have a graphing calculator, you might find it helpful when you are working on your homework. However, you will not be allowed to use a calculator during the exams.

Homework: Homework will be assigned weekly and is due on Tuesday before class starts. You may work with other students on your homework, but you must indicate who you worked with on the version you turn in. Homework should be placed in my mailbox, located outside of room 408. The lowest grade will be dropped. Homework guidelines:

There may also be computer-based WebWorks homework.
Late homework will not be accepted.

Grading: The grading scheme is as follows:

There will be no make-up exams without a note from a doctor or a dean.

Class Schedule and Homework Assignments

This schedule is tentative and might change as the class progresses. Please check regularly for current homework information, as I plan to post the homework assignments 1-2 weeks in advance.

Date Topics Sections Homework Problems (Optional Problems Parenthesized) 
1/16-1/18
 
Functions
Precalculus Review
Limits and Continuity
 
1.1
1.2
1.3
 
1.1: 1,3-5,7,21,25,26,40
1.2: 1,4,9,23,31,35,37
1.3: 1,2,4,9,10
 
1/23-1/25
 
More Limits
Limits at Infinity
Derivatives I (Definition)
 
1.4
1.5
1.6
2.1
 
1.4: 1,3,4,11,12
1.5: 3,9,13,14,23,27,29
1.6: 13,15,19,20
2.1: 3,5,11,13
 
1/30-2/1
 
Derivatives II (Rules)
Derivatives of trig. functions
 
2.2
2.3
2.4
 
2.2: 1,19,20
2.3: (1),2,(5),6,7,(8),(9),10,15,(16),(17),18,(21),(22),(27),(28)
2.4: 3,(4),(5),(6),7,8,11,(12),17,(18),19,20,(27),28
 
2/6-2/8
 
The Chain Rule
Implicit Differentiation
Exponential Functions
 
2.5
2.6
3.1
 
2.5: 1,(2),3,4,(5),(6),7,8,(11),12,21,24,(25),26
2.6: 1,(2),3,4,5,6,7,8,(13),14,16,17,(18),23,(24)

3.1: 15, 23,24,25,26
 
2/13
 
Inverse Functions and Logarithms
Derivatives of Log and Exp
Exponential Growth and Decay
 
3.2
3.3
3.4
 
3.2: 21,23,(25),35,(36),(37),38,39,(40),47,(48),49,(50),51,52
3.3: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
3.4: 1,2,3,4,5,8,11,13
 
2/15
 
Midterm I (In Class)
 
2/20-2/22
 
Inverse Trigonometric Functions
Hyperbolic Functions
 
3.5
3.6
 
3.5: 1,2,3,4,5,6,8,9,16,17
3.6: 1,2,3,4,9,10,26,27,28,29
 
2/27-3/1
 
L'Hospital's Rule
Maximum-Minimum Value
 
3.7
4.1
 
3.7: 1,2,(3),4,(5),6,7,8,(9),10,11,12,13,(14),15,16
4.1: 1,2,3,15,16,(23),24,25,(26),(27),31,32,(49)
 
3/6-3/8
 
The Mean Value Theorem
Shapes of Graphs
Curve Sketching
 
4.2
4.3
4.4
 
4.2: 2,12,(14),16,25
4.3: 1,(2),(3),(4),9,(10),12,13
4.4: 1,(2),(3),4,(11),12,17,(18),25,(26)
 
3/12-3/16
 
Spring Recess
 
3/20-3/22
 
Optimization
Newton's Method
 
4.5
4.6
 
4.5: 3,6,(8),9,10,(11),13,(15),(22),23,(24),(33),34
4.6: 5,(6),7,8,9,(10)
 
3/27-3/29
 
Antiderivatives
Areas and Distances
Sums and Sigma Notation
Definite Integrals (Intro.)
 
4.7
5.1
Appendix C
 
4.7: 1,(2),3,(4),5,(6),(7),9,(10),(12),15,(16),26,(27)
5.1: 1,3,4,(6),7,17(a)
Appendix C: 5,13,17,18,25,31
 
4/3-4/5
 
Review for Midterm II
Midterm II (4/5)
 
4/10-4/12
 
Definite Integrals (Cont.)
Fundamental Theorem of Calculus
 
5.2
5.3
5.4
 
5.2: 1,9,15,19
5.3: 1,(2),(3),4,(5),6,7,8,(9),10,17,18,27,37
5.4: 5,6,(7),8,14
 
4/17-4/19
 
Substitution Rule
Areas between Curves
 
5.5
7.1
 
5.5: 1,3,5,7,9,11,17,19,21,27,29,33,37,39
7.1: 1,(2),3,(4),8,11,(12),13,15
 
4/24-4/26
 
Volumes
Volumes by Cylindrical Shells
 
7.2
7.3
 
7.2: 1,(2),3,4,(5),6,13,15,(16)
7.3: 2,3,4,(5),6,(7),9,11
 
5/1
 
Review