MATH V1101.008:
Calculus I
Fall 2006

M, W, 6:10 - 7:25 PM, 520 Mathematics Building

Announcements

9/13 - Note the change in office hours below!!

9/20 - Note the NEW change in office hourse below!!

10/6 - Here is a sample of what the midterm might look like. And here is a review sheet that was created by someone else, but which is a fairly good guide for this midterm. Note that implicit and logarithmic differentiation will not be tested, so ignore that part.

11/3 - Here are some sample problems for Midterm 2. I'll try to have solutions up before long.

11/10 - Here are solutions to the sample midterm problems.

12/6 - One, Two, and Three are 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.

<12/16> Here is a scanned copy of solutions for one of the exams. Here .

Course Details

Instructor: John Baldwin (408 Mathematics, baldwin@math.columbia.edu)

Office Hours: Monday, and Wednesday, 5:30pm - 6pm, in 408 Mathematics, then 7:30-8pm in 520.

Text: James Stewart Calculus: Early Transcendentals, fifth edition, Brooks/Cole, 2003.

Course description: We'll cover the following (Chapters 1 - 6 of Stewart):

  1. Functions: definition, elementary functions, basic properties
  2. Limits and continuity
  3. Derivative: definition, computing the derivative, applications to curve sketching and optimization problems
  4. Integration: definition, Fundamental Theorem of Calculus, applications

Policies: Students are required to hand in homework every week, take the midterms and the final. Students are also expected to attend every class. Here are some suggested policies:

  1. Active participation is strongly encouraged.
  2. Reading the book is helpful. Please try to read the material we are going to cover before class.
  3. Should you miss a class, get the notes from your peers.
  4. While working on the homework, collaboration is encouraged, as long as the work you hand in is your own. Also, staple your homework.
  5. For all written work, solve the problems in organized fashion, with clear explanations. The grader can't read your mind.
  6. 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. 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 the following Monday before class starts. Homework should be placed in my mailbox, located outside of room 408. Two lowest grades will be dropped. Late homework will not be accepted.

Exams: There will be two midterms and a final.
There will be no make-up exams without a note from a doctor or a dean.

Grading: The tentative grading scheme is as follows:

Homework will be graded as follows: The homework is divided into "1-point problems" and "primary problems". You will receive one point for each of the 1-point problems you hand in. The primary problems will be graded more closely, worth 3-5 points each. Your homework average is the combined number of points you have accumulated between the "1-point" and "primary" problems divided by the total number of points possible. In order to receive full credit for your homework problems, you must show your work clearly. Merely writing down an answer will generally not suffice.

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 Sections/Topics Primary HW problems 1-point HW problems
09/06 Introduction. Functions (1.1-1.3, 1.5, 1.6, 2.1)   
1.1: 1,2,5-8,21,22,23,38
1.3: 3,32,36,41
1.5: 13,17,19
1.6: 5-8,17,31,35,36,41
09/11
09/13		 Limits, epsilon/delta (2.2-2.4) 
2.2: 4,23
2.3: 5,14

2.2: 9,14,25-30
2.3: 22,28,37,38,41,42,55
2.4: 3,15,31,39
09/18
09/20		 Continuity, tangents, velocities, derivatives (2.5,2.7-3.1) 
2.5: 45,61
2.8: 26
2.9: 38,43

2.5: 3,37,41,47
2.8: 13-20,25,29
2.9: 5-12,27,29,46
09/25
09/27		 More derivatives (3.2, 3.4, 3.5, 3.7). Derivatives of log and inverse trig (3.6, 3.8) 
3.1: 60
3.2: 32
3.4: 29
3.5: 55

3.1: 15,17,21,29,39
3.2: 3-8,31,35
3.4: 1,3,5,7,37,39
3.5: 9,11,13,15,23
10/02
10/04		 Implicit differentiation. Review. 
3.6: 25,48

3.6: 11,19,21,26,41,49
10/09 Midterm 1 (covers chapters 2 and 3) 
3.10: 7

3.10: 9,11,25,29,37
10/11 Related rates (3.10).    
10/16
10/18		 Linear approximation (3.11), Min and max (4.1). 
4.1: 7-10

3.11: 5-8,21,23,25,31,33,35
4.1: 3,5,47,49,55,56,61
10/23
10/25		 Derivatives and graphs. More optimization (4.3, 4.7). MVT. L'Hospital's rule (4.2, 4.4). 
4.2: 23
4.3: 1,2
4.7: 29

4.2: 1,3,11,12,13
4.3: 8,11,17,25,33,41
4.7: 2,4,19,33
10/30
11/01
11/08		 L'Hospital's rule (4.4). Graphing (2.6, 4.5, 4.6). <\td> 
4.4: 29,40
4.5: 49

4.4: 11,13,15,17,37,44,51
4.5: 7,15,21,31
11/13 Midterm 2 (covering 3.10, 3.11, 4.1 - 4.8)    
11/15 Antiderivatives (4.10). Area, Definite Integrals (5.1, 5.2). 
5.1: 17

4.10: 1,3,5,7,9,13,25,31,33,37,39
5.1: 3,4,18,19
11/20
11/22		 Definite integrals continued (5.2). The Fundamental Theorem of Calculus, indefinite integrals (5.3, 5.4).    
11/27
10/29		 Substitution rule (5.5). Computation of areas, average values (6.1, 6.5). 
5.3: 54
5.4: 48
5.5: 76, 80

5.4: 1,3,7,9,17,19,23,27,45,49
5.5: 1,3,7,11,13,49,53,55,57
12/04
12/06		 Areas, volumes, work (6.1, 6.5).    
12/12 Review    
Sometime towards the end of December Final exam.