Calculus I

Columbia University, Spring 2008
Math V1101 section 006

TR 6:10-7:25pm
Math 520

The content of this course is contained in Chapters 1-6 of Stewart's Calculus (Early Transcendentals; 6th edition).
A sample syllabus can be found here.
Also see my syllabus from Fall 2007 here.

The major themes of the course include: Grades will be determined by homework (weekly) and exams (two midterms, one final). Homework is intended to reinforce the material covered in class and to cover related topics. Exams serve as opportunities for students to demonstrate mastery of the subject. Grades will be determined primarily by exam performance (the final will be worth the midterms combined); homework will count for no more than 20% of the final grade, and webworks problems will comprise a small proportion of that. Superb performance on the final will be taken into consideration, and there will be opportunities to earn extra credit.

The TA for this course is Samantha John, smj2118. For homework assistance, use the help room in Milbank 333. The schedule can be found here.

I will usually be in my office (Math 408) for at least one hour immediately before class. You may also schedule an appointment.

Of course, please email me at joeross@math.columbia.edu if you have any questions or comments about the course. Too fast/slow? Too many/few examples? Let me know.

Homework may be turned in early (the night before it's due) in class, or should be placed in my box ("turn in") outside Math 408. Late homework will not be accepted under any circumstances. The lowest two homework grades will be dropped. It is your responsibility to stay up-to-date with the webworks assignments -- I will not post due dates here.

Schedule


Day Topic Section Recommended Problems/Sample Exams Homework
(* = extra credit)		 Due date
Jan 22 Motivation
Review 		Preview
Ch. 1		 skim the problems in Ch. 1 and
make sure you can do all of them		 1.1 (2, 20, 24, 40, 53*)
1.2 (4, 16, 19)
1.3 (27, 59, 63*) 		Wed Jan 30 at 10 a.m.
Solutions
Jan 24 Finish Review Ch. 1 1.5 (15, 19, 30)
1.6 (27, 58)
Jan 29 Tangent and Velocity
The Limit of a Function		 2.1
2.2		 2.1 (1, 9)
2.2 (8, 29, 40) 		2.1 (2, 7)
2.2 (5, 12, 28) 		Wed Feb 6 at 10 a.m.
Solutions
Jan 31 Limit Laws 2.3 2.3 (22, 34) 2.3 (2, 10, 13, 36)
Feb 5 Epsilon-Delta Definition of Limit 2.4 2.4 (6, 13, 39) 2.4 (1, 20, 32) Wed Feb 13 at 10 a.m.
Solutions
Feb 7 Continuity 2.5 2.5 (1, 3, 41) 2.5 (4, 37, 42, 45)
Feb 12 Limits at Infinity
Derivatives 		2.6
2.7
2.8		 2.6 (10, 27, 61)
2.7 (19, 24, 48)
2.8 (21, 49) 		2.6 (3, 22, 36, 70*)
2.7 (6, 14, 28, 52*)
2.8 (20, 24, 44) 		Wed Feb 20 at 10 a.m.
Solutions
Feb 14 Polynomials, Exponential Functions 3.1 3.1 (42, 51, 74) 3.1 (34, 50(a,b), 67)
Feb 19 First Midterm Solutions through 3.1 mean 54.3, median 52
Feb 21 Product and Quotient Rules
Derivatives of Trigonometric Functions		 3.2
3.3		 3.2 (3, 44, 58)
3.3 (5, 31, 32) 		3.2 (12, 14, 34)
3.3 (10, 16, 39) 		Wed Feb 27 at 10 a.m.
Solutions
Feb 26 The Chain Rule 3.4 3.4 (31, 48, 75) 3.4 (12, 20, 26, 41) Wed Mar 5 at 10 a.m.
Solutions
Feb 28 Implicit Differentiation 3.5 3.5 (34, 40) 3.5 (23, 26, 50)
Mar 4 Derivatives of Logarithmic Functions
Exponential Growth and Decay		 3.6
3.8		 3.6 (2, 23, 52)
3.8 (10, 16)		 3.6 (3, 25, 33, 45, 54*)
3.8 (12, 20(a,b)) 		Wed Mar 12 at 10 a.m.
Solutions
Mar 6 Related Rates
Linear Approximation 		3.9
3.10		 3.9 (7, 18, 30)
3.10 (1, 2, 25)
read "Laboratory Project" on
Taylor Polynomials (p.253) 		3.9 (5, 16, 42)
3.10 (4, 28, 44)
Mar 11 Hyperbolic Functions
Maximum and Minimum Values		 3.11
4.1		 3.11 (31, 43)
4.1 (29, 37, 49, 60)		 3.11 (32, 44)
4.1 (7, 44, 47, 62)		 Wed Mar 26 at 10 a.m.
Solutions
Mar 13 The Mean Value Theorem
Derivatives and the Shape of a Graph		 4.2
4.3		 4.2 (25, 29, 32)
4.3 (11, 27, 73, 78)
complete the assignment from 4.3		 4.2 (14, 17, 27)
Mar 25 L'Hospital's Rule 4.4 4.4 (5, 30, 69) 4.3 (10, 15, 21, 47)
4.4 (13, 46, 52, 60) 		Wed Apr 2 at 10 a.m.
Solutions
Mar 27 Curve Sketching 4.5 4.5 (7, 11, 54)
Solutions to Recommended Problems 3.2-4.5 		4.5 (22, 31, 32)
Apr 1 Second Midterm Solutions through 4.5mean 53.8, median 51.5
Apr 3 Optimization
Newton's Method		 4.7
4.8		 4.7 (13, 22, 40)
4.8 (7, 40)		 4.7 (11, 18, 38, 41)
4.8 (5, 8) 		Wed Apr 16 at 10 a.m.
Solutions
Apr 8 Antiderivatives
Areas and Distances
The Definite Integral		 4.9
5.1
5.2		 4.9 (11, 36, 37, 43)
5.1 (18, 19, 22)
5.2 (18, 22, 23, 36)		 4.9 (9, 12, 15, 34, 46)
5.1 (4, 17, 20)
5.2 (7, 17, 21, 34)
Apr 10 The Fundamental Theorem of Calculus 5.3 5.3 (8, 19, 38, 53, 74) 5.3 (2, 7, 14, 29, 41) Wed Apr 23 at 10 a.m.
Solutions
Apr 15 Indefinite Integrals and Net Change
Substitution Rule
 5.4
5.5		 5.4 (11, 17, 27, 51)
5.5 (3, 9, 23, 29, 43)		 5.4 (12, 30, 32, 44, 47)
5.5 (4, 5, 22, 30, 69)
Apr 17 Areas between Curves 6.1 6.1 (16, 17) 6.1 (6, 27, 31, 47*)
Apr 22 Volume 6.2 6.2 (7, 31, 65) 6.2 (3, 6, 50) Fri May 2 at 10 a.m.
Solutions
Apr 24 Volumes by Cylindrical Shells 6.3 6.3 (11, 19, 45) 6.3 (14, 18, 42, 43)
Apr 29 Average Value of a Function
Proof of L'Hospital's Rule
Integration by Parts		 6.5
4.4
7.1		 6.5 (3, 4, 13) 6.5 (5, 10, 23*)
May 1 Review
May 6 Office hours, 5:30-7pm, Math 408
May 7 Office hours, 5:30-7pm, Math 408
May 8 Office hours, 6-7pm, Math 408
May 12 Office hours, 5:30-7pm, Math 408
MAY 13
(Tuesday)		 Office hours, 5-6pm, Math 408

FINAL EXAM
7:10-10:00 pm
Math 520 (subject to change)		 Solutions to the Final Exam