Calculus I

Columbia University, Fall 2007
Math V1101 section 007


MW 6:10-7:25pm
203 Math
27 lectures


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.

The major themes of the course include: Grades will be determined by homework (weekly) and exams (at least one midterm, 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; 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.

I am the TA for this course. For homework assistance, use the help room in 333 Milbank. The schedule can be found here.

I will usually be in my office (408 Math) 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.

I will collect all homework in class. Late homework will be penalized. 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
(all homework due in class)
Sep 5 Motivation
Review: Functions
Preview
1.1-1.4
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*)
Sep 10
Sep 10 Finish Review
Tangent and Velocity
1.5-1.6
2.1


2.1 (1, 9)
1.5 (15, 19, 30)
1.6 (27, 58)
2.1 (2, 7)
Sep 17
Sep 12 The Limit of a Function
Limit Laws
2.2
2.3
2.2 (8, 29, 40)
2.3 (22, 34)
2.2 (5, 12, 28)
2.3 (2, 10, 13, 36)
Sep 17 Epsilon-Delta Definition of Limit
Continuity
2.4
2.5
2.4 (6, 13, 39)
2.5 (1, 3, 41)
2.4 (1, 20, 32)
2.5 (4, 37, 42, 45)
Sep 24
Sep 19 Limits at Infinity
Derivatives
2.6
2.7-2.8
2.6 (10, 27, 61)
2.7 (19, 24, 48)
2.6 (3, 22, 36, 70*)
2.7 (6, 14, 28, 52*)
Sep 24 Differentiation Rules:
Polynomials, Exponential Functions
Product and Quotient Rules
3.1
3.2
2.8 (21, 49)
3.1 (42, 51, 74)
3.2 (3, 44, 58)
2.8 (20, 24, 44)
3.1 (34, 50(a,b), 67)
3.2 (12, 14, 34)
Oct 1
Sep 26 Derivatives of Trigonometric Functions
The Chain Rule
3.3
3.4
3.3 (5, 31, 32)
3.4 (31, 48, 75)
3.3 (10, 16, 39)
3.4 (12, 20, 26, 41)
Oct 1 Implicit Differentiation 3.5 3.5 (34, 40) 3.5 (23, 26, 50) Oct 8
Oct 3 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))
Oct 8 Related Rates
Linear Approximation and Differentials
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)
Oct 15
Oct 10 Hyperbolic Functions
Review for First Midterm
3.11 3.11 (31, 43)
Notes on Induction
3.11 (32, 44)
Oct 15 First Midterm Ch. 1 - Ch. 3 Sample Midterm Midterm Solutions
Oct 17 Maximum and Minimum Values 4.1 4.1 (29, 37, 49, 60) 4.1 (7, 44, 47, 62) Oct 29
Oct 22 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)
4.2 (14, 17, 27)
4.3 (10, 15, 21, 47)
Oct 24 L'Hospital's Rule 4.4 4.4 (5, 30, 69) 4.4 (13, 46, 52, 60) Nov 7
Oct 29 Curve Sketching 4.5 4.5 (7, 11, 54) 4.5 (22, 31, 32)
Oct 31 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)
Nov 5 no class: University holiday
Nov 7 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)
Nov 14
Nov 12 The Fundamental Theorem of Calculus 5.3 5.3 (8, 19, 38, 53, 74) 5.3 (2, 7, 14, 29, 41)
Nov 14 Review for Second Midterm Ch. 4 & 5.1-5.3
Nov 19 Second Midterm Ch. 4 & 5.1-5.3 Sample Midterm Midterm Solutions
Nov 21 no class
Nov 26 Indefinite Integrals and Net Change
Substitution Rule
Notes
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)
Dec 3
Nov 28 Areas between Curves
Volume
6.1
6.2
6.1 (16, 17)
6.2 (7, 31, 65)
6.1 (6, 27, 31, 47*)
6.2 (3, 6, 50)
Dec 3 Volumes by Cylindrical Shells 6.3 6.3 (11, 19, 45) 6.3 (14, 18, 42, 43) Dec 10
Dec 5 Average Value of a Function 6.5 6.5 (3, 4, 13) 6.5 (5, 10, 23*)
Dec 10 Review for final everything Sample Final (5.4-6.5) Solutions
Dec 12 Review for final, 6-8pm, Math 520
office hours (as usual) 5-6pm
everything Sample Cumulative Final
Dec 13 (additional) office hours 3-4pm
Dec 17 (additional) office hours 4-6pm
Dec 17 FINAL, 7:10-10:00pm, Hamilton 303
(note room change)
Solutions to Final Exam