Calculus I (MATH V1101-001, Fall 2006)

[ Policies & Procedures | Schedule of Lectures ]

Day & Time: Monday and Wednesday 9:10am — 10:25am

Location: 207 Math

Office Hours: Tuesday, 2:45-3:45pm and Friday 11:30am-12:30pm in 525 Mathematics

Teaching assistants : Sixuan Li , Charles Ferraro (undergraduate TAs) and Tung To (graduate TA)

Textbook: James Stewart, Calculus: early transcendentals fifth edition, Brooks/Cole-Thomson Learning, Belmont, CA, 2003. ISBN 0534393217. It is available at the University bookstore or AddALL.

Examinations: There will be two in class tests. The first will be on Wednesday, October 11 and the second on Monday, November 13. The final exam is (confirmed) on December Wednesday, December 20, 9am-noon (same room as usual)

Policies & Procedures

Goals: At the end of the course, students should be able to

make calculations with agility, accuracy, intelligence and flexibility;
explain the basic concepts of calculus clearly and reason logically with them;
solve extended problems, with good judgment in the choice of tools and in checking answers.

Expectations: To achieve these goals, students are advised to

read each section of the textbook before the material is presented in class;
attend the lectures;
complete all homework assignments;
discuss mathematics with other students.

Assessment: The course grades will be computed as follows:: 20% Homework; 20% First test; 20% Second test; 40% Final exam

Homework: There will be two kinds of homework:

Exercises give you a chance to practice and refine your basic calculus skills. They will not be collected.
Written Problem sets consist of approximately 3 questions. They are not intended to be harder than the exercises although some may well be. Instead, they may ask you to apply a technique in a mildly novel context or combine concepts that you have only seen in isolation before. Problems sets are posted in PDF format; your browser can be trained to automatically open these files with the free program Acrobat Reader. Problem sets will be collected at the beginning of class and late homework will not be accepted. Graded homework can be found on a box on a table near the o ffice 521.
Note : in this section of calculus I, we will not use webwork

There will be one problem set each week, either written or on webwork. Your best ten problem sets will determine your homework grade

Written work: We write to communicate. Please bear this in mind as you complete assignments and take exams. You must explain your work in order to obtain full credit; an assertion is not an answer. For specific suggestions see A guide to writing in mathematics classes.

Academic honesty: It is the obligation of each student to understand the University's policies regarding academic honesty and to uphold these standards. Students are encouraged to talk about the problems, but should write up the solutions individually. Students should acknowledge the assistance of any book, software, student or professor.

Help: Help is available if you have trouble with homework or lecture material. My office hours are a good place to start. You may also take advantage of the Mathematics Help Room (333 Milbank Hall, on the Barnard campus). You may drop by whenever the Help Room is open; no appointment is necessary.

Calculators: Calculators — in particular graphing calculators — are not required for this course. If you have one, you are welcome to use it when you do your homework. However, calculators will not be allowed during any tests or exams.

Disabilities: Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, stop by the Office of Disability Services (BC, CC) to register for support services.

Extra Credit: A maximum of 4 points (added to your average grade, over 100, for the course) is available for extra credit. To earn those 4 points, you should completely solve two exercises (given below) from the book, carefully explain your reasoning, and put them into my mailbox before December 18th, 2pm. To determine what exercises you have to do, proceed as follows. Take the first letter and your family name. Consider its rank n in the alphabet (for example A is 1, B is 2, ... Z is 26). Do the problems plus numbered n and n+13 on page 366 and 367. if n or/and n+13 is greater than 24, remove 24 to that number.

Schedule of Lectures

Class	Topic	Read	Exercises	Due
Sep 06	Introduction. History of Calculus. Prerequisites	Chapter 1
Sep 11	Functions: definitions, domain and range, operations	§1.1,1.2,1.3	1.1: 1,12,15,21,22,23,24,25,26; 1.3: 31,32,34,35,54
Sep 13	Functions: properties, inverse of a function	§1.1,1.6	1.1: 60,61,62,63; 1.5: 17,19; 1.6:5,6,15,16,17,22,23,24	Problems set 1 Solutions
Sep 18	Functions: Exponential and logarithm, inverse trigonometric function; the tangeant and the velocity problems; Limits	§1.5,1.6,2.1,2.2	1.5:7,8,9,17,19,25; 1.6:25,27,28,39,40,49,53; 2.1:7,8
Sep 20	Limits. Infinite limits. Laws of limits	§2.2,2.3	2.2: 1,2,10,13,14,20	problems set 2 Solutions
Sep 25	Laws of limits	§2.3	2.3: 1,11,12,13,14,35,36,37
Sep 27	Laws of limit. Continuity	§2.3,2.5	p.123: 11,12,13,18,19,21,22,32,33,41,42,43,45,46,49,50,51,52,56	Problems set 3
Oct 2	Continuity. The Intermediate value theorem	§2.5	p.133: 1,4,10,15,16,17,35,37,44,45,46
Oct 4	The intermetdiate value theorem. Limits at infinity	§2.5,2,6	p.146: 1,2; p.147: 5,6,11,12,13,16,19,22,25,26	Problems set 4
Oct 9	Limits at infinity. Short Review. Tangents, velocity, rates of change derivatives	§2.6,2.7
Oct 11	Midterm 1: Functions and Limits	Chapter 1 and 2.1 to 2.6 but not 2,4	p.176: Review:1-8; Quiz:1-13. p.177-179: 3,4,5,6,7,13,18,19,21,25,31,33,34,35,36,54. Practice midterm Solutions (new version)	Problems set 5
Oct 16	The derivative as a function	§2.7,2.8,2.8	2.7: 7,8,9,20,27; 2.8:13,14,15,30; 2.9:5,6,7,8,16,17,18,21,22,26,45
Oct 18	Derivatives of polynomial and exponential functions. Rules of differentiations	§3.1,3.2
Oct 23	Rates of change in science. Derivatives of trigonometric functions	§3.3,3.4	3.3:7,8,15,29,30,31. 3.4:1,2,3,5,8,16,21,22,31,35,36,37,38,40,42.	Problems set 6
Oct 25	The chain rule.	§3.5	3.5:7 to 20. 3.6:5 to 17.
Oct 30	No class was given. Sorry.
Nov 1	Derivatives of logarithmic functions	§3.8	3.8:1,2,3,4,28,35,36,39,40,44,45,52
Nov 6	University Holiday
Nov 8	Implicit differentiation. Higher derivatives. Related rates. Review	§3.5,3.7,3.10	3.7:1,2,5,6,7,8,23,33,34,35,49,50; 3.10:
Nov 13	Midterm II	chapter 3 (excepted %sect;3.9 and 3.11)	Training midterm Solutions; Review page 270: 1,2 form (a) to (n),3,4,5; the True-Flase quiz (aexpetd 9); exercises page 271 : 1,2,3,4,19,20,55,56,69,70,87,88.
Nov 15	Maximum and minimum Values. Fermat's and Rolle's Theorem. The mean value theorem	§4.1,4.2	4.1:31,32,33,34,38,39,47,48,49,50
Nov 20	The mean value theorem and applications. Derivatives and graph	§4.2,4.3	4.2:1,2,11,19,23,24,27. 4.3:1,2,11,12,21.22,33,34,41,42
Nov 22	L'hospital's rule. Curve Sketching.	§4.4,4.5	4.4:5,6,9,10,16,17,18,21,22,23,41,42,51,52,61; 4.5:1,2,3,19,20,21	Problems set 9
Nov 27	Optimization problems and applications..	§4.7,4.8.4.10	4.7:9,19,25.2
Nov 29	Antiderivatives. Areas and distances	§4.10,5.1	4.10 : 19,20,21,22,23,26,27,28,29,35,36,37,45,46,59,62. 5.1:
Dec 4	The definite integral. The fundamental theorem of the calculus. Indefinite integral.	§5.2,5.3,5.4	5.2:27 5.3:7,8,9,10,15,16,17,18,19,20,21,22,26,28,30	Problems set 10
Dec 6	The substituion rule.	§5.5	5.5:7,8,9,10,17,18,21,23,49,50,51,52,53,54,79,80,81,82
Dec 11	Areas between curves. Review. Last day of class.	§ 6.1	6.1 : 1,2,3,4,11,12,13,14,47	Double problems sets 11 and 12
Dec 18	Due date for extra credit (2pm, in my mail box)	See above for the rules of extra credit.
Dec 20	Final exam 9am-12noon. (Cumulative)		Training final Solutions