Calculus I--Math 135--Spring 2012

Instructor: Li Guo

Announcement: I will regularly update this webpage and put my latest announcements.

Office: Smith 308; Phone: 973-353-3917; Email: liguo@rutgers.edu

Office Hours: Monday and Wednesday, 9:00am-9:50am or by appointment.

TA: Matthew Albano; Office: Smith 203; Email: malbano@rutgers.edu

Office Hours: Thursday 9-10am. 

Text Book: Calculus, Early Transcendentals +MyMathLab Student Access Kit. Briggs and Cochran Addison Wesley, ISBN 978-0-321-57056-7
Class times: Monday and Wednesday 10:00-11:20am in Conklin 100. You are also assigned a recitation section meeting every Friday, 9:00am-3:20pm in Smith B23. Attendance to the lectures and recitations are required. There will be attendance checks in the lectures and a quiz on most Fridays. A perfect attendance record is helpful when your course grade is on board lines.

Grading:    two midterms  20% each
          quizzes       20% total
          homework
(MML)10% total
          final exam    30%
Calculators are
NOT allowed in the midterms and final.

Course Objectives: This is a course in single-variable calculus, covering limits, derivatives, and the basics of integration. The approach will be rigorous, but with more emphasis on ideas and calculations, rather than proofs. A small fraction of final grade will depend on your ability to write simple proofs; if you are looking for a more proof-based approach, consider 20:640:155: Honors Calculus; if you are looking for a less rigorous approach, consider 20:640:119: Basic Calculus.

Prerequisites: 21:640:114: Precalculus. This means, according to the University Catalog, that you should be comfortable with algebraic, rational, trigonometric, logarithmic, and exponential functions; functions and inverse functions; solutions of nonlinear inequalities; advanced factoring techniques. For example: Which functions are called rational? Do you know the trigonometric identities? What is the sum of angle formula for sine and cosine? What is the exponential function and how it is related to exp(x). If you do not feel certain about these questions, you MUST spend extra time during the first weeks reviewing them by yourself. Also you may take advantage of recitations and office hours to ask for advice and fill in any gaps that you might have. We will start with Chapter 2 of your book. Chapter 1 is part of the prerequisites, so you should make sure that you are comfortable with the materials in that chapter.

Tutoring services are available in the Learning Resource Center in Room 140 Bradley Hall (973-353-5608). http://lc.newark.rutgers.edu. Check the web site for schedules.

Make-up exams will be allowed only in extreme situations (e.g. death in the family, serious illness with a doctor's note) and I MUST be notified BEFORE the scheduled exam. Also if you are a student with disability and might need extra time to finish the exam MUST inform the instructor BEFORE the scheduled exam date.

Disability Center and further support: If you have some disabilities, or even some recurring problems which may hinder your participation in class or at exams, please contact the University Office of Disability Services to request accommodations for your condition. Feel free to contact your instructor if you have any concerns about your condition and how it could affect your participation. Visit also the website: http://disabilityservices-uw.rutgers.edu/ for further information.
Homework is very important! Each of the entries in the weekly outline below contains a list of homework problems for that day. You should do those problems by the next class. In my experience, students who do each homework assignment carefully and on time do well. The students who don't don't.

MyMathLab (MML) and enrollment: See http://andromeda.rutgers.edu/~liguo/Class/MMLGuo.htm for MML information. After you use your purchased access code to create your personal account on MyMathLab, go to "Edit Profile". Please provide a valid email that you will check regularly in your profile. Choose "Enroll in classes" and type Class ID:guo12732. Please do so early, as the first MyMathLab homework will be due on Thursday Jan. 26th.

Note: hw-2A(quiz on Jan-27th) on MML means that the problems for the quiz on September 9th will be picked up from hw-2A. And you need to supply all the details on the quiz to get the full mark.          

Warning: Enrolling on MyMathLab does not register you for the class. You need to be officially registered for the class in order to receive any credit-no exceptions!

Note:  Please complete your homework by using MyMathLab ONLY and submit them electronically. Do not submit any homework on papers. The problems assigned on MyMathLab electronically are also listed below (in parentheses). However these are only tentative and one should follow the more up to date assignments on MyMathLab.

 

Tentative Weekly Outline:
Week 1: January 18
   Section 1.1 Review of functions (see MML)

   Section 1.2 Representing functions (see MML)

   Section 2.1The idea of limits (7, 9, 13, 15, 21)

Week 2: January 23 and 25
    Section 2.2
Definitions of limits (7, 8, 14, 17, 21, 23, 30, 31, 32)
    Section 2.3 
Techniques for computing limits (11-47 odd)
    Section 2.4 
Infinite limits (8, 9, 12, 17-29 odd) 

Week 3: January 30 and February 1
    Section 2.5 
Limits at infinity (9-36 odd)
    Section 2.6 
Continuity (9, 16, 19, 21, 23, 25, 27, 35, 37, 41, 43, 45, 46)
    Section 2.7 
Precise definition of limits (9-32 odd, 33, 34, 39-43)
Week 4:
February 6 and 8
    Section 3.1 
Introduction to the derivative (11-31 odd, 33, 39,40,41, 49, 51, 65-68)
    Section 3.2
  Rules of differentiation (25-37 odd, 47, 50,-53, 57-59, 74)
    Section 3.3 
The product and quotient rules (23-26, 37-42, 49-60, 64-68 even)
    Section 3.4 
Derivatives of trig functions (23-35 odd, 37, 38-42 even, 55,56, 60-63)
Week 5:
February 13 and 15
    Section 3.5 
Derivatives as rates of changes (9, 10, 25)
    Section 3.6 
The chain rule (33-45 odd, 47, 48, 52, 58, 60, 71-74)
    Section 3.7 
Implicit differentiation (21-25 odd, 27-39 odd,47, 48, 50)
Week 6:
February 20  

Section 3.8  Derivatives of log and exp functions (26-32 even,  43-51 odd, 52-64 even, 67, 70, 73)
     Section 3.9 
Derivatives of inverse trig functions (13-27 odd, 39-43)
   
February 22 Review 1
Week 7:
February 27 EXAM 1

February 29 Section 4.1 Maxima and minima (11-43 odd, 47, 48-52 even, 68)
Week 8:
March 5 and 7
    Section 4.2 
What derivatives tell us (31, 34, 37, 49, 54, 57-61 odd, 69-79 odd, 84)
    Section 4.3 
Graphing functions (21-31, 37, 42-43)
    Section 4.4
 Optimization problems (5-12, 16-18, 23)

Week 9: March 19 and 21
   Section 4.5
Linear approximation and differentials (7-11 odd, 13, 17, 21, 29-37 odd)
    Section 4.6
Mean values theorem (7-11 odd, 15-27 odd, 32, 33, 39)
    Section 4.7 
L’Hopital’s rule (13-37 odd, 39, 42, 45, 47, 49, 52, 55, 58, 61-63, 65-69 odd, 85-88)

Spring break: March 12-16

Week 10: March 26 and 28
   
Section 4.8  Antiderivatives (19-31 odd, 43-47 odd)
    Section 5.1 
Approximating areas (17-20, 23-27 odd, 31-33, 53-56, 70, 71)
    Section 5.2
  Definite integrals (19-41 odd, 45, 49, 51)
Week 11:

    April 2:
Review 2
   
April 4: EXAM 2
Week 12:

    April 9 and 11 

   
 Section 5.3 Fundamental theorem of calculus(11, 12,  23-39 odd, 51-55 odd, 58-62 even, 73, 74-80 even, 87-89)
    Section 5.4 
Working with integrals (7-13 odd, 37-41, 57)
    Section 5.5 Substitution rule (29-63 odd, 65, 67, 86-89)
    Section 6.1
Velocity and net change
Week 13: April 16 and 18:
    Section 6.2
Regions between curves (6,16, 27, 29, 31, 39-47 odd, 52)
    Section 6.3
Volume by slicing (23-27 odd, 32, 41, 42, 44)
    Section 6.4
Volume by shells (11-15 odd, 27-33 odd)
Week 14:
April 23 and 25
    Section 6.5 Length of curves (4, 6, 21-27 odd, 28)
    Section 6.7 Log and exp functions revisited (7-21 odd, 39-45 odd,  46-54 even, 56-61)
    Appendix: Nice link  to understand
Cylindrical shell method and Washer method.
Week 15:
 

    April 30: Review for final exam

FINAL EXAM: Friday May 4

Other dates of interest:
    Last day to drop a course: Tuesday, January 24
    Last day to add a course:  Wednesday, January 25
    Last day to drop a course and receive a
W grade: Tuesday, March 27

HELPFUL LINKS:
    
Calculus applets
    
3-D grapher
    
More Calculus applets
        Banchoff applets
   
Paul Seeburger (Very helpful to understand various method to compute the volume)

        Lagrange Multiplier applet