Official Syllabus for Calculus I, MAT 175, Spring 2006
Prerequisite: MAT 172 (C+ and up strongly recommended),
All students are encouraged to attend an Intensive Precalculus
Review Session offered by the department in the second week of class.
See our precalculus syllabus at
http://comet.lehman.cuny.edu/calculus.
Corequisite: MAT 155 to learn Maple Classic
Text: Larson, Hostetler and Edwards, Calculus
(Early Transcendentals) Edition 3, Houghton Mifflin,
Do not buy the single variable version.
(topics may not correspond to section numbers if you have the wrong edition)
The textbook has a webpage at college.hmco.com
Supplies: A spiral notebook of graph paper for notes.
A cheap scientific calculator with buttons for sin, cos, tan,
Ln, and Log. A more expensive calculator which can differentiate will
not be permitted.
Homework: Approximately 2 hours of homework will be assigned
each meeting and additional review assignments will be given on weekends.
We've included odd problems here but your professor may assign different
problems. The odd ones have answers in the back of the text.
Timing:
This syllabus corresponds directly to the MAT 155 syllabus and should
not fall more than one lesson behind schedule. Students who need extra
help on any topic should go to the department's tutoring center.
Grading:
Two exams have been scheduled in this syllabus.
Faculty may also grade biweekly or suprise quizes or homework.
An accumulative final exam will
given during finals week to all students.
Students who plan to take Calculus II should
aim for A's.
Syllabus:
Lessons 1: Review Functions and Trigonometry (Sections P3 and D3)
P.3/1,3,5,7,11, 35; D3/5,7,19,31,51 (go to the Math Lab for help)
D3 is available online
Lesson 2: Review Exponential and Log (P6)
P.6/1,3,5,7,11, 17, 49, 53, 71
MAT155 will deal with all sections of Chapter P in the first 3 weeks
Lessons 3-4: Limits (1.1-1.2)
1.2/11,13,15,19,21, 23, 29
The epsilon delta definition of limit should be stated
and math majors should learn to apply it (1.2)
Review homework on Trigonometry Online(D3)
Lessons 5-6: Evaluating Limits and the Squeeze Theorem (1.3)
including Three Special Limits on page 81
1.3/9,11,13,43, 45,
1.3/37,53,57,69,79,(118, 125)
Lesson 7:Continuity (1.4)
1.4/1,3,5,11,43
Lesson 8:Infinite Limits and Asymptotes (1.5)
1.5/1,3,9,11,13,15,31,33, 39, 45, 47
Lessons 9-10: Review and Exam I on all the above material
Students who do poorly on this exam should consider dropping this
course and attending a class on precalculus before taking calculus. Please consult with your professor or Mr. Rothchild in Gillet 104 for more personalized advise. Bring your exam and homework with you when seeking advise.
Lessons 11-12: Tangent Lines and Derivatives (2.1)
2.1/1,3,5, 7,11,21
2.1/ 39-42, 47, 71, 75
Review homework on Composition of Functions in P.3/example 4, 51, 53, 55
Lesson 13-14: Laws of Differentiation including the product rule (2.2-3)
Review Homework on Inverse Functions in P.5/1, 5, 7, 9-12, 13, 19
2.2/5,7,17,21,23, 43,
2.3/1, 3, 7, 25, 35, 37, 41, 49, 51
Lesson 15: Chain Rule (2.4)
2.4/11,21,49,57,65,81
Lesson 16: Implicit Differentiation (2.5-2.6)
2.5/7,21,35, 43, 2.6/7,15, 25
Lessons 17 and 18: Related Rates (2.7)
2.7/5,7,13,15, 25, 27, Chap 2 Review/43, 51, 57, 67, 73, 87
2.8 on Newton's Method will be done in MAT155
Lessons 19 and 20: Review and Exam II on Chapter 2
Review tables on 171-173
Lessons 21-22: Extrema, Mean Value Theorem, Increasing/Decreasing (3.1-3)
3.1/1,11,13, 15, 19, 23, 31,
3.2/31,35, 41, 59; 3.3/1,3, 17, 27
Review Old Homework on Limits (1.5).
Lesson 23: Concavity (3.4)
3.4/1,3,5,19,23,27, 29
Lesson 24: Limits at infinity (3.5) and, if time allows, L'hopital's Rule (7.7)
3.5/1,3,5,7,9,19, 23; 7.7/27, 29, 33, 35
Review Homework on the Definition of Derivative 3.1
Curve sketching (3.6) will be covered in MAT155
Lessons 25- 26: Optimization and Business Applications (3.7, appendix A)
3.7/3,5,7,9,27,33 A/3, 7, 9, 13, 15, 25,
Lesson 27: Antidifferentiation (4.1) if time allows
4.1/5,7,21, 31, 43, 53, 55, 57
Lesson 28: Review for the final
Final: The final will be given during Finals Week covering
the entire course especially topics needed in future courses.
This syllabus and others are available at:
http://comet.lehman.cuny.edu/calculus/ .