Calculus I Syllabus
MAT175 Calculus I: 4 hours, 4 credits. Differentiation of functions of one variable; applications to motion problems, maximum-minimum problems, curve sketching, and mean-value theorems, Riemann Sums and Fundamental Theorem of Calculus
Prerequisite: A grade of C (or better) in MAT 172 or placement by the department.
Corequisite: MAT 155 Calculus I Computer Laboratory
Meeting Times: 2:00-3:40 pm M/W in Gillet 205 Course Webpage: https://sites.google.com/site/professorsormani/calculus-f16
Office: 200A Gillet Hall, Office Hours: 1:30-2:00, 3:45-4:15 M/W Email: sormanic@gmail.com
Grading Policy
Expectations: Students are expected to learn both the mathematics covered in class and the mathematics in the textbook and other assigned reading. Completing homework is part of the learning experience. Students should review topics from prior courses as needed using old notes and books.
Homework: Approximately four hours of homework will be assigned in each lesson as well as additional review assignments over weekends. The answers to all homework problems are in the back of the book. Go to the math lab for help with the homework immediately. The quizzes will test the material on the homework with no prior review.
Exams: There will be two exams and regular quizzes on homework. Students who do not pass the departmental final exam will not pass the course.
Grades: Exam 1 (30%) Exam II (30%) Quizzes (10%) Final (30%)
Materials, Resources and Accommodating Disabilities
Textbook: Larson, Hostetler and Edwards, Calculus (Early Transcendentals), Houghton Mifflin, You may purchase Ed 4 or Ed 5. ISBN:0538735503 or 9780538735506 Tutoring: Departmental tutoring is available in Gillet Hall 222.
Reliable Web Resources: See http://comet.lehman.cuny.edu/calculus
Reserve: Selected books have been placed on reserve in the library. Accommodating Disabilities: Lehman College is committed to providing access to all programs and curricula to all students. Students with disabilities who may need classroom accommodations are encouraged to register with the Office of Student Disability Services. For more info, please contact the Office of Student Disability Services, Shuster Hall, Room 238, phone number, 718-960-8441.
Course Objectives
At the end of the course students should be able to:
1. Evaluate limits (as part of Departmental Objectives in Mathematics a,b and e)
2. Prove basic theorems using limits of the difference equation (as part of a,b and f)
3. Differentiate algebraic and trigonometric functions using key theorems (a,b and e)
4. Find the tangent line to a given graph at a given point (as part of a,b and e)
5. Solve maximum and minimum problems using differentiation (as part of a,b,c and e) 6. Solve related rates problems (as part of a,b and c)
7. Apply methods of calculus to curve sketching (as part of a,b)
8. Antidifferentiation, Riemann Sums and Fundamental Theorem of Calculus (a,b, and e)
These objectives will be assessed on the final exam along with other important techniques.
Course Calendar
This course and its corequisite are carefully timed to match topics, so stay on schedule. The homework listed below is different in the different editions of the textbook but cover the same types of problems. Check your answers in the back of your textbook.
Lesson 1 (Mon 8/29): Review Precalculus (Sections 1.1-1.3, 1.6 and D3)
1.1/ 1-14, 19, 21, 53, 55, 63; 1.2/ 19, 23-32, 35, 43, 49-55 odd, 77.
1.3/ 5-9 odd, 13, 17-21 odd, 57-63 odd; 1.6/ 7-15 odd, 19, 25, 27, 49, 59, 91, 93 Trigonometry Appendix Edition 5: C3/11, 13, 15, 19, 31, 37, 51
Edition 4 has an online trigonometry appendix D3 at:
http://college.cengage.com/mathematics/larson/calculus_early/4e/assets/app/appendixd3.pdf
Please seek help in MAT 155 and in the Math Lab for this precalculus homework.
Lesson 2 (Wed 8/31): Limits (2.2)
2.2/ 1, 3, 5, 11, 13, 15, 17, 19, 21, 23
Review 1.5/ 1, 5, 53, 57, (ed 4: 89, 91, 93) (ed 5: 95, 97, 99) Email the professor proof that you have taken Precalculus
(math majors should also read Appendix A Thm 2.2-2.5 and do 2.1/31,33)
No Lehman classes on Labor Day (Mon 9/5)
Lessons 3 (Wed 9/7): [Precalc Quiz] Evaluating Limits and the Squeeze Theorem (2.3) including Three Special Limits
2.3/ 9-21 odd, 37, 43, 45, 53, 57, 69, 79, (math majors should also read Appendix A Thm 2.8 and do 2.2/ 39, 2.3/ 118, 125
Lesson 4 (Mon 9/12): [Limits Quiz] (students who miss class for Eid al-Adha may schedule the quiz for a different date)
No HW due to Eid al-Adha, catch up on old work
Lesson 5 (Wed 9/14): Continuity (2.4) 2.4/ 1, 3, 5, 11, 31, 37, 39, 41, 43, 47
Lesson 6 (Mon 9/19): [Quiz on Continuity or Retake Precalc quiz] Infinite Limits and Asymptotes (2.5)
2.4/ 49, 51, 55, 57, 59; 2.5/ 1, 3, 7, 9-15 odd, 31, 33, 39, 45, 47,
Lesson 7 (Wed 9/21): Tangent Lines and Derivatives (3.1)
3.1/ 1, 5, 7, 11, 13, 21, 37, 39, 41, 61
Review 1.3/ Example 4, 59, 61, 63
Lesson 8 (Mon 9/26): [Quiz on Tangent Lines] Velocity and Laws of Differentiation (3.2)
3.2/3-23 odd, 43-61 odd; (Ed 5 3.2/101, 103) or (Ed 4. 3.2/93, 95)
Review 1.5/ 1, 5, 7, 9, 11, 13
Lesson 9 (Wed 9/28): Product and Quotient Rules (3.3)
3.3/ 1-7 odd, 17, 19, 25, 31, 41, 43, 45, 69; (Ed 5 3.2/ 105, 107, 111) or (Ed. 4 3.2/ 93, 99, 103)
No Lehman classes on Rosh Hoshanah (Mon 10/3) Extra Office Hours during class time
Lesson 10 (Wed 10/5): [Quiz on Differentiation 3.2-3.3] Chain Rule (3.4)
3.4/ 9-15 odd, 23, 25, 29, 49, 51, 55, 59, 63, 67, 79-83 odd, 115, 117 (math majors read Appendix A Thm 3.11)
Lesson 11 (Thursday 10/6): Review for Exam I
Review all examples in 1.1-3.4, and all prior homework problems and practice doing them quickly.
There will be problems like each quiz and also problems using the product rule, the quotient rule and the chain rule.
No Lehman Classes Columbus Day (Mon 10/10) or Yom Kippur (Wed 10/12)
Lesson 12 (Mon 10/17): Exam I on 1.1 -3.4 (not including continuity) No calculators or phones allowed on this exam or any other exam.
Students who do poorly on this exam should consider dropping this course and attending a class on precalculus before taking calculus next semester. Please consult with your professor or math adviser for more personalized advice. Bring your exam and homework with you when seeking advice.
Lesson 13 (Wed 10/19): Implicit Differentiation (3.5-3.6)
3.5/ 1, 7, 29, 33, 35, 47; 3.6/ 7, 15, 25, 45
Lesson 14 (Mon 10/24): [Chain Rule and Implicit Differentiation Quiz] Related Rates (3.7)
3.7/ 1, 5, 13, 15, 27, 39, 41, (3.8 on Newton's Method will be done in MAT155)
Lesson 15 (Wed 10/26): More Related Rates
Lesson 16 (Mon 10/31): [Related Rates Quiz] (students who miss class for Halloween may schedule the quiz for a different date)
Lessons 17 (Wed 11/2): Extrema (4.1-4.3)
4.1/ 1, 7, 11-15 odd, 21-35 odd;
Review Old Homework on Limits (2.5).
Lesson 18 (Mon 11/7): [Extrema Quiz] Mean Value Theorem, Increasing/Decreasing (4.2-4.3) 4.3/ 3, 5, 9-13 odd, 17, 29-35 odd, 43
Lesson 19 (Wed 11/9): Review of Continuity (2.4) and Increasing Decreasing (4.3) including Graphing (4.6)
2.4/ 1, 3, 5, 11, 31, 37, 39, 41, 43, 47
4.3/ 3, 5, 9-13 odd, 17, 29-35 odd, 43
Lesson 20 (Mon 11/14): [Inc/Dec Quiz] Concavity (4.4) and Limits at infinity (4.5) and Graphing 4.6 [Continuity Quiz in Office Hours]
4.4/ 1, 3, 5, 7, 11, 13, 15, 19, 21, 23, 27, 29, 39, 43, 47
4.5/ 1, 3, 5, 17-25 odd, 35 Go over 4.6 Examples 1-6.
Curve sketching (4.6) will be covered in MAT155
Lesson 21 (Wed 11/16): Review for Exam II on Chapters 3-4 and Continuity 2.4
4.2 and 4.8 are not covered on this exam or the final.
Review all examples in 2.4, 3.1-3.7, 4.1, 4.3-4.6 and all prior homework problems. Practice doing them quickly.
There will be problems like each quiz including using the product rule, the quotient rule and the chain rule.
There will be problems involving concavity, 2nd deriv test and limits at infinity as well.
Lesson 22 (Mon 11/21): Exam II on Chapters 3-4
Lesson 23 (Wed 11/23): Optimization (4.7) and Review Exam II
4.7/ 3-9 odd, 17, 25, 27, 29, 33; Learn what you did incorrectly from Exam II, and practice doing problems quickly.
On Monday you will be given a retake of Exam II but only one hour to complete the retake.
So you must practice working quickly. The retake will not be multiplied by .8 so that you can improve your grade to 100%.
Lesson 24 (Mon 11/28): [Retake Part of Exam II] Antiderivatives, Position, Velocity, Acceleration,
HW 5.1/ 1,3,17,19,21,25,27,35,81,87,89,91,
Lesson 25 (Wed 11/30): [Quiz on Antiderivatives] Area, Riemann sums, definite integrals
HW 5.2/ 7, (ed4 23,25,27,29,35) or (ed5 33,35,41,43,45)
HW 5.3/ 1,3,5,7,11,15, 17, 19, 25,27,35,41,
Lesson 26 (Mon 12/5): [Quiz on Riemann Sums] Fundamental Theorem of Calculus
HW 5.4/ 27,31,39, 45,47,51,59,61,81,83,87,89,91,95,97,101, (ed 4 109) or (ed 5 113)
Lesson 27 (Wed 12/7): u substitution
HW 5.5/1,3,5, 11-29 odd, 49-65 odd, (ed4 87, 117, 119, 147, 149) or (ed5 91, 121, 123, 151, 153)
Lesson 28 (Mon 12/12): [Quiz on Integration and u substitution] Review for the Departmental Final
The department will also schedule reviews for the final.
Final Exam: Monday Dec 19 2:00-4:00pm