Calculus-S13

• Calculus I Spring 2013

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.

Prerequisite: A grade of C (or better) in MAT 172 or placement by the department.

Corequisite: MAT 155 Calculus I Computer Laboratory

Meetings: 2:00-3:40 pm Monday Wednesday in Gillet 333

Course Webpage: https://sites.google.com/site/professorsormani/teaching/calculus-s13

Instructor: Professor Sormani see http://comet.lehman.cuny.edu/sormani

Office: 200B Gillet Hall Contact by Email: sormanic@gmail.com

Office Hours for this class: 1:30-2:00 & 3:40-4:10 Mondays and Wednesdays

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 two hours of homework will be assigned in each lesson as

well as additional review assignments over weekends. It will be graded by a grader.

Exams: There will be at least three midterm exams and a final exam. Students who do

not pass the departmental final exam will not pass the course.

Grades: Each midterm exam is worth 20%, and the final is worth 40% of the grade.

Materials, Resources and Accommodating Disabilities:

Textbook: Larson, Hostetler and Edwards, Calculus (Early Transcendentals) Ed. 4, Houghton Mifflin

Edition 4 is a special discount edition for Lehman College students available at the bookstore

The homework below corresponds to this edition.

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 (as part of 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)

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.

Lesson 1 (01/28): Review Graphs and Trigonometry (Sections 1.1, 1.2 and D3) and Quantifiers (worksheet)

1.1/ 1-14, 19, 21, 27-37 odd, 39-56, 61-68;

1.2/ 19, 23-32, 35, 43, 49-56, 77. (go to Gillet 222 for help)

Review online trigonometry appendix D3 at:

http://college.cengage.com/mathematics/larson/calculus_early/4e/assets/app/appendixd3.pdf

Lesson 2 (01/30): Review Elementary Functions (Sections 1.3, 1.6)

1.3/5-9 odd, 13, 17-28, 31-37 odd, 59-64, 95(a).

1.6/ 7-16, 19-27 odd, 35-38, 45-50, 59-63 odd, 77-81 odd, 85, 91, 93.

Lesson 3 (02/04): Limits (2.1-2.2)

2.2/ 11-26, (math majors should also do: 31, 33, 39, 49).

Lesson 4 (02/06): Evaluating Limits and the Squeeze Theorem (2.3)

2.3/ 5-39 odd, 43, 45, Review Unit Circle definitions of sine and cosine.

Lesson 5 (02/11): Three Special Limits (2.3)

2.3/ 51-64, 69-81 odd, (118, 125).

Lesson 6 (02/13): Continuity (2.4)

2.4/ 1-19, 29, 33, 37-53 odd, 55, 63-66.

Lesson 7 (02/20): Infinite Limits and Asymptotes (2.5)

2.5/ 1, 3, 9-21 odd, 29-33 odd, 39, 45, 47.

Chap 2 Review/15-25 odd, 29, 31, 35-42, 47, 49, 55, 57, 61, 69, 73, 77;

Lesson 8 (02/25): Review of Chapters 1-2

Practice doing examples from the text before looking at their solution and then check the solution: 1.1/2; 1.2/pages 10-11, 1,3,4; 1.3/1,2,3; 1.4/ page 37, 1,2,3,4; 1.5/2,4; 2.2/2,3,4,5; 2.3/1,2,3,4,5,6,7,8,9,10; 2.4/1,2,3,7; 2.5/1,2,3,4,5

Lesson 9 (02/27): Exam I on Chapters 1-2

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 math advisor for more personalized advice. Bring your exam and homework with you when seeking advice.

Lessons 10 (03/04): Tangent Lines and Derivatives (3.1)

3.1/ 1-7 odd,

Lesson 11 (03/06): Velocity and Derivatives

3.1/ 11, 21, 37-41, 47, (71, 79)

Review Composition of Functions in 1.3/example 4, 59, 61, 63

Lesson 12 (03/11): Laws of Differentiation including the Product Rule (3.2-3)

(Review Inverse Functions in 1.5/ 1, 5, 7, 9-12, 13)

3.2/ 3-24, 31-62. (Pick up graded homework on my office door 200B Gillet Hall)

Lesson 13 (03/13*): Practice with Differentiation

3.3/ 1-12, 16-20, 27-57 odd, 69, 71, 77. (Pick up graded homework on my office door 200B Gillet Hall)

Lesson 14 (03/18): Chain Rule (3.4)

3.4/ 1-35 odd, 55-95 odd, 103, 115, 117. (Pick up graded homework on my office door 200B Gillet Hall)

Lesson 15 (03/20): Implicit Differentiation and Derivatives of Inverse Functions (3.5-6)

3.5/ 1-13, 25-35 odd; 3.6/ 3, 7, 15, 19, 21, 69. (Pick up graded homework on my office door 200B Gillet Hall)

During Spring Break be sure to memorize all the theorems related to differentiation

and catch up on material you did not know on Exam I. Study all the examples listed

to study for Exam I plus all examples in Sections 3.1-3.4. If you have any difficulty with

a precalculus topic (eg trigonometry or exponents) practice that topic.

Lesson 16 (04/03): Extra Exam I: This Exam is on Chapters 1-2 and 3.1-3.4. If you score

better on this exam than on Exam I, then your Exam I grade will be replaced by your grade on

this exam. For those who did very well on Exam I this is an opportunity to pull your grade even higher.

As before, be careful with your precalculus! Format: this will be exactly like Exam I

but the first page will ask you to find derivatives using the limit definition (so again limits but

now part of harder problems) and the third page will now also ask you to find a tangent line

at a certain point and graph that as well, and fourth page will be a page where you use the

many theorems we've learned to find derivatives of functions and the formulas for their tangent

lines. You will not need to know implicit differentiation nor derivatives of inverse functions but you

must know product, quotient and chain rules as well as the derivative of sin, cos, and the exponential

function.

Before Lesson 17: See the above assignment "During Spring Break..." Repeat this assignment focusing

on examples related to problems you had difficulty with on the Extra Exam I. This means, for each example,

you read the question, then you try to solve it yourself, then check how the book has solved and fix your work.

You should be aiming to be able to do all questions perfectly. If your work is not correct, study it, and try it

again the next day. Exam III is coming very soon and you must master this material first!

Also, 3.5/ 1-13, 25-35 odd; 3.6/ 3, 7, 15, 19, 21, 69. which was assigned in Lesson 15 should be done already.

These types of questions are on Exam III.

Lesson 17 (04/08): Related Rates (3.7)

3.7/ 1, 5, 13, 15, 18, 20-22,27,39 (Pick up graded homework on my office door 200B Gillet Hall)

Lesson 18 (04/10): Review for Exam II

Chap 3 Review/ 1, 3, 7, 11, 17-32, 39, 41-59, 67-91 odd, 105, 119-125 odd, 144.

3.8 on Newton's Method will be done in MAT155,

Lesson 19 (04/15): Exam II on Chapter 3: This exam will have no limits but it will have many

applied problems with velocity, acceleration, finding tangent lines, and related rates and

every type of derivative including products, quotients, chain rules, and implicit differentiation.

You will be asked to graph tangent lines and can use the practice sheet to practice this.

Lesson 20 (04/17): Extrema and Critical Points (4.1-2)

4.1/ 1, 7, 11-17 odd, 21-35, 69-72.

Lesson 21 (04/22): Mean Value Theorem, Increasing/Decreasing (4.2-4.3)

4.3/ 3-14, 17-39 odd, 63-68, 87, 88, and

• Every day: practice five derivatives and check your answers in the back of the book or using Maple.

• Every day: practice five limits and check your answers in the back of the book or using Maple.

• There will be problems on the final similar to Exam III Problems Part I (1), Part II (1)-(3), Part III (1)-(8) so if you did any of these problems wrong be sure to study examples and homework questions similar to that problem. The other problems are too hard to test on a final but will come up in future courses so you must master that material sometime after the final.

• There is one topic in chapter 4 that we have not yet tested: relative extrema (see Chapter 4.4 Ex 4 and Exercises 29, 31, 41, 45, 49 and class notes from 5/13)

• There will be problems similar to Exam II (1)-(6) but the related rates question will be easier (still requiring implicit differentiation but the formulas will be given).

• There will be problems similar to all the problems in Exam I and Extra Exam I. There will also be a continuity problem in a different style (see Section 2.4 Examples 1 and 7, and Exercises 63, and 65 and class notes from 5/13).

On Monday: Practice the Sample Final Exam as if it were a timed final and then come to my office.

I will hold office hours on Monday 1:30-6:00 pm with a couple short breaks.

Final Exam: The Departmental Final Exam will be given during Finals Week covering the entire course especially topics needed in future courses. Sample exams will be distributed. Wed May 22 1:30-3:30 pm in Gillet 333. Keep in mind that you must pass this departmental final in order to pass the course

Department of Mathematics and Computer Science, Lehman College, City University of New York