Course Outline: If you draw the graph of a function and then pick a point on the graph, you should be able to draw the line tangent to the graph at that point. You can then estimate the slope of this tangent line by taking the quotient of the rise over the run. The beautiful notion is that for most functions given by a formula one can find another formula (called the derivative) which will enable you to find the exact value of the slope at any given point on the function. This may not seem to be such a big deal at first, but consider the fact that at points where a smooth function reaches a maximum or minimum value the slope of the tangent line must be 0. Thus, one can locate the exact maximum and minimum values achieved by a smooth function by using its derivative to locate the places where the function has a flat tangent line. One can probably imagine that this is an important idea. For example, an economist may wish to determine the number of units to produce in order to maximize profit.

In Math 120 we will begin by introducing tangent lines and their possible uses. We will then learn about the tools needed to calculate the derivative. Once we have a thorough understanding of the derivative and how to calculate it, we will move on to explore its applications. Finally, we will talk about a method for calculating the exact area between a given function and the x-axis between any two fixed points. This method (called integration) is surprisingly linked to the derivative. When you leave Math 120, you will carry with you concepts and ideas from calculus that can be applied later, both in mathematics and in other fields.

Necessary Background: Some of you have had calculus before. However, those of you who haven't need not be alarmed: in the past, students without a calculus background have done as well as those with it. Doing well in Math 120 requires a solid background in precalculus.

Classes and Recitation Sessions: Class meets MWF from 12:30 to 1:20 in Baker A53. Your Teaching Assistant (TA) will also hold two weekly recitation sessions. I strongly encourage you to attend these recitation sessions as they are an integral part of the course and will be devoted primarily to amplifying the material and working problems reasonably similar to the homework. Click here for more information about your TA and the recitation sessions.

Office: Wean 7130        Phone:268-2545       Email:jmackey@andrew.cmu.edu

Course Web Site:  www.math.cmu.edu/~jmackey/math120/math120.html

Office Hours: Monday from 1:30-2:30, Tuesday from 12:00-1:00, and by appointment.

Help: In addition to class, recitation sessions, and office hours, the University operates a walk-in Peer Tutoring Center in the Mudge Library and the Donner Reading Room on Sunday-Wednesday evenings from 8:30 to 11:00pm. Individualized tutoring and other help options are also available through Academic Development.

Homework: Homework exercises are an essential part of the course. It is difficult to understand the material and do well on the exams without working through the homework problems in a thoughtful manner. Discussion of the homework with your peers is encouraged, but copying any part of another person's homework is not permitted. Please think about the problems posed, your strategies, and the validity of your logic and explanations.

Homework is due at the beginning of recitation on Tuesdays. Homework turned in after Tuesday's recitation has begun, but before the solutions are posted on Wednesday afternoon will receive half credit (with an asterisk to get full credit if the course grade is borderline). Late (or early) homework may be turned in to your TA's mailbox in Wean 6113, but you must first alert your TA to this fact with a brief email of explanation. No credit will be given for homework turned in without explanation or after the solutions have been posted on Wednesday afternoon.

Online homework, administered through webassign, will also be periodically assigned. Students will go to www.webassign.net and enter the class key I give out in class to work the online homework. Registration instructions can be found here: registration.

Text: Calculus: Early Transcendentals, 8th edition, by James Stewart. It is available at the bookstore and directly from cengage at cengage.

Midterms: There will be three in-class midterms and a cumulative final exam. The dates of the midterm exams are as follows:

Midterm 1: Wednesday, February 10

Midterm 2: Friday, March 18

Midterm 3: Wednesday, April 13

Grading: Your course grade will be determined as follows:

Each of the two high midterm scores: 20%
The low midterm score: 15%
Homework: 15%
Final Exam: 30%

Calculators: We encourage you to not rely too heavily on a graphing calculator as you work through your homework problems. Use the calculator to check your graphs if you must. That said, the use of a quality calculator can prove very helpful in understanding a good number of topics in the course from limits and successive approximation to graphing. Calculators will not be allowed during exams.

Week by week schedule (tentative):

Week 1 (January 11-15):

• Welcome and Section 2.1 The Tangent and Velocity Problems
• Section 2.2 The Limit of a Function
• Section 2.3 Calculating Limits Using the Limit Laws

Week 2 (January 20-22):

• Section 2.5 Continuity
• Section 2.6 Limits at Infinity; Horizontal Asymptotes

Week 3 (January 25-29):

• Section 2.7 Derivatives and Rates of Change
• Section 2.8 The Derivative as a Function
• Section 3.1 Derivatives of Polynomials and Exponential Functions

Week 4 (February 1-5):

• Section 3.2 The Product and Quotient Rules
• Section 3.3 Derivatives of Trigonometric Functions
• Section 3.4 The Chain Rule

In-class Review for Midterm; Monday, February 8

First In-class Midterm; Wednesday, February 10

Week 5 (February 8-12):

• In-class Review for Midterm 1
• Midterm 1
• Section 3.5 Implicit Differentiation

Week 6 (February 15-19):

• Section 3.6 Derivatives of Logarithmic Functions
• Section 3.7 Rates of Change in the Natural and Social Sciences
• Section 3.8 Exponential Growth and Decay

Week 7 (February 22-26):

• Section 3.9 Related Rates
• More Practice with Related Rates
• Section 3.10 Linear Approximations and Differentials

Week 8 (February 29 - March 2):

• Section 3.11 Hyperbolic Functions
• Section 4.1 Maximum and Minimum Values

In-class Review for Midterm; Wednesday, March 16

Second In-class Midterm; Friday, March 18

Week 9 (March 14-18):

• Section 4.2 The Mean Value Theorem
• In-class Review for Midterm 2
• Midterm 2

Week 10 (March 21-25):

• Section 4.3 How Derivatives Affect the Shape of a Graph
• Section 4.4 Indeterminate Forms and L'Hospital's Rule
• Section 4.5 Summary of Curve Sketching

Week 11 (March 28 - April 1):

• More Practice with Curve Sketching
• Section 4.7 Optimization Problems
• More Practice with Optimization Problems

Week 12 (April 4-8):

• Section 4.9 Antiderivatives
• Section 5.1 Areas and Distances
• Section 5.2 The Definite Integral

In-class Review for Midterm; Monday, April 11

Third In-class Midterm; Wednesday, April 13

Week 13 (April 11-13):

• In-class Review for Midterm 3
• Midterm 3

Week 14 (April 18-22):

• Section 5.3 The Fundamental Theorem of Calculus
• Section 5.4 Indefinite Integrals and the Net Change Theorem
• Section 5.5 The Substitution Rule

Week 15 (April 25-29):

• Section 7.1 Integration by Parts
• In-class Review for Final Exam
• In-class Review for Final Exam

Final Examination, Scheduled by the Registrar

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