# Calculus I, Spring 2015

Home Teaching Research Fun Math

## Math 1131, Sections W31 and W32

### Office Hours (312 Waterbury):

• Monday, Wednesday and Friday from 11:00-12:30.
You can also drop in and ask me a question:
• Any time you find me in my office (Room 312).

If none of these times don't work, let me know and we can find a something that does.

### Syllabus and Homework

• The Syllabus for Math 1131. This is your source for course pacing, grading, and some helpful hints on group work and calculators.

• You can access WebAssign using HuskyCT. Just go to our section's page, and click the link for "WebAssign Homework" on the left. If you are having trouble logging in, try using another browser. Internet Explorer and Safari do NOT appear to work. Mozilla Firefox and Google Chrome appear to work.

• A list of good practice problems in the textbook.

• To approximate your course grade, enter each of the following averages (out of 100%). Then click "Compute Grade"
 Quiz Homework Exam 1 Exam 2 Final Exam

## Resources for Calculus I

### Selected Class Handouts and Worksheets:

Class 1: Functions and Composition
We begin with a review of functions, composition, and the four ways that a function can be represented.
To suppliment this, we have handouts reviewing algebra and functions, and discussing sketching and mathematical models.

You should also be very comfortable reasoning about the graph of a function:

Class 2: Exponential and Logarithmic Functions

To get a good gut feeling for the graphs of exponential functions with different bases, try playing around with this interactive graphic:

You can also explore general exponential functions using a graphing calculator or computer algebra system and this worksheet. This was created using a free and open source computer algebra system called Sage.

Class 4: The Velocity and Tangent Problems
To get used to seeing the tangent line as the limit of the secant lines, try playing around with this interactive graphic

Class 6: Limit Laws
Due to the snowstorm, I have recorded a video of today's class. Let me know if you have any questions.

You will also benefit from the handout handout summarizing the many limit laws.

Class 7: Limits and Eventual Behavior
To help you on the homework, I have recorded an additional video example. Better yet, this example is both a nice concrete application and also an illustration of using the squeeze theorem.

Class 9: Derivatives and Rates of Change
Due to the snowstorm, I have recorded a video of today's class and created PDF notes. Let me know if you have any questions.

To get used to seeing the derivative as the limit of the average rate of change of $$f(x)$$, try playing around with this interactive graphic

Class 10: The Derivative as a Function
To get a good gut feeling for the derivative, try playing around with this interactive graphic:.

Class 14: Trig Derivatives
This fill-in-the-blank handout handout illustrates where the several trigonometric derivatives come from.

Class 19: Implicit Differetiation
A handout for trigonometric derivatives. The first half summarizes the definitions and derivatives of the standard trig functions. The second half shows how to graphs the main trig inverses based on the original function, and summarizes their derivatives.

Class 20: Derivatives and Logarithms
A new handout on Efficiently Finding Hard Derivatives and Solutions. The first page of the handout discusses some shortcut versions of the chain rule. On the second page, the handout reviews some important first steps you should consider when taking derivatives of complicated functions.

Class 21: Related Rates
The Worksheet and Solutions summarizes the main related problems we looked at in class. It also describes how to use a good "sketch" to set up and solve new related rates problems.

Class 23: Linear Approximations and Newton's Method
To get a better sense for the accuracy of linear approximations, try playing around with this interactive graphic.

Watch this video on Newton's Method to see a very nice application of linear approximations. You can also download the slides, which contain a few corrected typos from the video.

The textbook also has a good Newton's Method interactive graphic.

Class 24: Compound Interest and L'Hospital's Rule I
A Video explaining compound interest, and its relation to underdetermined limits and the slides from the video..

You'll probably need to take out loans, or to invest money, at some point in your life. To help you get a concrete sense of what different interest rates mean, I've made an Interactive Graphic on Compound Interest. Try changing the different parts of the equation. What happens if you change the Starting Value? What about changing the Interest Rate, or the Period?

Class 27: Local Maxes and Mins, and Concavity

Class 33: Approximating The Area Under a Curve

Class 34: Approximating Net Area
There are a couple of different ways to write down sums formulas. This handout summarizes the different ways, and explains when each is the most valuable.

Class 35: The Definite Integral
To emphasize the geometric meaning of the definite integral, we will occasionally need to compute integrals geometrically. This video, and PDF notes gives three examples of computing integrals geometrically.

### Important Textbook Information

You will need both the textbook and a WebAssign access key. The University Bookstore sells a bundle that contains both the book and the WebAssign access code. Using a link below, you can also buy the bundle online for a slightly lower price. Books purchased from other sources might not contain an access code, which can be expensive to buy on its own.

The following is adapted from the Storrs Website:

You can buy the bundled version of Calculus Early Transcendentals, Single Variable by James Stewart either at the UConn Coop or online directly from the publisher (linked below). Both the text and the Webassign code are required for this course.

The unbundled version of the book (that is, the book without a WebAssign access code) can be obtained in many places, but the cost of buying the unbundled text and the WebAssign code separately may be significantly greater.

There are three ways to purchase the text and the WebAssign access code:
1. Get the text and WebAssign access code bundled together from the publisher's special website for either single variable (1131-1132) or single variable and multivariable (1131-1132-2110). The single variable book is $75 online. 2. Get the text and WebAssign access code bundled together at the UConn Co-op. The single variable book is$100 in the bookstore.
3. You can, but we do not recommend, buy the WebAssign access code when you access your homework through HuskyCT. If you do this, the access code will cost between 95 and 110 dollars (based on the number of semesters the access code is good for). This costs much more than the bundled book with access code. Furthermore, the bundled access code will work for the life of the edition of the textbook.

How can you decide which version of the text to buy?

• If you only plan to take Math 1131 and 1132 then you should purchase the single-variable version of the textbook.
• If you plan to take Math 1131, 1132, and 2110 (multivariable calculus) then you should purchase the heavier book Calculus Early Transcendentals by Stewart. This version also includes chapters on multivariable calculus.