Courses   <-  Sean Forman   <-  You Are Here Calculus I

October 14, 2005

Second Exam Review. The second exam is Friday, October 22, 2005.

You will not need a special calculator, one able to do basic arithmetric will be sufficient. Any calculator capable of doing symbolic differentiation will not be allowed (for example the TI-89 and above). You will not have any notes or formulas available to you. Here is a summary of topics covered in the first part of the course. There may be other topics not listed here. You are responsible for all material covered in class and on homework.

The solutions to all assigned homework problems will be available on reserve in the library on Friday afternoon. Go to the front desk and ask for the homework solutions to Dr. Forman's Math 1351 class. The exam will be designed so that you should be able to complete it in 50 minutes.

1. Section 3.1 Derivatives of polynomials and exponential functions. You need to know how to find the derivative of $f(x) = a^x$ and $e^x$, the power rule, addition and subtraction. You should have an idea of how we decided to define $e^x$.

2. Section 3.2 Product and quotient rules. And you should be able to use them in concert with other rules like the chain rule.

3. Section 3.4 Derivatives of trig functions. You need to have $\sin(x), \cos(x),$ and $\tan(x)$ memorized.

4. Section 3.5 Chain rule and using it with different rules.

5. Section 3.6 Implicit differentiation. The basics of this and also how to plug in numbers, etc.

6. Section 3.7 Higher derivatives: finding patterns for higher order derivatives, acceleration, what the second derivative tells us about the first derivative. High order implicit differentiation.

7. Section 3.8 Derivatives of log functions, logarithmic differentiation (the hammer), derivatives of things like $x^x$.

8. Section 3.10 Related rates problems, will have one.

9. Section 3.11 Linear approximation: the differential and related ideas.

The exam is not yet completed, but I anticipate the test looking very similar to the homework problems. There may be a couple of extra questions that aren't homework questions, but knowing how to do all of the homework will prepare you very well. Obviously, you should also read through the text and notes as well.