Math 1571H Honors Calculus Fall Semester 2001

Assignment 13 - Due Thursday 12/6/2001.

There will be a 50 minute exam on Wednesday 12/5/2001, on the material we have covered in Chapters 5 and 6 and Sections 7.1 and 7.2. You may use calculators, but not the book or notes.

Revision tips: You should be fluent in computing the standard antiderivatives that we have seen: powers of x, sin, cos and sec². Distinguish between an antiderivative and an indefinite integral, please. An antiderivative is a single function, and an indefinite integral is a collection of functions, all of which are antiderivatives of the same function. If you write down the value of an indefinite integral, be sure to include a constant. We have done integration by substitution, which enables us to do more elaborate integrals and to solve differential equations by separating the variables. We used this to consider motion under constant acceleration and under Newton's law of gravitation. You need to be familiar with the constant acceleration case (how to obtain the solutions, what they look like). We also did an approximation method described in section 5.2.

In chapter 6 we constructed Riemann sums and did some manipulation with sums of squares, cubes etc. You should be able to construct upper sums and lower sums, and recognize Riemann sums when you see them. You will not be tested on proofs, such as the proof of the fundamental theorem of calculus, but you do need to be familiar with the use of such a result. For instance, it enabled us to compute areas between curves more readily.

Read: Simmons sections 7.4, 7.5, 7.6, 7.7.

Exercises:
7.4: 1*, 3, 4*, 5, 6, 7, 8, 9*, 10,
7.5: 2, 4*, 6, 8
7.6: 2, 4*, 6, 7, 8, 9, 10*, 11
7.7: 2, 3, 4*, 6, 8*, 14, 16, 18*, 19, 21*