IMPORTANT NOTE ON MATHEMATICA ON ENGINEERING UNIX MACHINES: The Engineering system support group has fixed the problem which we had with corrupted files. In order to run Mathematica with their fix, start Mathematica by typing mathcalc at the unix command line.
Assignment 1.
Download a copy of the class demo from August 25, and do the exercises, using Mathematica.
First part: handwritten: Section 3.1, Exercises 14, 16, 18*, 28, 41, 38*, 79. Section 3.2, Exercises 12, 14, 16, 18, 21, 37, 38, 39, 43*. The exercises marked with (*) are presentation problems. Look at the class syllabus again to remind yourself what that means!
Second part, computer exercises. Click here to download.
First part: handwritten:: Section 3.3, Exercises 1,4,7,10,13,16,19, 22, 25, 28, 31, 34, 37, 40, 43, 44, 52, 53, 55, 56.
Second part, computer exercises. Click here to download.
First part: handwritten:: Section 3.4, Exercises 1, 4, 6*, 9, 12, 15, 20*, 23, 26, 30, 33, 37, 50*, 55, 66*, 72, 76, 81*, 82*.
Second part, computer exercises. Click here to download.
First part: handwritten:: Section 3.5, Exercises 9, 12, 17, 22*, 31, 36, 68*, 71*, 78, 85. Section 3.6, Exercises 3, 8, 14, 32, 33, 35, 38, 39, 54*, 57*. Note that there will be an in-class exam on Friday Sept. 24, which will cover the course up through section 3.6. So you will be better off to do this assignment earlier rather than later!
Second part, computer exercises. Go through this computer demonstration on the folium of Descartes. No need to submit anything, but work through the demo with active attention. Click here to download the demo.
The following exercises are to be done using Mathematica. Review the Mathematica demo NewtonMethod.nb, which you can download here, in order to remind yourself of the use of the programs SingleStep, NewtonStep, and NaiveNewton. Use these programs, as appropriate, to do the exercises, which are taken from the text.
Start by opening the notebook NewtonExercise.nb, which you can download here.
Section 3.8, Exercises 29, 30, 35*, 36. (For each exercise, first plot the function in order to obtain an initial guess for Newton's Method.) Exercises 40, 41, 42 (Compare the examples in the demo notebook.) Exercises 43*, 44 (Again, plot the function to obtain the intial guess(es).) 46, 47* (For these exercises, use the NewtonStep program to investigate graphically some funny things which can happen with Newton's Method.) 52, 53* (These exercises involve the Secant Method, for which I have not provided programs. Write your own Mathematica code, or use an ordinary calculator.) Exercises 56, 57 (These exercises involve linear approximation.)
You can do whatever combination of electronic submission of Mathematica material, and submission on paper of handwritten material which you deem appropriate.
Section 3.7, Exercises 6, 10*, 11, 13, 15, 23*, 28, 36.
Section 4.1, Exercises 7, 13, 17, 19, 23, 34*, 35, 37, 39, 47, 48, 53*, 54*.
Assignment 8. Due Friday, October 15.
Section 4.1, Exercises 52, 55, 56*, 59*, 60*.
Section 4.2, Exercises 11, 12*, 13, 14, 15*.
Section 4.3, Exercises 3-6, 13-16, 23, 24, 30*, 31-34.
Section 4.3, Exercises 59*, 66.
Section 4.4. Exercises 6, 7, 8*, 14*, 20-22.
Section 4.5 Exercises 9, 12, 15, 18*, 25, 28*, 31, 34.
Section 4.5 Exercises 55, 56, 57, 58*. On these exercises, find the candidates for local extrema by solving f'(x) = 0, using Newton's Method (and ignore the instruction about the zoom function on your calculator.) Of course, you will need to find an appropriate initial guess for each zero, and you may do this using a computer or calculator graphing tool.
Ssection 4.6 Exercises 4, 6, 8*, 11, 13, 17, 20*.
Section 4.6 Exercises 33, 34*, 35, 36*
Section 4.7 Exercises 3, 5, 9, 10, 15, 23, 29.
Section 4.8 Exercises 7, 11, 14, 17, 20*, 27, 28, 37, 40*.
Assignment 12. Due Friday, November 12.
Section 4.9 Exercises 2, 5, 23*, 41*, 45*
Read the class demonstration Introduction to the Integral.
Download and do the computer exercise, integration_homework.nb
Assignment 13. Due Friday, November 17.
Section 5.2 Exercises 55, 56, 57, 61, 62*, 63*.
Section 5.3 Exercises 13, 19, 22, 23, 24, 25*.
Section 5.4 Exercises 2, 3, 7*, 17, 20, 32, 33, 38, 39, 40*, 45, 52, 53, 54*, 66. 67*.
Assignment 14. Due Friday, December 3 .
Section 5.4 Exercises 72, 73, 74*, 75*.
Section 5.5 Exercises 1, 4, 7, 10, 13, 16*, 19, 22, 25, 28, 31, 44, 57, 59*, 60, 68*.
Section 5.6 Exercises 1, 4, 7, 10, 13, 16*, 19, 22, 25, 28, 31, 32*, 39, 44, 45, 48, 51.
Section 5.7 Exercises 3, 7, 10, 13, 14, 17, 20*, 23, 25, 28, 31, 34, 36*, 39*, 41, 44*.