Math 142 Chapter 8 Homework Homework will be posted as it becomes available. |
|||
---|---|---|---|
section |
handouts |
remark |
homework problems |
in case the bookstore runs out of books |
Calculus is so popular that sometimes the bookstore runs out of Calculus books
at the beginning of the semester and has to order more. If you are currently
without of book because of this, below are copies of
the first few sections of the course (along with the answer to the odds in the back
of the book). Of course, you must have a book for the semester so
you will need to get one. The below posting is just to tie you
over until more books arrives to the bookstore, at which point
copies of the sections will not be posted.
When we finish the lectures for
the below sections, please let me know if the books are
still not at the bookstore and I will further investigate the
problem. Sections: 8.1 & 8.2 & 8.3 |
||
8.0 Basic Skills Check | Online HW | ||
For sources of help with this online homework set, see
| |||
Integration Basics | This Integration Basics handout collects some basics from Math 141 that you need to know
in Math 142. I highly suggest you take a look the first problem from
any Exam 1 since 2006 from my
previous exams.
On our Exam 1:
If you do not make at least half of the points on Problem 0, then your score for the entire exam will be whatever you made on Problem 0. There really is no need to look further through your exam.A practice quiz to help reinforce the Integration Basics handout. |
||
8.1 Integration by u-du Substitution Calc I material | Online HW | ||
§8.1 covers u-du substitution, which is Calc I material and thus no lecture will be given on §8.1. In our calculus book (by Thomas), u-du sub was covered in §5.5&5.6. For lots of worked out examples of u-du substitution, see §6.1 (pages 263-282) of the APEX Calculus book (a great book for example!). | |||
Hints for Online HW (2nd number refers to problem from book in §8.1)
| |||
Below is a u-du sub. review from another book. Stewart (6th ed, ET), §5.5. | |||
need more practice? | Having troubles or want more practice? Work through some more of the above 88 exercises. This is a good source and you have the solutions. | ||
need more practice? |
Want or need even more practice with u-du substitution? Try these 23(=30-7) u-du substitution problem (answers included). Anton (8th ed, ET) | ||
8.2 Parts | Online HW | ||
You do not need to know tabular integration, which basically is a method (which students tend to misuse) to accomplish something that can easily be done with high-school algebra. | |||
Parts is just one (of many) techniques (of integration) we will learn
in this chapter.
Which technique to use on a given integral -
a good ansatz is a techique already taught.
Thus far, in this second section in the chapter on Techniques of Integration,
we have only 2 techniques in our tool box: substitution and parts.
As we learn more techniques,
it becomes tricker to answer the question: which technique to use?
The answer lies in true understanding and pattern recognition (useful skills).
So take out a sheet of paper and do the following.
| |||
need more practice? |
Try these
exercises.
Answers
to the odd problems. Give the exercises an honest shot before peeking at the
solutions
to all of them. Stewart (6th ed, ET) | ||
8.1&8.2 | A Sample Recitation Quiz over Sections 8.1&8.2, along with the solution. Would you be able to work this quiz at the end of a recitation over Sections 8.1&8.2, in 10 minutes, without your books/notes? | ||
8.3 trig integrals |
Online HW | ||
need more practice? |
Try these
exercises.
Answers
to the odd problems. Give the exercises an honest shot before peeking at the
solutions to all of them.
Stewart (6th ed, ET) | ||
8.4 trig substitution |
Online HW | ||
Also do these (click here) two problems (hint: complete the square) | |||
need more practice? |
Try these
exercises.
Answers
to the odd problems. Give the exercises an honest shot before peeking at the
solutions to all of them.
Stewart (6th ed, ET) |
||
8.5 partial fractions |
Online HW | ||
need more practice? |
Try these
exercises.
Answers
to the odd problems. Give the exercises an honest shot before peeking at the
solutions to all of them.
Stewart (6th ed, ET) |
||
Review of 8.1-8.5 | Time to test your pattern recognition skills (valuable skill no matter where your academic pursuit leads you). For each of Sections 8.1 through 8.5, look over the section's examples with an eye on what properties are shared by integrals that can be solved using that section's technique. | ||
81 Integrals |
Do these
81 Integrals
Stewart (6th ed, ET) | ||
100 Integrals | need more practice? |
Try these
100 Integrals
| |
8.6 | We are not covering this section on Tables and CAS's. | ||
8.7 | No Online HW. HW is as given in a Maple Lab. | ||
8.8 Improper Integrals
without comparison tests (DCT/LTC)
and
with comparison tests (DCT/LTC) |
For §8.8 OFF-LINE homework, use the below source (note, not our textbook).
Remarks on the above solutions.
| ||
ON-LINE HW | Two Online HW sets. One set without, and one set with, the DCT/LCT. Take notice of the number of attempts per problem for each set. | ||
OFF-LINE HW with comparison tests (DCT/LCT) | For the above (not the textbook) source of problems, use
the specified comparison test (DCT or LCT) to determine if the integral is conervgent or divergent.
| ||
For the above (not the textbook) source of problems: 71, 72, 73 (an introducation to the Laplace transform, which is used in many branches of the sciences and engineering) | |||
need more practice? | For more practice without the comparison tests,
from the above (not the textbook) source of problems,
a good selection is: 1, 2, 5, 7(dvg to ∞), 13, 15(dvg but not to ±∞), 19, 23, 27(dvg to ∞) , 31(dvg to ∞), 41, 59, 61, 71. | ||
Then Exam 1 over 8.1-8.5, 8.8. |