MATH 142
Calculus 2
We began the semester by reviewing several concepts from Calculus 1: Limits, the Intermediate Value Theorem, and Derivatives. The syllabus was provided, as was Problem Set #1 which is due on Friday, 8-31-07.
PowerPoint Assignment Problem Set #1 Syllabus
The syllabus was reviewed today. We then continued our discussion of the important concepts from Calculus 1.
Syllabus PowerPoint PowerPoint Assignment
Today we made sure everyone understood the basic rules for differentiation by finding the derivative of several different functions. We also answered a few questions on the Problem Set assignment.
PowerPoint Assignment Problem Set #1 Solutions
Problem Set #1 was returned (we will examine a few problems from it next time). We discussed finding the area under a curve and its relation to integration.
The Fundamental Theorem of Calculus was developed today!
The Method of Substitution for Integration was discussed. Before this, a few problems from Problem Set #1 were discussed and the Guidelines for putting graded assignments on your own paper were distributed.
PowerPoint Assignment Guidelines for graded assignments
Homework was discussed. The Method of Substitution for Integration was then discussed as it pertains to definite integrals. We finished with an investigation of Inverses, Natural Logarithmic, and Natural Exponential Functions.
PowerPoint Assignment Investigation Paper on Inverses, Natural Logarithmic, and Natural Exponential Functions
There was no class meeting today. Your quiz has been posted below.
Quizzes were submitted. Hints on HW from 4.5 were given. We then overviewed chapter 5 and began discussing Inverse Functions.
We finished our discussion on Inverse Functions today, examining the calculus of them. We then developed
the Natural Logarithm Function, which we will complete during the next class meeting.
We continued and completed our discussion on the Natural Logarithmic function and its inverse, the
Natural Exponential Function. Quiz #1 was returned.
PowerPoint Assignment Quiz #1 Solutions
We began class by examining some problems from Quiz #1 and our HW. Quiz #2 was then given.
Unfortunately, the quiz and its solutions cannot be posted here at this time due to the fact that a couple
of students still have to take it.
We developed the general exponential and
logarithmic functions, differentiating and integrating each.
Quiz #2 was returned.
PowerPoint Assignment Quiz #2 Solutions
We worked on several HW problems and reviewed Quiz #2. We then developed the number e as a limit in
order to introduce growth and decay problems. Problem Set #2 was then given.
We completed our discussion on exponential growth/decay problems. We also discussed inverse trigonometric functions and their inverses. Problem Set #2 was submitted.
PowerPoint Assignment Problem Set #2 Solutions
We discussed the hyperbolic functions today. Problem Set #2 was returned.
We discussed HW problems from 5.5 and Problem Set #2.
We examined some HW problems from 5.6 and 5.7 and then began discussing how to find limits of indeterminate forms using L'Hopital's Rule.
We completed our discussion of L'Hopital's Rule. A quiz was also given.
PowerPoint Assignment Quiz #3 Quiz #3 Solutions
Quiz #3 was returned and reviewed. We then carefully examined the HW from 5.8.
We began our discussion of different techniques of integration. Integration by parts was discussed in detail.
We carefully reviewed some of the more difficult HW problems using L'Hopital's Rule and some of the HW from 6.1 using Integration by Parts.
We developed Reduction Formulas, discussed how to integrate trigonometric integrands, and learned how to use Trigonometric Substitution. Problem Set #3 was submitted (solutions will be provided on Monday)
Problem Set #3 was returned (solutions could not be attached in electronic format so they were handed out in class in hardcopy format). We examined a couple of problems dealing with Trigonometric Integrals and Trigonometric Substitution. We then proved the area formula for a circle with radius r. Finally, we motivated Partial Integration.
We closely examined Partial Fractions today.
We continued to examine Partial Fractions, learned to use Tables of Integrals, and explored the use of Computer Algebra Systems on the TI-89 and Mathematica to Integrate functions.
We reviewed a few HW problems and then took Quiz #4. No assignment was given except to complete the past one.
We completely reviewed Quiz #4. A self-study was given for the next topic.
Numerical Integration Self-Study
We discussed both Numerical Integration and Improper Integrals today.
PowerPoint Numerical Integration Self-Study Solutions Assignment
We examined a HW problem on Numerical Integration and completed our discussion of Improper Integrals.
We began our unit on Applications of Integrals today, discussing the area between graphs and the length of an arc.
We did not meet for class today, as Steve is away at a conference. However, a Problem Set is given.
We went over some HW problems from 7.1 and 7.4 and then discussed solving volume problems using the disk method and the washer method.
PowerPoint Assignment Problem Set #4 Solutions (to be posted soon)
We completed our discussion on finding volumes of solids of revolution, specifically discussing the Method of Cylindrical Shells.
We went over some HW problems from 7.2. We started the quiz but did not have time to complete it. We will do so on Monday. No new assignment was given.
We completed the quiz that was started on Friday. We then went over a few HW problems from 7.3 and left about 10 minutes early.
Quizzes were returned. We then discussed Work applications of the definite integral.
PowerPoint Assignment Quiz #5 Solutions
We solved a problem involving work pumping water out of an aquarium and then discussed finding the Center of Mass.
We did several HW problems from 7.5 and then took Quiz #6. The solutions will not be posted until Monday.
Assignment Quiz #6 (final exam part 1) Quiz #6 Solutions
We went over Quiz #6, did several HW problems from 7.5, and then took Quiz #7. The solutions will be posted on Tuesday.
Assignment Quiz #7 (final exam part 2) Quiz #7 Solutions
We went over Quiz #7, discussed Conic Sections, and then took Quiz #8 (Final Exam part 3). The solutions will be posted on Wednesday.
PowerPoint Assignment Quiz #8 (final exam part 3) Solutions
We went over Quiz #8, went over some HW on Conic Sections, and took Quiz #9 (Final Exam part 4).
Assignment Quiz #9 (final exam part 4) Solutions