Math 221: Calculus II
Spring 2003, 4 Credits, MWRF 8:00 a.m., MC 420
Instructor: Rich Maresh, Associate Professor of Mathematics
Office: MC 522, 796-3655; Hours: MWF 9-10, WR 12-1
Final Exam: Friday, 9 May 2003, 12:50-2:50
Applications of the integral and techniques of integration. Trigonometric, logarithmic and exponential functions. Prerequisite: grade of C or higher in 220.
Text: Calculus: Concepts and Contexts (2nd Edition), James Stewart. (Brooks-Cole, 2001)
Core Abilities (Note: since this course may be taken in partial fulfillment of the general education requirements, this syllabus includes the following set of core ability goals.)
1. Thinking: Students engage in the process of inquiry and problem solving that involves both critical and creative thinking.
- Students will be exposed to the logic of mathematical proof
- Students will develop their problem-solving skills
- Calculus is a major intellectual development in human history and students will think through the concepts
2. Communication: Students communicate orally and in writing in an appropriate manner both personally and professionally.
- Students will develop their skills of written mathematical communication, specifically learning to properly use the language and notation of the Calculus
- Students will develop their verbal mathematical communication skills, both in small groups and in class discussions
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
- Students will see the importance of integrity regarding their own scholarship
4. Community Involvement: Students demonstrate skills of interdependent group participation and decision-making.
- Students will work in groups, learning to share their ideas and skills, and respecting the ideas and skills of others
Specific Course Goals:
1. From the perspective of mathematical content, this course should allow the student to expand and apply skills and knowledge gained in the first semester of Calculus to the topics of integration and applications of integration.
2. The student will gain knowledge and skills, and the ability to apply these, to a variety of situations which might be encountered in the world of mathematics, science, or engineering.
3. The student will further improve his/her ability to communicate mathematical ideas and solutions to problems.
4. The student will improve her/his problem-solving ability.
5. From a most general perspective, the student should see growth in his/her mathematical maturity. The three-semester sequence of calculus courses form the foundation of any serious study of mathematics or other mathematically-oriented disciplines.
Course Philosophy and Procedures:
I am a firm believer in the notion that you as the student must be actively engaged in the learning process and that this is best accomplished by your DOING mathematics. My job here is not to somehow convince you that I know how to do the mathematics included in the course, but to help guide YOU through the material; I am to be a “guide on the side, NOT a sage on the stage”. I may not always say things in the way which best leads to your full comprehension, but I will try to do so and I ask that you try to see your learning as something YOU DO rather than as something I do to you. PLEASE feel free to come see me to discuss questions or concerns you may have during the course; I will not bite! PLEASE ask questions in class if you have them; the only dumb question is the one you fail to ask!
Homework: Let me therefore urge you to make it a regular part of your day to try working the homework problems. There will never be enough time for us to go through every listed problem in class, and it is probably unrealistic to think that you will be able to find the time to work through every listed problem, but you should at least spend some time thinking about virtually every problem, and working the more interesting or challenging to completion. The daily homework assignments will not generally be collected or graded. They are intended to structure your learning so that you regularly challenge yourself to see that you understand the material we are looking at. The important thing is that you at least look at all the assigned problems. You should also feel free to work other problems if you deem it necessary for your comprehension of the content.
You should view homework assignments as a test to see how well you understand the material and you should bring to the next class any questions you might have.
Group Work: In general, I think students can benefit greatly by working together on problems. While there is some danger of the “blind leading the blind” syndrome, or of students deceiving themselves into thinking they understand the material better than they actually do, for the most part grappling with ideas and trying to explain them to another student or learning to listen to others explain an idea is a wonderful way to see that you really do understand the material. In class we will spend an occasional day working on a group “lab”, and we sill also typically have a group “practice exam” before the individual exams, and I also encourage you to find a “learning group” outside of class.
Portfolio: I will be asking you to keep a PORTFOLIO of your work. This portfolio will be collected twice during the semester, once upon our return from our spring break, on Monday 17 March, and again at the end of the course, on Friday 2 May. Each of these portfolios should be a representative collection of your work during that half of the semester; each collection you turn in should include 5 problems, written up in a finished form, along with a brief discussion of why you chose to include that particular problem. These problems should represent work you are proud of, or problems which brought you to a breakthrough point. Each of these portfolios of your work will be worth 40 points, 8 points per problem. Presumably you will hand in 5 sheets of paper, each of which will include a nicely organized solution to the problem, which might be from homework, or from a lab or worksheet, of from an exam, along with that reflection mentioned above.
Grading: I use a rather traditional Grading Scale: A = 90% (or better), AB = 87%, B = 80%, BC = 77%, C = 70%, CD = 67%, D = 60%. I do try to come up with a mix of points so that exams are not weighted too heavily; about two-thirds of the points during the semester will come from individual, in-class exams - the rest will come from group labs, take-home problems, group practice exams, journals, and portfolios.
Late Assignments: It is rarely much of a problem at the level of a calculus course, but it remains important that students turn in work in a timely manner, so that they do not get behind. Consequently, Late Assignments will be penalized 20% of the possible points for each class period late, up to a maximum of three periods. Assignments more than three days late will not be accepted.
Attendance: I do not prefer to quantify your attendance in terms of a grade, but I can assure you that your chances of success will be much improved by regular attendance.
Americans with Disability Act:
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski in MC 320 (796-3085) within 10 days to discuss your accommodation needs.
Schedule, Spring Semester 2003
13 Jan [1.7] Parametric Functions p81 #1-11 odd
15 Jan p 81 #17-21 odd, 25, 27
16 Jan [4.1] Related Rates p 264 #5-15 odd
17 Jan p 270 #19-25 odd, 29
20 Jan [4.9] Anti-derivatives p 334 #1-15 odd, 25, 43
22 Jan Lab #1
23 Jan [5.1] Area, Distance p 355 #1-7 odd, 11-15 odd
24 Jan [5.2] The Definite Integral p 367 #1-11 odd
27 Jan p 367 #15, 19, 21, 29
29 Jan [5.3] Evaluating Definite Integrals p 377 #1, 3, 9-27 odd, 49
30 Jan Lab #2
31 Jan [5.4] The Fundamental Theorem of Calculus p 386 #3-15 odd, 19
3 Feb [5.5] Substitution Rule p 395 #1-27 odd, 37-45 odd
5 Feb [5.6] Integration by Parts p 401 #1-21 odd
6 Feb p 401 #25-33 odd
7 Feb Lab #3
10 Feb [5.7] More Integration Techniques p 408 #1-15 odd
12 Feb p 408 #17-31 odd
13 Feb [5.8] Integration Tables, Using CAS p 414 #1-21 odd, 25
14 Feb Group Practice Exam #1 (25 points)
17 Feb EXAM #1 (100 Points)
19 Feb [5.9] Approximation Techniques p 425 # 1-9 odd, 15-19 odd
20 Feb [5.10] Improper Integrals p 436 #1-23 odd
21 Feb p 436 #39-49 odd
24 Feb [6.1] More on Areas p 452 #1-13 odd, 21, 23, 27
26 Feb [6.2] Volumes – Solids of Rotation p 463 #1-13 odd
27 Feb p 463 #21, 23, 35
28 Feb Lab #4
3 Mar [6.3] Arc Length p 471 #1-7 odd, 11, 17, 21
5 Mar [6.4] Average Value of a Function p 475 #3-11 odd
6 Mar Group Practice Exam #2 (25 points)
7 Mar EXAM #2 (75 points)
8 Mar – 16 Mar -- S P R I N G B R E A K --
17 Mar [7.1] Differential Equations p 511 #1-9 odd
19 Mar [7.2] Directions Fields, Euler’s Method p 519 #1-15 odd, 21
20 Mar [7.3] Separable Differential Equations p 527 #1-13 odd, 19, 29, 35
21 Mar [7.4] Exponential Growth and Decay p 538 #1, 3, 5, 9, 13
24 Mar Lab #5
26 Mar [7.5] Logistic Equations p 548 #1-7 odd
27 Mar [7.6] Predator-Prey Systems p 555 #1-7 odd
28 Mar Lab #6
31 Mar Group Practice Exam #3 (25 points)
2 Apr EXAM #3 (75 points)
3 Apr [8.1] Sequences p 571 #1-27 odd, 35, 37
4 Apr [8.2] Series p 580 #3-19 odd, 29, 31, 33, 39
7 Apr [8.3] Integral and Comparison Tests p 591 #1-21 odd, 27, 29
9 Apr [8.4] Other Convergence Tests p 598 #1-17 odd
10 Apr Lab #7
11 Apr [8.5] Power Series p 604 #3-17 odd
14 Apr [8.6] Representing Functions as Power Series p 610 #1-13 odd
16 Apr p 610 #15-29 odd
17 Apr – 21 Apr -- E A S T E R B R E A K --
23 Apr [8.7] Taylor and Maclaurin Series p 621 # 1-13 odd, 17-41 odd
24 Apr [8.8] Binomial Series p 625 #1-13 odd
25 Apr [8.9] Applications of Taylor Series p 633 #3-23 odd
28 Apr [8.10] Using Series to Solve Differential Equations p 633 #2-23 odd
30 Apr Lab #8
1 May Review …
2 May Group Practice Final Exam (25 points)
FINAL EXAM (125 Points) - Friday, 9 May 2003, 12:50-2:50