MATH 221: Calculus II
Fall 2000, 4 Credits, 1:10-2:00 pm, MWF, 1:00-1:50 pm T, MC 420
Instructor: Rich Maresh, Associate Professor & Chair, Mathematics Department
Office: MC 522 Hours: MWF 9-10, TW 2-3, or by appointment
Phone: 796-3655 (office), 526-4988 (home)
Final Exam: Thursday, 21 Dec 2000, 7:40-9:40 am
Applications of the integral and techniques of integration. Trigonometric, logarithmic and exponential functions. Prerequisite: grade of C or higher in 220.
Text: Arnold Ostebee & Paul Zorn, Calculus from Graphical, Numerical, and Symbolic Points of View (Saunders College Publishing, 1997)
Core (General Education) Skill Objectives:
1. Thinking Skills:
(a) Students will use reasoned standards in solving problems and presenting arguments.
2. Communication Skills: Students will ...
(a) ... read with comprehension and the ability to analyze and evaluate.
(b) ... listen with an open mind and respond with respect.
(c) ... access information and communicate using current technology.
3. Life Value Skills:
(a) Students will analyze, evaluate and respond to ethical issues from an informed personal value system.
4. Cultural Skills: Students will ...
(a) ... understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.
(b) ... demonstrate knowledge of the signs and symbols of another culture.
(c) ... participate in activity that broadens their customary way of thinking.
5. Aesthetic Skills:
(a) Students will develop an aesthetic sensitivity.
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.
General Education Course Objectives:
1. Thinking Skills: Students will ...
(a) ... understand the basic concept of the integral as the limit of a sum.
(b) ... understand the Fundamental Theorem of Calculus and learn how to use it to evaluate definite integrals.
(c) ... explore differentiation and integration formulas for a variety of functions, including exponential and logarithmic, trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic functions.
(d) ... explore a variety of integration techniques, such as integration by parts, partial fractions, various substitution methods, and methods of approximation for integrals which have no easy anti-derivative.
(e) ... investigate a wide variety of applications of integration, including solving simple differential equations, finding areas and arc lengths, and finding volumes and surface areas of solids of rotation.
(f) ... broaden their ability to work with functions by exploring parametric and polar functions, including graphing, and differentiation and integration applications.
(g) ... explore conic sections, including their treatment in polar form.
2. Communication Skills: Students will ...
(a) ... collect a portfolio of their work during the course and write a reflection paper.
(b) ... do group work (labs and practice exams) throughout the course, which will involve both written and oral communication.
(c) ... use technology (graphing calculators and Maple V) to solve problems and communicate solutions and explore options.
(d) ... improve their ability to write logically valid and precise mathematical proofs and solutions.
3. Life Values Skills: Students will ...
(a) ... develop an appreciation for the intellectual honesty of deductive reasoning.
(b) ... understand the need to do one’s own work, to honestly challenge oneself to master the material.
4. Cultural Skills: Students will ...
(a) ... develop an appreciation of the history of Calculus and the role it has played in mathematics and in other disciplines.
(b) ... learn to use the symbolic notation correctly and appropriately.
5. Aesthetic Skills: Students will ...
(a) ... develop an appreciation for the austere intellectual beauty of deductive reasoning.
(b) ... develop an appreciation for mathematical elegance.
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!
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 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.
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.
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 mid-semester long weekend, on Monday 26 October, and again at the end of the course, on Friday 11 December. 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.
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 half 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.
It is rarely much of a problem at the level of a calculus course, but it remains important that students turn work in 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.
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.
MATH 221 Course Schedule, FALL 2000
5 Sep <5.1> Areas and Integrals p 352 # 1-7, 10, 11, 15, 17, 21, 23, 25, 29, 31, 39
6 Sep <5.2> The Area Function p 363 # 1-4, 6, 7-21 odd
11 Sep <5.3> The Fundamental Theorem of Calculus p 374 # 1-3, 6, 7, 11, 15
12 Sept Lab
13 Sept <5.4> Approximating Suns: Integrals as Limits p 384 # 1-5, 7, 8, 9-15 odd
15 Sept <5.5> Approximating Suns: Interpretation p 394 # 1-7, 9-15 odd
18 Sep <6.1> Antiderivatives: The Idea p 404 # 1-27 odd
19 Sept <6.2> Antidifferentiation by Substitution p 411 # 1-75 odd
20 Sept<6.3> Integration Aids: Tables & Computers p 419 # 1-31 odd
22 Sept Lab
25 Sept Group Practice EXAM #1
26 Sept EXAM #1
27 Sept <7.1> The Idea of Approximation p 428 # 1-13, 19, 21, 25, 27, 41
29 Sept <7.2> More on Error: Sums and the Derivative p 436 # 1-11, 13, 17
2 Oct <7.3> Trapezoid & Midpoint Sums p 443 # 1-14, 17, 19
4 Oct <7.4> Simpson’s Rule p 451 # 1-7, 9, 11, 13
6 Oct Lab
9 Oct <8.1> Introduction to Applications of Integration p 458 # 1-7
10 Oct <8.2> Finding Volumes by Integration p 463 # 1-11, 13, 15, 17, 19, 21, 23, 25, 32
11 Oct <8.3> Arc Length p 469 # 1-4, 7, 9
13 Oct Lab
16 Oct <8.4> Work p 476 # 1-8
17 Oct <8.5> Present Value p 482 # 1, 2, 4, 5, 6
18 Oct <8.6> Fourier Polynomials p 489 # 1-4
23 Oct Lab
24 Oct Group Practice Exam #2
25 Oct EXAM #2
27 Oct <9.1> Integration by Parts p 499 # 1-13, 15, 16-27
30 Oct <9.2> Partial Fractions p 508 # 1-13, 21, 23
1 Nov <9.3> Trigonometric Antiderivatives p 516 # 1-13, 17-31 odd
3 Nov <9.4> Miscellaneous Exercises p 517 # 1-79 odd
7 Nov Lab
8 Nov <10.1> Improper Integrals p 524 # 1-19, 21, 25, 27, 29, 31, 33, 41, 45, 49
10 Nov <10.2> Detecting Convergence, Estimating Limits p 534 # 1-31 odd
14 Nov <10.3> Improper Integrals and Probability p 542 # 1-19 odd
15 Nov <10.4> l’Hopital’s Rule p 549 # 1-49 odd, 53-61 odd
17 No v Lab
20 Nov Group Practice Exam #3
21 Nov EXAM #3
27 Nov <12.1> Differential Equations: The Basics p 623 # 1-11
28 Nov <12.2> Slope Fields p 631 # 1-5
29 Nov Lab
1 Dec <12.3> Euler’s Method: Solving DE Numerically p 640 # 1-5
4 Dec <12.4> Separating Variables: Solving DE Symbolically p 649 # 1-15
5 Dec Lab
6 Dec <13.1> Polar Coordinates and Polar Curves p 661 # 1-51 odd
11 Dec <13.2> Calculus in Polar Coordinates p 670 # 1-27 odd
12 Dec Lab
13 Dec Review ...
15 Dec Group Practice Final Exam [25 Points}
21 Dec FINAL EXAM, Thursday, 7:40-9:40 am [125 Points]