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Gustavus Adolphus
College |
Minnesota Board of Teaching
Program Approval 2006 |
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MCS 122 Calculus II |
| MCS 122 -- Calculus II Fall 2005 Calculus in many ways is the culmination of 17th century European mathematics. Problems in integral calculus (finding complicated areas) and differential calculus (finding instantaneous rates of change and tangents) date back to antiquity, but the genius of Newton and Leibniz was connecting differential and integral calculus with ``The Fundamental Theorem of Calculus''. The presentation of the material in the course does not represent the historical development of calculus which was piecemeal and halting. The topics are covered with the intention of building each new idea upon the previous ones. One of the most fundamental, and most slippery, topics in mathematics is the relationship between the finite and the infinite. A recurring theme throughout the course will be the relationship between an approximation and the exact value. We will spend quite a bit of time trying to determine just how good any approximation is. One of the most beautiful insights of calculus is that by taking better and better approximations and extending from the finite to the infinite, we will often be able to find a precise solution. The emphasis in this course is on concepts and problem solving rather than theory and proof. MCS122 presents the concepts of integral calculus from four points of view: geometric, numerical, algebraic, and verbal. Topics We will proceed through most of chapters 7 through 11 in the textbook. In doing so, we will learn about: &Mac183; techniques of integration, approximating definite integrals and improper integrals, &Mac183; applications of integration (including applications to geometry, physics, economics and probability and statistics), &Mac183; infinite series and approximating functions, &Mac183; introduction to differential equations and modeling. Course Objectives &Mac183; To reinforce prior understanding of derivatives and how they relate to integration. &Mac183; To be able to find antiderivatives systematically. &Mac183; To be able to estimate definite integrals numerically and understand how to measure and compare error. &Mac183; To be able to represent sums of physical quantities as definite integrals. &Mac183; To be able to model with differential equations and to solve by separation of variables. &Mac183; To understand how Taylor polynomials approximate functions and to be able to find and use Taylor polynomials. &Mac183; To develop critical thinking and problem solving skills. &Mac183; To have fun doing mathematics Web Page Announcements, course information and assignments will be posted on the course web page. The URL for this course is http://gustavus.edu/~mmcdermo/mcs122/f05/ Prerequisites MCS-121 or placement exam. Text Calculus by Hughes-Hallett, Gleason, et. al. (John Wiley & Sons, New York, Third Edition, 2002). Note: MCS121 is using the 4th ed. Don't buy the wrong edition. Calculators You should have a graphing calculator available for use in class and on exams. If you do not own a calculator, please talk to your instructor. The department recommends the TI-83. You may use other calculators (especially other TIs, Casios, HP or Sharp) as long as you are able to enter a simple program into your calculator and you are comfortable with basic graphing features. Calculators with symbolic algebra capability (e.g. TI-89, TI-92) will not be allowed during exams. Academic Integrity As a student at Gustavus you are expected to uphold the Honor Code and abide by the Academic Honesty Policy. A copy of the honor code and academic honesty policy can be found in the Academic Bulletin and in the Gustie Guide. Tests: You are expected to work completely by yourself on tests. I will put the standard honor pledge on the front of each exam for you to sign. The first violation of this policy on an exam will result in a 0 on that exam, and the Dean of the Faculty will be notified, as mandated by the policy. The second such violation will result in failing the course as well as notification of the Dean of the Faculty. Homework: I encourage you to work on the homework together, but you are expected to work together in an honorable way. This means that while you can discuss problems and their solutions, each of you should make a real effort to solve each problem by yourself, and you should give credit to any people or texts that helped you find solutions. I expect that you will write up your work individually and never copy someone else's writeup. Should I detect students copying each other's work, I will on the first occasion talk with the people having similar work. In case of a second infraction, I will give you a 0 for that assignment and notify the Dean of the Faculty. Any further violation will result in increasing penalties, up to failing the course. Accessibility It is the policy of Gustavus Adolphus College to provide for the needs of enrolled students who have disabilities. The Advising Center has a Disabilities Services Coordinator to assist you with reasonable accommodation. If you have a learning, psychological, or physical disability for which a reasonable accommodation can be made, you can provide documentation of your disability to the Advising Center (204 Johnson Student Union) or call Laurie Bickett (x7027). It is generally best if this can be done as soon as possible. General Education Calculus II (MCS-122) satisfies the Quantitative Reasoning criteria of the Curriculum I area requirements for students who matriculated before September 2005. QUANT courses are intended to acquaint the student with the application of quantitative and empirical reasoning both to the study of biological and physical phenomena and to the logic and abstractions of the mathematical and informational sciences. MCS-122 also satisfies the Mathematical and Logical Reasoning (MATHL) requirement of the Curriculum I area requirements for students who matriculate in or after September 2005. &Mac183; Knowledge of the language of mathematics and logic. (understanding of the notion of integral, series, differential equation) &Mac183; Familiarity with logical or algorithmic methods of symbolic reasoning (finding antiderivatives, definite integrals, Taylor polynomials and solutions to differential equation) &Mac183; Knowledge of the practical applications of mathematical modeling and axiomatic systems (applications of integrals in physical, biological and social sciences, modeling using differential equation) &Mac183; Appreciation of the role of the formal sciences in the history of ideas, and their impact on science, technology, and society (historical development of calculus) Class Format We learn by thinking and doing, not by watching and listening. Learning is an active process: it is something we must do, not have done to us. Class time will be a mixture of lectures, discussions, problem solving and presentation of solutions. At various times you will be asked to present problems, reflect on the reading and generate questions for your classmates. It is essential that you come to class prepared to do the day's work. In particular, you should read the text and attempt homework before coming to class. Class meetings are not intended to be a complete encapsulation of the course material. You will be responsible for learning some of the material on your own. ``A good lecture is usually systematic, complete, precise -- and dull; it is a bad teaching instrument.'' -- Paul Halmos ``The best way to learn anything is to discover it by yourself... . What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises.'' -- George Polya Homework I hear, and I forget; I see, and I remember; I do, and I understand. -Proverb Weekly homework is assigned for each section and is collected each Friday at the beginning of class. Homework assignments will be collected about once a week, but you are advised to do the problems from each section right after the class meeting on that section. Only selected problems will be graded. You are allowed (even encouraged) to discuss both preparation problems and weekly homework problems with others. However, ultimately you must work the problems and write up the assignment entirely by yourself. As a general rule, you must justify your answers. Explain, or show your work. See the Homework Guidelines Prep Problems, Participation and Performance WebWork preparation problems are meant to help you prepare for classes. Note that preparation problems for a section are assigned at the same time as the reading for that section. This means that you are being asked to read and digest a section and attempt problems before we discuss the material in class. This is intentional. These problems will often serve as the starting point for class discussions. The following factors (borrowed from John Holte) contribute to participation and performance: Positives Negatives Regular attendance Missing classes, showing up late Being prepared Being unprepared Paying attention in class Not paying attention, sleeping, doing something else Contributing to class discussions Asking relevant questions Disruptive behavior Actively working on group problems in class Sitting alone and refusing to work with a group Curiosity, appreciation, cheerfulness Apathy, resentment, sullenness Turning work in on time Turning work in late Neat, well-written work Messy work Working hard Hardly working Improvement during the term Going downhill Attendance the day before and the day after break Skipping class the day before or the day after break Exams We will have one skills test, three exams during the semester and a final exam. They are tentatively scheduled for &Mac183; September 23 (Skills Test) &Mac183; October 10 &Mac183; October 31 &Mac183; November 21 &Mac183; December 17, 3:30-5:30 Evaluation Your course grade will be determined using the following percentages as a guide: Weekly Homework 20% WebWork and Class Work 5% Antiderivative Basic Skills Test 6% Exams (3) 18% Final Exam 20% My assessment of your participation and performance (see above) may be used to adjust your WebWork grade or to make decisions about final grades that are on a borderline. Advice from Your Peers When asked what advice they would give a student about to take Calculus II, previous students most often responded with the following suggestions: &Mac183; Study frequently, in small doses. &Mac183; Work on calculus every night. Stay caught up with the homework. &Mac183; Read the text sections to be covered before and after class. &Mac183; Ask questions early and often. Don't just assume you'll figure it out later. 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