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Course Syllabus Calculus and Analytic Geometry II Course Instructor: Andy Miller Office: PHSC 801 Office Phone: 325-4986 e-mail: [email protected] Office Hours: MWF 12:30 PM, Th 2:30-3:30 PM, F 9:30-10:30 AM or by appointment. Problem Sessions: To be held every two weeks or so, Monday or Tuesday evenings 6-7 PM Discussion Class Instructors: Taechang Byun Office: PHSC 903 Office Hours: Mon 4:30–5:00, Thur 12–1:30, Fri 9:30–10:30 in PHSC 425A. Matt Lynam Office: PHSC 1028 Office Hours: Wed 2:30-3:30, Wed 4:30–5:30, Thur 4:30–5:30 in PHSC 425A. Kashyap Rajeevsarathy Office: PHSC 1028 Office Hours: Tues 3:00–4:30, Thur 10:30–12:00 in PHSC 425A. Mathematics Help Center: The Mathematics Help Center is located in Room 425A of the Physical Sciences Center (on the fourth floor, near the Math Department office). It is open Monday 9:30AM–5:00 PM, Tuesday/Thursday 9:00 AM – 5:30 PM and Wednesday/Friday 9:30AM–5:30 PM. During these times the Help Center is staffed with mathematics graduate students who are highly capable and able to answer questions and give feedback on calculus problems. The Discussion Class Instructors will be available in the Help Center at the hours given above. Please take advantage of this valuable resource to help get your math questions answered! Course Web Site: A web site will be used as a central means for the dissemination of information for this course. The site will be updated incrementally over the semester. All of the homework assignments will be posted there. Review materials and other basic information relevant to the course will be posted there as well. The internet address for the main web page is http://www.math.ou.edu/ amiller/Calculus2 Brief Course Description: The course description which appears in the OU General Catalog gives a condensed outline of the topics to be covered: 2423 Calculus and Analytic Geometry II. Prerequisite: Math 1823. Integration and its applica- tions; the calculus of transcendental functions; techniques of integration; and the introduction to differential equations. This course is the second of a four semester sequence of calculus courses. It provides an introduc- tion to the concepts and theory of integration of functions of one real variable. An emphasis will be put on applications of definite integrals in a variety of different settings. A significant portion of the course will also be spent developing properties of important transcendental functions— such as logarithms, exponentials and inverse trig functions—which were not introduced in the Calculus I course. Here is a more specific list of topics to be covered: the definition of the definite integral as a limit of Riemann sums, the fundamental theorem of calculus, indefinite integrals, method of substitution for computing antiderivatives, areas between curves, volumes of solids of revolution, the natural logarithm and exponential functions, the inverse trig func- tions, hyperbolic trig functions, indeterminate forms of limits and l’Hospitals’s rule, various techniques of integration such as integration by parts, trig substitutions, and partial fractions, improper integrals, approximate integration, arc length, surface area, applications of integration in physics.

Course Syllabus Calculus and Analytic Geometry IIamiller/calculus2/info.pdf · Course Syllabus Calculus and Analytic Geometry II Course Instructor: Andy Miller Office: PHSC 801 Office

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Page 1: Course Syllabus Calculus and Analytic Geometry IIamiller/calculus2/info.pdf · Course Syllabus Calculus and Analytic Geometry II Course Instructor: Andy Miller Office: PHSC 801 Office

Course SyllabusCalculus and Analytic Geometry II

Course Instructor: Andy MillerOffice: PHSC 801Office Phone: 325-4986e-mail: [email protected] Hours: MWF 12:30 PM, Th 2:30-3:30 PM, F 9:30-10:30 AM or by appointment.Problem Sessions: To be held every two weeks or so, Monday or Tuesday evenings 6-7 PM

Discussion Class Instructors:Taechang Byun Office: PHSC 903

Office Hours: Mon 4:30–5:00, Thur 12–1:30, Fri 9:30–10:30 in PHSC 425A.Matt Lynam Office: PHSC 1028

Office Hours: Wed 2:30-3:30, Wed 4:30–5:30, Thur 4:30–5:30 in PHSC 425A.Kashyap Rajeevsarathy Office: PHSC 1028

Office Hours: Tues 3:00–4:30, Thur 10:30–12:00 in PHSC 425A.

Mathematics Help Center: The Mathematics Help Center is located in Room 425A ofthe Physical Sciences Center (on the fourth floor, near the Math Department office). It isopen Monday 9:30AM–5:00 PM, Tuesday/Thursday 9:00 AM – 5:30 PM and Wednesday/Friday9:30AM–5:30 PM. During these times the Help Center is staffed with mathematics graduatestudents who are highly capable and able to answer questions and give feedback on calculusproblems. The Discussion Class Instructors will be available in the Help Center at the hoursgiven above. Please take advantage of this valuable resource to help get your math questionsanswered!

Course Web Site: A web site will be used as a central means for the dissemination ofinformation for this course. The site will be updated incrementally over the semester. All ofthe homework assignments will be posted there. Review materials and other basic informationrelevant to the course will be posted there as well. The internet address for the main web pageis http://www.math.ou.edu/∼amiller/Calculus2

Brief Course Description: The course description which appears in the OU General Cataloggives a condensed outline of the topics to be covered:

2423 Calculus and Analytic Geometry II. Prerequisite: Math 1823. Integration and its applica-tions; the calculus of transcendental functions; techniques of integration; and the introductionto differential equations.

This course is the second of a four semester sequence of calculus courses. It provides an introduc-tion to the concepts and theory of integration of functions of one real variable. An emphasis willbe put on applications of definite integrals in a variety of different settings. A significant portionof the course will also be spent developing properties of important transcendental functions—such as logarithms, exponentials and inverse trig functions—which were not introduced in theCalculus I course. Here is a more specific list of topics to be covered: the definition of thedefinite integral as a limit of Riemann sums, the fundamental theorem of calculus, indefiniteintegrals, method of substitution for computing antiderivatives, areas between curves, volumesof solids of revolution, the natural logarithm and exponential functions, the inverse trig func-tions, hyperbolic trig functions, indeterminate forms of limits and l’Hospitals’s rule, varioustechniques of integration such as integration by parts, trig substitutions, and partial fractions,improper integrals, approximate integration, arc length, surface area, applications of integrationin physics.

Page 2: Course Syllabus Calculus and Analytic Geometry IIamiller/calculus2/info.pdf · Course Syllabus Calculus and Analytic Geometry II Course Instructor: Andy Miller Office: PHSC 801 Office

Text: The course textbook will be Calculus (Sixth Edition) by James Stewart (Brooks/Cole,2008). The course will cover most of chapters 5 through 8 and parts of chapters 9 and 10 (astime permits). To succeed in this class, it is important to read and study the textbook as thesemester progresses. If confusions arise or if you get stuck with this reading then please don’thesitate to ask about it during discussion classes, office hours or at the Math Help Center.While all textbooks have some drawbooks, I greatly admire this book and feel that it is the bestpossible book for this course.

Course Prerequisites: The Calculus I (Math 1823) prerequisite is very important for thiscourse. Specifically, you will need to be well experienced with topics such as: fundamentalprinciples of algebra, graphing functions in the plane, basic concepts and theory of limits andderivatives, rules of differentiation, rational and trigonometric functions, the mean value theo-rem and its corollaries, maximum/minimum theory and curve sketching. Deficiencies in yourunderstanding of any of these topics will make it difficult for you to perform well in this course.

Computers and Calculators: Computer technology has had a major impact on how cal-culus and other areas of mathematics are applied to solve problems, and this is something thatyou should become more aware of you proceed through the calculus sequence. In particular,mathematical software packages such as MATHEMATICA or MATHLAB (each of which areavailable on university computers and can be downloaded by students from the IT web site)provide extremely powerful platforms for doing calculus. We will discuss some aspects of thisfrom time to time over the semester and make some information available at the course website, however this will not be a major focal point for the course.

You are encouraged to use calculators and/or computers when appropriate or helpful in workingon assignments for the course. On the other hand, class exams will be constructed so that cal-culators are not necessary, and the use of calculators or laptops on exams will not be permitted.

Exams: There will be three midterm tests and a final exam scheduled as follows:

Exam 1: Friday, September 25Exam 2: Friday, October 23Exam 3: Friday, November 20Final Exam: Thursday, December 17, 1:30–3:30 PM

Grading: Grades will be determined according to the breakdown:Assignments: 15%Discussion Grade: 5%Midterms: 50%Final Exam: 30%

(The lowest midterm score will be weighted at 10% and the other two will be weighted at 20%.)and final course grades will be based on the scale:

A: 90%, B: 80%, C: 70%, D: 60%, F: below 60%Please note that the assignment and discussion grades comprise a significant portion of yourcourse grade.

Class Lectures: The MWF class lectures form the backbone of this course. Routine atten-dance at lectures is essential and expected of students. Class roll will be taken at each lectureto remind you of the importance of this.

Weekly Discussion Classes: Roll will be taken at these classes. There will sometimes beshort quizzes given in these classes. Both attendance and the quiz scores will contribute to thediscussion portion of your grade.

Page 3: Course Syllabus Calculus and Analytic Geometry IIamiller/calculus2/info.pdf · Course Syllabus Calculus and Analytic Geometry II Course Instructor: Andy Miller Office: PHSC 801 Office

Homework Assignments: Homework problems will be assigned and due on a regular basisover the semester, generally once per week. Assistance on these and related problems is availableduring weekly office hours and at the Math Help Center, and you are also encouraged to e-mailthe class instructors with questions that might arise. Because our class meeting time is limited,it is to be expected that there will occasionally be homework problems involving concepts whichhave not been discussed in class—in this case a perusal of the textbook should easily locatethe needed information. Almost always there are worked out examples in the text that willgive you some good ideas on how to approach the assigned problems. You are encouragedto discuss assignments with classmates, at the rough draft stage. However each student mustindependently prepare their own written version of the final draft of the assignment.

Each assignment may be turned in at the start of class on the due date, or brought to yourDiscussion Class instructor’s office no later than 3:00 PM on the same day,—late papers willnot be accepted (no exceptions). Assignments should be written on 8.5 by 11 inch paper,folded lengthwise and stapled with your name and your Discussion Section clearly marked onthe outside. Homework assignments will be graded in a cursory fashion. Usually a subset ofthe assigned problems will be selected and analyzed to determine the assignment grade. Eachhomework assignment will be graded out of 20 points. In calculating the assignment portion ofthe total course grade, the lowest 20% (roughly) of the assignment grades will be dropped atthe end of the semester.

Recommendations: The main objective for the course is to acquaint you with fundamentalcalculus concepts, and to help you to understand these concepts deeply and to see how they maybe applied in a variety of different settings. Much thought and persistent work on your part willbe necessary in order for you to achieve these goals. To prepare for exams, it is recommendedthat you try working as many problems from the book as possible—this certainly includes goingbeyond the assigned homework assignments. Condensed answers to the odd numbered problemscan be found in the back of the book to assist in determining whether your approach is correct.If questions arise or if you get stuck working on any problem, it is important that you tryto isolate the problem and ask about it, either during the discussion classes, office hours orthe Math Help Center. You are strongly encouraged to take advantage of office hours to helpclear up mathematical questions that you may have and to help you progress toward a fullerunderstanding of the subject. Above all, please remember that new material will be developedrapidly, and so keeping up with the course on a day-to-day basis, and not allowing yourself tofall behind, is extremely important.

Student Disabilities: The University of Oklahoma is committed to providing reasonableaccommodations for all students with disabilities. If you require special accommodation in thecourse please discuss this with me as soon as convenient so that we can take steps to ensureyour full participation in the course and to facilitate your academic opportunities.

Academic Misconduct: Students should be familiar with the Academic Misconduct Codewhich may be found at http://judicial.ou.edu/content/27/32. The rules governing cases ofacademic misconduct may be found at http://www.ou.edu/provost/integrity.