22M:26 (MATH:1860) Calculus II sec FFF

22M:26 (MATH:1860) Calculus II
Lecture FFF
Spring 2013

Contact/class information

Instructor:	Dr. David Stewart
Phone:	335-3832
Email:	dstewart@math.uiowa.edu
WWW URL:	http://www.math.uiowa.edu/~dstewart/
Office:	325B MLH
Office hours:	10:30–11:30am MW and 10-11:30am Tu
Class times:	11:30–12:20pm MWF
Class location:	110 MLH
Discussions:	F30: 9:30–10:20am TuTh 214 MLH
	F31: 7:30–8:20am TuTh 221 MLH
	F32: 8:30–9:20am TuTh 221 MLH

You can see me outside the office hours provided it is mutually convenient. You can use email to set up an appointment time.

Description

This course is about developing methods to evaluate integrals, especially for computing physical quantities such as arclength of curves, surface areas, forces and probabilities. You will also see differential equations, which are vital for modeling physical, biological, economic, and other systems; we will see how to solve equations like this. Parametric methods for describing curves and surfaces will be used to compute things like the surface area of a curved surface. Finally, we will study infinite sequences and series (= infinite sums). The end point of this is the representation of functions using infinite sums such as

e^{x} = \sum_{k = 0}^{\infty} \frac{x^{k}}{k!} .

Textbook

Single variable calculus (Early Transcendentals) by J. Stewart, 7th Edition, 2011; Published by Brooks/Cole. This textbook is available through the University bookstore.

Syllabus

Chapter 7: Techniques of integration: integration by parts; trigonometric integrals; trig substitutions; partial fractions; computer algebra systems; approximate (numerical) techniques; improper integrals.
Chapter 8: Further applications of integration: arclength; area of surface of revolution; hydrostatic pressure; centers of mass; probability.
Chapter 9: Differential equations: modeling; direction fields and Euler's method; separable equations; exponential growth and decay; logistic equations; linear equations; predator-prey models.
Chapter 10: Parametric equations and polar coordinates: parametric representation of curves; tangents and areas; arclength and surface area; polar coordinates.
Chapter 11: Infinite sequences and series: convergence and limits of sequences; series (= infinite sums) convergence and limits; integral test; comparison test; ratio and root tests; absolute versus conditional convergence of series; power series; Taylor series.

Goals

The goals of this course are that the student will be able to

symbolically compute definite and indefinite integrals using various methods including integration by parts, substitution, and partial fractions;
use such methods to compute geometric and physical quantities such as arclength, area, volume, surface area, forces, etc., of various shapes;
be able to use the techniques above to symbolically solve certain simple differential equations, and apply these to various situations;
be able to understand the representation of curves by parametric equations, and use such representation to compute various geometric quantities;
understand the difficulties associated with convergence of infinite sequences and series, and be able to identify circumstances in which this convergence occurs;
be able to evaluate certain infinite sums such as geometric sums ( $\sum_{k = 1}^{\infty} a r^{k}$ ).

Assessment

There will be weekly homework assignments, two mid-semester exams, and a final comprehensive exam. The homework will count for 30% of the final assessment, the mid-semester exams will count 20% of the final assessment each, and the final exam will count for the remaining 30% of the assessment. There will also be ungraded exercises to help you exercise your skills.

The homework is a vital part of the course. If you don't do it, you won't just miss out on 30% of the assessment, but you probably won't get the practice or learn what you need for doing the exams either.

The mid-semester exams will be held on Friday March 1st and Friday April 12th. The date and time of the final exam will be announced around the 5th week of class.

Grading

+ / -

grading scheme will be used. Although the College of Liberal Arts and Sciences has some guidelines for the percentages of A's, B's, C's, etc., these are only guidelines, and the class may vary substantially from these values depending on the overall abilities of the members of the class. Note that A+ will be given only for exceptional work of unusual quality.

Notes

Final Exam: The final examination date and time will be announced during the first half of the semester by the Registrar. I will announce the final examination date and time for this course at the course ICON site once it is known. Do not plan your end of the semester travel plans until the final exam schedule is made public.
Attendance: Attendance in class and timely completion of assignments are naturally expected. If you cannot satisfy this requirement, please talk to me as soon as possible about the problem.
Administrative Home: The College of Liberal Arts and Sciences is the administrative home of this course and governs matters such as the add/drop deadlines, the second-grade-only option, and other related issues. Different colleges may have different policies. Questions may be addressed to 120 Schaeffer Hall, or see the CLAS Academic Policies Handbook.
Electronic Communication: University policy specifies that students are responsible for all official correspondences sent to their University of Iowa e-mail address (@uiowa.edu). Faculty and students should use this account for correspondence (Operations Manual, III.15.2. Scroll down to k.11).
Accommodations for Disabilities: A student seeking academic accommodations should first register with Student Disability Services and then meet privately with the course instructor to make particular arrangements. See http://www.uiowa.edu/~sds/ for more information.
Academic Honesty: All CLAS students have, in essence, agreed to the College's Code of Academic Honesty: “I pledge to do my own academic work and to excel to the best of my abilities, upholding the IOWA Challenge. I promise not to lie about my academic work, to cheat, or to steal the words or ideas of others; nor will I help fellow students to violate the Code of Academic Honesty.” Any student committing academic misconduct is reported to the College and placed on disciplinary probation or may be suspended or expelled (CLAS Academic Policies Handbook).
CLAS Final Examination Policies: The date and time of every final examination is announced during the fifth week of the semester by the Registrar. No exams of any kind are allowed during the last week of classes. All students should plan on being at the UI through the final examination period.
Making a Suggestion or a Complaint: Students with a suggestion or complaint should first visit with the instructor (and the course supervisor), and then with the departmental DEO. Complaints must be made within six months of the incident (CLAS Academic Policies Handbook).
Understanding Sexual Harassment: Sexual harassment subverts the mission of the University and threatens the well-being of students, faculty, and staff. All members of the UI community have a responsibility to uphold this mission and to contribute to a safe environment that enhances learning. Incidents of sexual harassment should be reported immediately. See the UI Comprehensive Guide on Sexual Harassment for assistance, definitions, and the full University policy.
Reacting Safely to Severe Weather: In severe weather, class members should seek appropriate shelter immediately, leaving the classroom if necessary. The class will continue if possible when the event is over. For more information on Hawk Alert and the siren warning system, visit the Public Safety website.