MATH 165-02
Calculus II
Syllabus for Fall 2010
Mon, Tues, Thurs, & Fri, 9:00 – 9:50am
Gildemeister 325
Prerequisite: MATH160 or a qualifying score on the mathematics placement exam
About This Course: This course continues to build on the ideas introduced in Calculus I (MATH160). Specifically, this course covers the techniques and applications of integration, calculus with polar coordinates and parametric equations, and functions in power series form.
Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Mastery of prerequisite material, (ii) Evaluate integrals using a variety of techniques, (iii) Set-up/apply integration in the appropriate manner, (iv) Compute within various coordinate systems and geometric set-ups, (v) Determine the behavior of sequences and series, (vi) Construct and use functions as power series.
Text: Calculus: Early Transcendentals, James Stewart, 6th ed.
Course Website: http://course1.winona.edu/eerrthum/math165
Instructor: Dr. Eric Errthum Office: 124A Gildemeister
Winona Email Username: eerrthum Office Phone: 474-5775
Office Hours: See schedule on my home page. Or by appointment on any day.
Grading: WebAssign
Homework (scaled as needed) 135 points----- 13.5%
Quizzes
(12 @ 15 points, drop lowest) 165
points------ 16.5%
Midterms (4 @ 125
points) 500
points------ 50.0%
Final 200
points------ 20.0%
--------
1000
points total
Grades: A = 90% (900 pts), B = 80% (800 pts), C = 70% (700 pts), D = 60% (600 pts). There will be no curving of individual exams, quizzes or assignments.
Homework: Homework will be assigned daily and will be due at 9:00am on the day of the next quiz (i.e. the quiz that covers that material). All homework is to be submitted via the WebAssign website. At the same time, you should work out the problems in a separate notebook. Some good tips for doing homework in WebAssign can be found below.
WebAssign: After the first two weeks of class, you will have to purchase a WebAssign access through the WebAssign website to complete the assignments. The Class Key is “winona 5751 0794”. Click here for more about the WebAssign Login Procedure. If you have any problems logging in or doing any of the homework assignments, please contact the instructor.
Quizzes: We will have a short (approx. 15-minute) quiz periodically (about once a week, see schedule below). Each quiz will count for 15 points and the lowest quiz will be dropped from your grade. Quiz problems will be loosely based on the homework and the “Additional Quiz Preparation” questions listed in the homework instructions.
Exams: There will be four in-class exams and one comprehensive final exam. Exam dates are tentative until officially announced in class. The final exam is tentatively scheduled for Tuesday, December 7, 8:00am – 10:00am.
Late/Missed Work: Late homework or missed quizzes will result in a score of zero. Make-up quizzes and make-up exams before the time of the normal quiz or exam will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.
Desire2Learn: Many course materials can be found on D2L including solutions to quizzes and exams and approximate grades. If at any point during the semester you would like to know your exact grade, please email the instructor.
Technology: No calculators will be allowed on any quiz or exam, but might be required for some homework problems. Some of the in-class demonstrations require Mathematica, which is available on the WSU laptops. If you’d like to view them on your own laptop and need help installing Mathematica, see either the instructor or tech support.
Resources: There is tutoring available in the Math Achievement Center on the first floor of Gildemeister Hall from 10am-3pm on Mondays through Friday and 5pm-7pm on Monday through Thursday. Also, you are encouraged to visit me in my office (see schedule on my home page, or by appointment on any day) or e-mail me.
Academic Dishonesty: Any type of academic dishonesty (cheating, copying, etc.) will result in failure and will be reported to school authorities. If you are having trouble with an assignment, please see the instructor first.
Note: This syllabus is subject to change if deemed necessary by the instructor.
Tentative Schedule of Events – Math 165
(subject to change)
|
Week Beginning |
Monday |
Tuesday |
Thursday |
Friday |
|
8/23 |
Introductions |
Review Chapters 4 & 5 |
Quiz Chapters 1 – 5 |
6.2 |
|
8/30 |
6.3 |
Quiz 6.1 – 6.3 |
6.4 |
6.5 |
|
9/6 |
Labor Day |
7.1 |
Quiz 6.4 – 6.5, 7.1 |
Review for Exam I |
|
9/13 |
EXAM I |
7.2 |
7.3 Trig Substitution |
7.4 |
|
9/20 |
7.5 |
Quiz 7.2 – 7.5 |
7.6 |
7.7 |
|
9/27 |
7.8 Improper Integrals |
Quiz 7.6 – 7.8 |
11.1 |
11.1, cont. 11.2 |
|
10/4 |
11.2, cont. |
Quiz 11.1 – 11.2 |
Review for Exam II |
EXAM II |
|
10/11 |
11.3 |
11.4 |
11.5 |
Quiz 11.3 – 11.5 |
|
10/18 |
11.6 |
11.7 |
University Improvement Day |
11.8 |
|
10/25 |
Quiz 11.6 – 11.8 |
11.9 |
11.10 |
11.10 |
|
11/1 |
11.11 |
Quiz 11.9 – 11.11 |
Review for Exam III |
EXAM III |
|
11/8 |
8.1 |
8.2 |
Veteran’s Day |
8.3 |
|
11/15 |
Quiz 8.1 – 8.3 |
10.1 |
10.2 |
Quiz 10.1 – 10.2 |
|
11/22 |
10.3 |
10.4 |
Thanksgiving Break |
|
|
11/29 |
Quiz 10.3 – 10.4 |
Review for Exam IV |
EXAM IV |
Final Review |
Final Exam
Tuesday, December 7
8:00am – 10:00am
Welcome to college math!
If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.
#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”
#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.
#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.
#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.
#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.
#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.
#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.
Good luck on a happy and successful semester!
WebAssign Tips
#1: Use the Mozilla Firefox browser. The flash applications in WebAssign cause Microsoft Internet Explorer to lock up, thus losing all of your work from that session. If you need help installing Firefox, click here or contact the instructor.
#2: Do not try to sit down at a computer and just do your homework on Webassign. Print off the problems and work through them in a notebook first. When you have completed the assignment on paper, then go back and enter your answers into WebAssign. This way you will have a good paper record to study from, to examine for errors if WebAssign marks something incorrect, and to show to a tutor or the instructor when getting help.
#3: Do not wait until the night before the assignment (or collection of assignments) is due to do it. If you lose your internet connection or experience technical problems, you will not be able to hand in the assignment on time. Some WebAssigns are short (3 – 4 problems) and some can be quite long (11 – 12 problems). Make sure you leave yourself enough time to take full advantage of the multiple attempts.
#4: WebAssign will only accept the 100% correct answer. So you will not likely be able to guess the answer. At the same time, if you have almost the right answer, but you’re missing something small like a minus sign, WebAssign will still mark it incorrect without any hint of how close you are to the correct answer. Also, WebAssign can be very particular about how you enter an answer. For all these reasons it is important that you are careful about how you work out the problem and report the solution. This is, in general, an important lesson to learn.
#5: Don’t use any method on WebAssign that won’t work on an exam. For example, many questions on WebAssign will be presented as multiple-choice and you can “solve” it by checking each option. However, on a quiz or exam the same question will probably not be multiple-choice, so you need to know how to find the correct answer from scratch. If you don’t know how to do an assignment without “shortcuts”, ask a fellow student, a tutor, or the instructor.
#6: After the due date has passed, go back and look at the solutions for the problems you missed. (To find old assignments, look under “My Assignments” and click “Past”.) Often there will be a link to a pdf file with a detailed solution to the problem. If you still can’t understand the solution, ask a fellow student, a tutor, or the instructor to help you.
This course can be used to satisfy the University Studies requirements for Basic Skills in Mathematics. This course includes requirements and learning activities that promote students’ abilities to...
a. use logical reasoning by studying mathematical patterns and relationships;
•
understand the relationship of derivatives and
errors made when using numerical approximation of definite integrals
• understand the reasoning behind the existence of limits in improper integrals
• explain why and when an improper integral converges and why and when it diverges
• be able to compare an improper integral with another and explain its convergence
• be able to use apply geometry knowledge e.g. similar triangle, Pythagoras theorem and create a function to integrate for finding areas, volumes, arc lengths, density, center of mass, work and force
• accurately apply and compare the convergence tests for infinite series and improper integrals, demonstrating an understanding of the limitations of the tests and the difference between the behavior of the integrand/summand and the integral/series
• understand the concept of radius of convergence and use it correctly for the convergence of power series
• understand the role of higher order derivatives near/at a point and find Taylor’s series/polynomial for functions
• understand the role of higher order derivatives in finding the error bounds for Taylor polynomials
• understand when and why we use Fourier polynomials instead of Taylor’s polynomials for a function
• understand the relationship of trig functions, sine and cosine for Fourier polynomials
• be able to use logical reasoning to sketch slope fields for a differential equation
• given a function in 3-D be able to characterize the solid and vice versa
• apply distance function accurately with vectors
• understand the meaning of dot product, cross product of vectors and projection of a vector
b. use mathematical models to describe real-world phenomena and to solve real-world problems - as well as understand the limitations of models in making predictions and drawing conclusions;
•
accurately model pressure and work problems
involving continuously changing quantities.
• given a particular solid, accurately formulate an integral which will provide the surface area and volume of that solid.
• accurately model situations relating to growth, decay, heating, cooling and mixing using differential equations and solve the resulting equations using separation of variables or an integrating factor.
• accurately model situations relating to oscillations using second order differential equations and solve and interpret the solution meaning fully to the context of the problem
• be able to apply contour diagrams and graphs in context to real-world problems
• understand why and how the contour diagrams looks like for a linear functions (in two variables)
• understand why and how level surfaces are used to represent a function (in three variables)
• apply the concept of limit, continuity and differentiability to functions in several variables
• accurately model real-world problems using vectors to find direction of movement, velocity etc.
c. organize data, communicate the
essential features of the data, and interpret the data in a meaningful way;
•
accurately sketch a graph using the data sets in
two variables
• accurately interpret the behavior of a function representing a physical phenomenon using the given data set in more than one variable
• use data to find average and instantaneous rate of change of a function (in more than one variable) and/or the rate of increasing or decreasing of a function (in more than one variable) in the direction of a particular variable
• use data to find the limiting value of a function (in two or three variables) when (x,y) approaches (a,b) or (x,y,z) approaches (a, b, c)
• use data to find upper and lower estimates for a certain quantity for e.g. given a data relating speed (mph) and corresponding fuel efficiency (mpg) find the lower and upper estimates of the quantity of fuel used
• apply tables to sketch contour diagrams
d. do a critical analysis of
scientific and other research;
•
Do assigned projects and group work with
appropriate research and analysis of mathematical concepts
e. extract
correct information from tables and common graphical displays, such as line
graphs, scatter plots, histograms, and frequency tables;
•
given the graph of a function, determine what
can be said about all of the coefficients in general, and the first three
coefficients in particular, and the interval of convergence in a Taylor Series
for that function about a point x=a.
• given the graph of a simple wave-form, determine what can be said about the coefficients of the Fourier Expansion of that wave-form.
• given the graph of a function f(x,y), determine the nature of various cross-sections (directly or by a matching exercise) and of any critical points.
f. use appropriate technology to describe and solve
quantitative problems.
•
demonstrate proficiency in using the TI-89 to
solve messy algebraic equations and compute integrals and derivatives that
arise from real-world problems with real data.
• use a spreadsheet and various numerical methods to estimate the value of the integral of an unknown function whose values we know at a finite number of points.
Commitment
to Inclusive Excellence: WSU recognizes that our individual
differences can deepen our understanding of one another and the world around
us, rather than divide us. In this class, people of all ethnicities, genders,
religions, ages, sexual orientations, disabilities, socioeconomic backgrounds,
regions, and nationalities are strongly encouraged to share their rich array of
perspectives and experiences. If you
feel your differences may in some way isolate you from WSU’s community or if
you have a need of any specific accommodations, please speak with the
instructor early in the semester about your concerns and what we can do
together to help you become an active and engaged member of our class and
community.
Winona Campus Resources
• Student Support Services, Krueger
Library 219, 457-5465 (www.winona.edu/studentsupportservices/)
• Inclusion and Diversity Office, Kryzsko
Commons Room 122, 457-5595 (www.winona.edu/culturaldiversity/)
• Disability Services, Maxwell 314,
457-2391 (www.winona.edu/disabilityservices/)
• Counseling Center, Integrated Wellness
Center 222, 457-5330 (www.winona.edu/counselingcenter/)
• Writing Center, Minné Hall 348,
457-5505 (www.winona.edu/writingcenter/)
• Math Achievement Center, Gildemeister
135, 457-5370
• GLBTA Advocate*, 507-457-5330
• Advising and Retention, Maxwell 314,
457-5878 (www.winona.edu/advising/)
Details about Campus Resources
• Two good places to help you find
resources of all kinds on campus are Student Support Services and the Inclusion
and Diversity Office. Both offices are
dedicated to helping students of all races, ethnicities, economic backgrounds,
nationalities, and sexual orientations.
They can facilitate tutoring and point you to a wide range of
resources. Student Support Services is
in Krueger Library 219, and they can be reached at 457-5465. The Inclusion and Diversity Office is in
Kryzsko Commons Room 122, and they can be reached at 457-5595.
• If you have a disability, the Disability
Services office can document it for your professors and facilitate
accommodation. Their office is in Maxwell Hall, 3rd floor, and they
can be reached at 457-2391. If you have
a documented disability that requires accommodation, please let me know as soon
as possible. If you suspect you may have a disability, you are encouraged to
visit Disability Services as soon as possible.
• College can be very stressful. The Counseling Center is there to help you
with a wide range of difficulties, ranging from sexual assault, depression, and
grief after the loss of a loved one to stress management, anxiety, general
adjustment to college, and many others.
Their office is located in Wabasha Hall 220, and they can be reached at
457-5330.
• For help with writing and the
development of papers, the English department has a Writing Center available to
students and staffed by trained graduate students pursuing their Master’s
degree in English. The Writing Center is
located in Minné Hall 348. You can make
an appointment on the sign-up sheet on the door or call 457-5505.
• For help with understanding math
concepts and solving problems, the Math Achievement Center (MAC) is staffed
with friendly undergraduate tutors who will help you work through difficult
material. The MAC is located in Gildemeister 135 and provides free
tutoring for all students in math, stat, or math education courses. The
center is open 10am-3pm Monday through Friday, and 5pm-7pm Monday through
Thursday.
The GLBTA
Advocate is responsible for documenting homophobic incidents on campus and
working with the appropriate channels to get these incidents resolved. In
addition, the advocate can direct people to GLBT resources on campus and in
Winona.
* Contact the Counseling Center for the
name and number of the current GLBTA Advocate (Integrated Wellness Center 222, 457-5330).
The Standard Disclaimer
applies.