MATH 165-02 Calculus II

MATH 165-02 Calculus II
Syllabus for Fall 2008

Mon, Tues, Thurs, & Fri, 9:00 – 9:50am

Maxwell 287

Prerequisite: MATH 160 or a qualifying score on the mathematics placement exam

Text: Calculus: Early Transcendentals, James Stewart, 6^th ed.

Course Website: http://course1.winona.edu/eerrthum/math165

Instructor: Dr. Eric Errthum Office: 203L Stark Hall

Winona Email Username: eerrthum Office Phone: 474-5775

Office Hours: See schedule on my home page. Or by appointment on any day.

Grading:    Video Attendance:                                        30 points------- 3.0%
                    WebAssign Homework (scaled as needed) 135 points----- 13.5%
                    Homework Notebook                                    25 points------- 2.5%
                    Quizzes (10 @ 15 points, drop lowest)       135 points------ 13.5%
                    Midterms (4 @ 125 points)                          500 points------ 50.0%
                    Final                                                             175 points------ 17.5%
                                                                                     --------
                                                                                       1000 points total

Grades: A = 90% (900 pts), B = 80% (800 pts), C = 70% (700 pts), D = 60% (600 pts)

Homework: Homework will be assigned daily and will be due the following Thursday at 9:00am. All homework is to be submitted via the WebAssign website. At the same time, you should work out the problems in a separate notebook (NOT one that you use for class notes) which will be handed in during midterms and checked for completeness.

WebAssign: After the first two weeks of class, you will have to purchase a WebAssign access card at the WSU bookstore or on the WebAssign website to complete the assignments. Your user name is your WSU email username and the institution is “winona”. The first time you login your password is your WSU Tech ID (including the beginning zeroes). You should change your password after the first login. More help can be found here. If you have any problems logging onto WebAssign or doing any of the homework assignments, please contact the instructor. Some good WebAssign Tips can be found below.

Quizzes: We will have a short (approx. 15-minute) quiz each Thursday. 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 9, 8:00am – 10:00am.

Video Lectures: On August 27^th, my wife and I will be travelling to Ethiopia to bring home our newly adopted son. In replace of standard lectures, you can find video lectures linked to below. These videos require Adobe Flash player (which should already be on any WSU Laptop) and a high-speed connection. As you watch the videos you should take notes just like you would in class. Each video contains a set of questions and at the end of the video an email with your responses will be generated to be sent to the instructor. Although you will not be graded on the correctness of your responses, these will be used to measure video attendance. Make sure you actually send the email at the end. If for some technical reason you cannot send the email, you will have to email me manually after watching each video. In addition to the video lectures, during regular lecture time you can visit the listed instructor below for additional help. It is strongly suggested that you do NOT attempt to watch all five videos at once. Instead, watch one a night, attempt the homework problems, and seek help from the other instructor during the regular lecture hour if needed. Here is a complete list of resources available to you during those two weeks.

Late/Missed Work: Late homework or missed quizzes will result in a score of zero. There are no make-up quizzes. Make-up exams 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 on the third floor of Gildemeister Hall from 4pm-9pm on Mondays through Thursdays.

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
8/25	Introductions Review Chapters 1 – 4	BRING YOUR LAPTOPS TO CLASS Review Chapter 5 Video Lecture Intro	Quiz Chapters 1 – 5 Discussion Day with Pf. Lee Video Lecture: 6.1: Areas Between Curves (16 min 0 sec)	No Class Video Lecture: 6.2: Volumes (21 min 28 sec) Optional Office Hours with Dr. Jarvinen in GI308: 2:00pm – 3:20pm
9/1	Labor Day No Class	Discussion Day with Pf. Lee Video Lecture: 6.3: Volumes by Cylindrical Shells (21 min 34 sec)	Quiz 6.1 – 6.3 Discussion Day with Pf. Lee Video Lecture: 6.4: Work (21 min 35 sec)	No Class Video Lecture: 6.5: Average Value (15 min 38 sec) Video Lecture Error: When I talk about the IVT, I really mean the MVT theorem on page 282 in section 4.2 Optional Office Hours with Dr. Jarvinen in GI308: 2:00pm – 3:20pm
9/8	Recap of Video Lectures	Review for Exam I	EXAM I	7.1 Integration by Parts
9/15	7.2 Trig Integrals	7.3 Trig Substitution	Quiz 7.1 – 7.3 Discussion Day	7.4 Integration by Partial Fractions
9/22	7.5 Integration Strategies	7.6 Integration with Tables	Quiz 7.4 – 7.6 Discussion Day	7.7 Approximate Integration
9/29	7.8 Improper Integrals	8.1 Arc Length	Quiz 7.7 – 8.1 Discussion Day	8.2 Area of a Surface of Revolution
10/6	8.3 Applications of Integration	Review for Exam II	EXAM II	Fall Break Day No Class
10/13	9.1 Modeling with Differential Equations	9.3 Separable Equations	Quiz 9.1, 9.3 Discussion Day	No Class Video Lecture: 9.5: Linear Equations (15 min 19 sec)
10/20	10.1, 10.2 Parametric Curves Calculus on Parametric Curves	10.2 Calculus on Parametric Curves, cont.	Quiz 9.5, 10.1 – 10.2 Discussion Day	10.3 Polar Coordinates
10/27	10.4 Area and Length in Polar Coordinates	Review for Exam III	EXAM III	11.1 Sequences
11/3	11.1, cont. 11.2 Series	11.2, cont.	Quiz 11.1 – 11.3 Discussion Day	11.3 Integral Test and Sum Estimates
11/10	Veteran’s Day No Class	11.4 Comparison Tests	Quiz 11.4 – 11.5 Discussion Day	11.6 Ratio and Root Tests
11/17	11.7 Series Strategies	11.8 Power Series	Quiz 11.6 – 11.8 Discussion Day	11.9 Functions as Power Series
11/24	11.10 Taylor and MacLaurin Series	11.10 Taylor and MacLaurin Series, cont.	Thanksgiving Break No Class
12/1	11.11 Applications of Taylor Polynomials	Review for Exam IV	EXAM IV	Final Review

Final Exam

Tuesday, December 9

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: Don’t use any method on WebAssign that won’t work on an exam. For example, if you’re not allowed to use a calculator on an exam to calculate a limit, do not use one on the homework. If you don’t know how to do an assignment without “shortcuts”, ask a fellow student, a tutor, or the instructor.

#4: After the due date has passed, go back and look at the solutions for the problems you missed. 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 co-efficients 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 co-efficients 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.