MATH 151: Calculus II

 

Spring 2016

 

Course Syllabus and Class Policies

 

1.        Major Course topics:

·         Review of Differentiation and Integration (3 class meetings)

·         Techniques of Integration (8 class meetings)

·         Applications of Integration (12 class meetings)

·         Infinite Sequences and Series (10 class meetings)

·         Power Series; Taylor and Maclaurin Series and their Applications (10 class meetings)

·         Differential Equations (5 class meetings)

The tentative detailed syllabus of the course can be found at http://home.sandiego.edu/~pruski/m151s16schedule.html .

 

2.        Course Learning Outcomes:

Upon successful completion of the course, the student will be able to:

·         Explain calculus concepts such as improper integral, convergence of sequences and series, power series, Taylor series, and solutions of differential equations,. This includes the knowledge of theorems with complete assumptions.

·         Apply calculus concepts to evaluate lengths, areas, and volumes, to solve simple differential equations, to model practical problems from various areas, and to interpret solutions obtained from the models.

·         Determine convergence of sequences and series using a variety of methods, represent functions with Taylor and Maclaurin series, and determine error of approximating functions with Taylor polynomials.

·         Clearly communicate complete solutions to problems verbally and in writing. This involves using complete sentences to explain individual steps in the solutions, correct notation and proper units.

·         Explain, interpret and correctly apply definitions.  Provide examples and non-examples to illustrate definitions.

·         Use valid reasoning (be able to provide a logical sequence of statements that follow each other) and be able to identify invalid reasoning.  Provide counterexamples to disprove statements that are not always true.

·         Determine and explain when particular theorems apply to a situation and apply them correctly. 

·         Prove simple theorems.

 

3.        Regular attendance is really necessary. It is quite difficult to catch up with the material when you miss a class. It becomes virtually impossible, if you miss several classes.

 

4.        The pace of the course will be quite fast. We cannot omit any of the topics as the course is a prerequisite for other math courses. Your success in these upper-division courses depends on your mastery of Calculus II material. Please brace yourself for possibly a rough ride. I am here to help you.

 

5.        A student is supposed to spend at least two hours at home for each class hour. Thus, you should expect spending at least 8 hours a week (more likely about 10 hours) doing your homework and preparing for quizzes/exams.

 

6.        Since Calculus II is a course in mathematics, we will be doing some simple proofs. You will be expected to do some proofs in your homework assignments as well as during exams.

 

7.        Because of the increased availability of various symbolic algebra/calculus tools such as computer packages (MATLAB, Mathematica, Maple, etc.) and advanced calculators, the computational aspect of the course has been somewhat reduced. Computations are less important than setting up the problem correctly. Calculators and computers can do the computations; only people, however, can set the problems for computations. In this course, the concepts count much more than computations. In class I will sometimes omit the computational details of, say, integrations. When doing your homework, in addition to problems that I will ask you to solve completely manually, and where I will require that you show all the steps of your work, you may be encouraged to use integration tables, advanced calculators, or various Web tools to solve other problems.

 

8.        The textbook: James Stewart, Single Variable Calculus: Concepts and Contexts. 4e. I cannot lecture on everything in class (simply, there is not enough time), so you will have to learn quite a lot of material on your own. Reading the assigned material is absolutely essential! Quizzes may include questions on the assigned reading as a gentle method of enforcing your reading.

 

9.        Office hours (Dr. Lukasz Pruski, Serra 149, x. 4035):

 

Monday

10:45 - 12:15

Tuesday

2:20 - 3:50

Wednesday

3:30 - 4:30

Friday

1:20 - 2:20

 

and at other times, by appointment.

 

10.     Contact: The best way to contact me is by using e-mail (pruski@sandiego.edu). I read e-mail many times during the day and night, except for a few weekends when I am out of town. I have voice mail (x. 4035), but I sometimes forget to check it. You may call the Mathematics Department Executive Assistant, Tina, at x. 4706, as well.

 

11.     A webpage for the course is at http://home.sandiego.edu/~pruski/m151s16.html . You should check the webpage daily for assignments, announcements, and links.

 

12.     Homework Assignments will be assigned and collected once or twice a week. The assignments will be graded partly on effort. I will assign many odd-numbered exercises that have answers at the BOB (Back-Of-Book). The total homework assignment score will count for 20% of the course grade. No late assignments will be accepted unless you arrange it with me in advance.

 

13.     There will be about 10 short pop-quizzes (not announced in advance). Quiz questions will refer to the recently covered material and to the new material you were supposed to read on your own. Three lowest quiz scores will be dropped, and the remaining scores will count for 20% of the course grade. Quizzes cannot be made up unless you have a valid reason for not taking the quiz and you notify me in advance of your absence.

 

14.     There will be three tests (hour exams); the dates are February 19, March 18, and April 29. Tests will be of closed-book variety. The test scores will count for 30% of the course grade. A test can be made up only if you have an actual emergency and if you notify me in advance about your absence.

 

15.     The final exam (Wednesday, May 18, 2:00 - 4:30) will be cumulative, also closed-book, and its score will count for 30% of the course grade.

 

16.     Calculator policy on all quizzes and exams: No calculators, smart phones, iPods, tablets, etc. are allowed. (Also, bathroom breaks are not allowed on exams: I am embarrassed but this draconian rule has been imposed because of several cheating cases in recent years.)

 

17.     Grading criteria are as follows:

 

Total percentage

Grade

90% and above

A

80% - 90%

B

60% - 80%

C

50% - 60%

D

below 50%

F

 

Of course, pluses and minuses will be used, close to cutoff boundaries. (In the unlikely case that the number of A's and B's falls below about 35-40%, I will curve the grades up appropriately.)

 

18.     The Mathematics and Computer Science Department strongly promotes Academic Integrity. I hope issues related to academic integrity will not arise in our course. There have been some cases of cheating in math courses in the past – mainly the cases of submitting someone else’s work as well as cases of cheating during exams. Depending on the severity of the case, the possible consequences include: assigning the score of 0 on the given assignment, lowering the course grade, or even assigning an F in the course.