Syllabus for MAC 2312 - Calculus and Analytic Geometry 2

Spring, 2002

 

Instructor:    Prof. Blake Mellor

                    MHC 165

                    Phone:  6-8614

                    E-mail:  bmellor@fau.edu

                    URL:  http://www.fau.edu/~bmellor

 

Office Hours:  M 2-5, Th 2-4, F 11-12

 

Class Meeting:  TTh 9:30-10:50, F 10-10:50, MAC 206

 

Text: Calculus: Single Variable, Hughes-Hallett, Gleason, et al., John Wiley & Sons, 2002 (Third Edition)

 

Required:  TI-83 (Plus) Graphing Calculator

 

Objective:  Integration is the reverse of differentiation.  In Differential Calculus you learned how to study rates of change (speeds).  In Integral Calculus you will begin with a rate of change, and learn how to compute total change.  This process is called integration.  The purpose of this class is to learn the theory and techniques of integration, and its applications in several areas, including the study of differential equations.  We will also study infinite sequences and series, leading to the Taylor and Fourier series approximations of functions.

 

Grading:    Homework/Projects 40%

                 Midterm 1                            15%

                 Midterm 2                            15%

                 Final                                    30%

 

Homework/Projects:  There will be homework assignments from the textbook, specified (tentatively) on the syllabus below.  They are mostly selected from the odd-numbered problems, which have answers provided in the back of the book.  These assignments will not be collected; however, some of these problems will appear (perhaps slightly modified) on the midterms and final exam.  Keeping up with the weekly homework is the key to success in the class – it is not possible to do it all the night before the exam!

In addition, there will be regular homework projects (about every two weeks), which may be done in groups of up to 4 people.  Each group will turn in a single project, and every member of the group will receive the same grade.  The projects are also listed (again, subject to change) on the schedule below.

 

Plagiarism:  Each group is expected to work independently.  You may discuss the projects with other groups, but you must (1) cite any assistance obtained from another group, a tutor, or a professor (which means cite exactly what you obtained help on) and (2) write up the solution independently.  This means that, after your discussion with your classmate, etc, you (or your group) should be able to return to your room and write up the solution without looking at the notes of your discussion.  If you cannot do this, you do not understand the solution, and the work is not yours.  A violation of either of these conditions is plagiarism, a violation of the Honor Code, and will be dealt with accordingly.

 

Exams:  The midterms will be 1 hour exams in class on February 15 and April 5.  The final will be 2 1/2 hours on Thursday, May 2, 7:45 -10:15 a.m.  You will be allowed one page of notes and your calculator.  I will provide a copy of the table of integrals at the back of the book for your use.

 

Gateway Test:  Students will have to pass a Gateway Test of basic integration skills in order to pass the class.  The Gateway Test consists of 9 questions, taken online, and may be taken as many times as necessary.  A student must get 8 of the 9 questions correct to pass.  The test will be administered for the first time during class on Thursday, February 14.

 


Schedule:

 

Day

Topic

Reading

Homework

Tues, Jan 8

Professor Mellor out of town

 

 

Thurs, Jan 10

Introduction

Ch. 2-3

p. 159  1-52 odd, 55, 65, 69, 75, 77, 81, 83

Fri, Jan 11

Review of Riemann Sums

Ch. 5

p. 252  1, 3, 11, 17, 23, 27, 31, 33, 35, 37

Air Pollution due 1/15

Tues, Jan 15

Antiderivatives

Substitution

Ch. 6, 7.1

p. 284  1-29 odd, 39, 45, 49, 51, 61

7.1    1, 5, 9, 13, 17, 21, 25, 29, 33, 41, 45, 49, 53, 57, 61, 71, 73, 75

Thurs, Jan 17

Integration by Parts

7.2

7.2    1, 5, 9, 13, 17, 21, 25, 29, 33, 41, 45, 53

Fri, Jan 18

Table of Integrals

7.3

7.3  1, 7, 13, 19, 25, 31, 37, 39

Tues, Jan 22

Slope Fields

11.1, 11.2

11.1   1, 5, 9, 15

11.2   1, 3, 5, 7, 9

Thurs, Jan 24

Euler's Method

11.3

11.3  1, 3, 5, 7, 9

Fri, Jan 25

Separation of Variables

11.4

11.4              1, 7, 13, 19, 25, 31, 37, 39, 45, 46, 47

Raindrops due 1/29

Tues, Jan 29

Growth and Decay

11.5

11.5  1, 3, 7, 9, 15, 17, 19, 21, 23

Thurs, Jan 31

Applications of Differential Equations

11.6

11.6  1, 3, 5, 7, 13, 15, 17, 21, 23

Fri, Feb 1

Catch up

 

 

Tues, Feb 5

More Integration

7.4

7.4  3, 7, 9, 13, 17, 21, 25, 27, 31, 35, 41, 43, 45

Thurs, Feb 7

Approximating Integrals

7.5, 7.6

7.5    1, 3, 5, 7, 9, 11, 13, 19, 23

7.6    1, 3, 5, 7, 9, 11, 12

Fri, Feb 8

Improper Integrals

7.7

7.7    1, 3, 5, 9, 13, 17, 21, 25, 29, 33, 35, 37, 39

World Population Growth due 2/12

Tues, Feb 12

Improper Integrals

Comparison Test

7.7, 7.8

7.8  1, 5, 9, 13, 17, 21, 25, 27, 29, 31, 33

Thurs, Feb 14

Gateway Test and Review

 

 

Fri, Feb 15

Midterm 1

 

 

Tues, Feb 19

Population Models

11.7

11.7  1, 3, 5, 7, 9, 11, 13, 15

Thurs, Feb 21

Systems of Differential Equations

11.8

11.8  1, 2-10, 11, 13, 15, 17, 18-20, 21, 23

Fri, Feb 22

Catch up

 

SIR model due 2/26

Tues, Feb 26

Areas and Volumes

8.1

8.1  1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

Thurs, Feb 28

Applications to Geometry

8.2

8.2  5, 9, 11, 13, 15, 17, 21, 23, 27, 29, 31, 35

Fri, Mar 1

More Geometry

8.2

 

Tues, Mar 5

Spring Break

 

 

Thurs, Mar 7

Spring Break

 

 

Fri, Mar 8

Spring Break

 

 

Tues, Mar 12

Distributions

8.6

8.6  1, 3, 5, 7, 8, 11, 13, 15, 17, 19

Thurs, Mar 14

Probability

8.7

8.7  1, 3, 5, 7, 9, 11, 13, 15

Fri, Mar 15

Catch up

 

Tile Design due 3/19


 

Tues, Mar 19

Geometric Series

9.1

9.1  1, 3, 5, 7, 9, 15, 17, 19, 21, 23, 24, 25, 27

Thurs, Mar 21

Convergence

9.2

9.2  1, 5, 7, 9, 11, 13, 19, 21, 23, 27, 29, 31, 33

Fri, Mar 22

Convergence

 

 

Tues, Mar 26

Tests for Convergence

9.3

9.3  1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 27, 29, 30, 31

Thurs, Mar 28

Power Series

9.4

9.4  1, 3, 5, 9, 11, 13, 15, 17, 19, 21, 23, 25

Fri, Mar 29

Power Series

9.4

The von Koch Snowflake due 4/2

Tues, Apr 2

Taylor Polynomials

10.1

10.1  1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31

Thurs, Apr 4

Review

 

 

Fri, Apr 5

Midterm 2

 

 

Tues, Apr 9

Taylor Series

10.2

10.2  1, 5, 11, 15, 19, 21, 24, 25, 27, 31, 35, 37, 39, 41

Thurs, Apr 11

Taylor Series

10.2

 

Fri, Apr 12

Finding Taylor Series

10.3

10.3  1, 5, 9, 13, 15, 17, 19, 25, 27, 31, 32

Tues, Apr 16

Error in Taylor Approximations

10.4

10.4  1, 3, 5, 7, 10, 11, 15

Thurs, Apr 18

Fourier Series

10.5

10.5  1, 3, 5, 7, 9, 11, 15, 19, 23, 25

Fri, Apr 19

Fourier Series

 

Fourier Series and Music due 4/23

Tues, Apr 23

Review

 

 

Thurs, May 2

Final Exam

7:45 a.m. - 10:15 a.m.