# Mathematics

## MATH 320:  Calculus III

Fall 2004, 4 Credits, MWF: 9:00-9:50 a.m., R: 8:00-8:50 a.m., MC 415

Instructor: Rich Maresh, Associate Professor & Chair, Mathematics Department

Office: MC 522 Hrs: MWF 10-11, TW 2-3 or by appt, Ph: 796-3655, 526-4988 (home)

Email: rjmaresh@viterbo.edu

Final Exam:  Friday, 17 Dec 04, 9:50-11:50 a.m.

Catalog Description:

Multivariate calculus: three-dimensional coordinate system, vectors and applications, partial differentiation, multiple integration and applications.

Prerequisite: grade of C or higher in 221.

Text:  Calculus – Concepts and Contexts (2nd edition), by James Stewart, Brooks/Cole Publishing, 2001.

General Education Core Abilities:

These skills are related to the Gen Ed core abilities document. Since MATH 320 may be taken in partial fulfillment of the General Education component of a degree, these are listed in this syllabus.

1.  Thinking Skills:

• Uses reasoned standards in solving problems and presenting arguments.

2.  Communication Skills:

• Reads with comprehension and the ability to analyze and evaluate.

• Listens with an open mind and responds with respect.

• Accesses information and communicates using current technology.

3.  Life Values:

• Analyzes, evaluates and responds to ethical issues from an informed personal value system.

4.  Cultural Skills:

• Understands culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.

• Demonstrates knowledge of the signs and symbols of another culture.

• Participates in activity that broadens the student’s customary way of thinking.

5.  Aesthetic Skills:

• Develops an aesthetic sensitivity

Mathematics Program Course-level Outcomes:

As part of the assessment process, I also list here the specific student outcomes desired for math majors in this course. Even though we want to use this list to help us assess the success of the mathematics program, to judge how well we are doing what we think we are doing, these outcomes are also important for those of you who are not math majors.

Content

¨   Students will understand the concepts three-dimensional space, vectors, multivariable functions and their derivatives, multiple integration and their applications.

Reasoning

¨   Students will be able to reason deductively to prove the truth or falsity of a conjecture (Outcome 2.2)

Problem Solving

¨   Students will apply calculus techniques to novel or non-routine problems (Outcome 3.1)

¨   Students will demonstrate the ability to solve a problem in multiple ways (Outcome 3.2)

Technology

¨   Students will use a calculator for basic computation and for graphing functions with an appropriate viewing window and scale (Outcome 4.1)

¨   Students will demonstrate an understanding of the limitations of a calculator (Outcome 4.2)

¨   Students will use DERIVE (CAS software) to solve problems (Outcome 4.3)

Communication

¨   Students will use mathematical notation and language to accurately and appropriately write solutions to problems (Outcome 5.1)

From a most general perspective, the student should see growth in his/her mathematical maturity. The three-semester sequence of calculus courses form the foundation of any serious study of mathematics or other mathematically-oriented disciplines and this course is the capstone of that sequence.

Course Content Outline:

The student will study three-dimensional space and vectors, lines, planes and general surfaces.

The student will study derivatives and partial derivatives of functions in 3D space.

The student will study the concept and process of multiple integration, and explore a variety of applications of such processes.

COURSE PHILOSOPHY AND PROCEDURES:

I am a firm believer in the notion that you as the student must be actively engaged in the learning process and that this is best accomplished by your DOING mathematics. My job here is not to somehow convince you that I know how to do the mathematics included in the course, but to help guide YOU through the material; I am to be a “guide on the side, NOT a sage on the stage”. I may not always say things in the way which best leads to your full comprehension, but I will try to do so and I ask that you try to see your learning as something YOU DO rather than as something I do TO you. PLEASE feel free to come see me to discuss questions or concerns you may have during the course; I will not bite! PLEASE ask questions in class if you have them; the only dumb question is the one you fail to ask!

Let me therefore urge you to make it a regular part of your day to try working the HOMEWORK problems. There will never be enough time for us to go through every listed problem in class, and it is unrealistic to think that you will be able to find the time to work through every listed problem, but you should at least spend some time thinking about virtually every problem, and working the more interesting or challenging to completion. The daily Homework assignments will not generally be collected or graded. They are intended to structure your learning so that you regularly challenge yourself to see that you understand the material we are looking at. The important thing is that you at least look at all the assigned problems. You should also feel free to work other problems if you deem it necessary for your comprehension of the content.

In general, I think students can benefit greatly by WORKING TOGETHER on problems. While there is some danger of the “blind leading the blind” syndrome, or of students deceiving themselves into thinking they understand the material better than they actually do, for the most part grappling with ideas and trying to explain them to another student or learning to listen to others explain an idea is a wonderful way to see that you really do understand the material. In class we will spend an occasional day working on a group “lab”, and we sill also typically have a group “practice exam” before the individual exams, and I also encourage you to find a “learning group” outside of class.

I will be asking you to assemble a PORTFOLIO. The portfolio will be collected at the end of the semester, on Friday 10 December. This “portfolio” should be a representative collection of your work during the semester, and should include 5 problems, written up in a finished form, along with a brief discussion of why you chose to include that particular problem. These problems should represent work you are proud of, or problems that brought you to a breakthrough point. This portfolio of your work will be worth 40 points, 8 points per problem. Presumably you will hand in 5 sheets of paper, each of which will include a nicely organized solution to the problem, which might be from homework, or from a lab or worksheet, of from an exam, along with that reflection mentioned above.

I use a rather traditional GRADING SCALE:  A = 90% (or better), AB = 87%, B = 80%, BC = 77%, C = 70%, CD = 67%, D = 60%. I do try to come up with a mix of points so that exams are not weighted too heavily; about half the points during the semester will come from individual, in-class exams - the rest will come from group labs, take-home problems, group practice exams, and portfolios.

It is rarely much of a problem at the level of a calculus course, but it remains important that students turn in work in a timely manner, so that they do not get behind. Consequently, LATE ASSIGNMENTS will be penalized 20% of the possible points for each class period late, up to a maximum of three periods.

AMERICANS WITH DISABILITY ACT:

If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski in MC 320 (796-3085) within 10 days to discuss your accommodation needs.

MATH 320 Fall 2004 Course Schedule

30 Aug    [9.1] 3D Coordinate System                                                   p 651, #1-13, 17-31 odd

1 Sep       [9.2] Vectors                                                                           p 659, #1-27 odd

2 Sep       [9.3] The Dot Product                                                            p 666, #1-29 odd

3 Sep       [9.4] The Cross Product                                                         p 674, #1-25 odd

8 Sep       Lab #1

9 Sep       [9.5] Equations of Lines and Planes                                       p 683, #1-25 odd

10 Sep     … more on [9-5]                                                                     p 683, #27-47 odd

13 Sep     [9.6] Functions and Surfaces                                                  p 692, #1-25 odd

15 Sep     Lab #2

16 Sep     [9.7] Cylindrical and Spherical Coordinates                           p 698, #1-25 odd

17 Sep     Group Practice Exam #1  (25 Points)

20 Sep     EXAM #1  (75 Points)

22 Sep     [10.1] Vector Functions and Space Curves                            p 710, #1-25 odd

23 Sep     [10.2] Derivatives and Integrals of Vector Functions             p 716, #1-21 odd

24 Sep     … more on [10.2]                                                                  p 716, #23-35 odd

27 Sep     [10.3] Arc Length and Curvature                                            p 723, #1-25 odd

29 Sep     [10.4] Motion in Space                                                           p 733, #1-23 odd

30 Sep     Lab #3

1 Oct       Review…

4 Oct       Group Practice Exam #2

6 Oct       EXAM #2

7 Oct       [11.1] Functions of Several Variables                                     p 756, #1-1-29 odd

8 Oct       [11.2] Limits and Continuity                                                  p 765, #1-27 odd

11 Oct     [11.3] Partial Derivatives                                                        p 776, #1-25 odd

13 Oct     … more on [11.3]                                                                  p 777, #27-57 odd

14 Oct     [11.4] Tangent Planes and Linear Approximations                p 788, #1-27 odd

15 Oct     Lab #4

18 Oct     [11.5] The Chain Rule                                                            p 796, #1-27 odd

20 Oct     [11.6] Directional Derivatives and the Gradient Vector         p 808, #1-31 odd

21 Oct     [11.7] Maximum and Minimum Values                                  p 818, #1-23 odd

25 Oct     … more on [11.7]                                                                   p 819, #25-43 odd

27 Oct     [11.8] Lagrange Multipliers                                                    p 827, #1-19 odd

28 Oct     Lab #5

29 Oct     Review …

1 Nov      Group Practice Exam #3

3 Nov      EXAM #3

4 Nov      [12.1] Double Integrals over Rectangles                                 p 847, #1-11 odd

5 Nov      [12.2] Iterated Integrals                                                          p 853, #1-21 odd

8 Nov      [12.3] Double Integrals over General Regions                        p 861, #1-27 odd

10 Nov    [12.4] Double Integrals in Polar Coordinates                         p 867, #1-25 odd

11 Nov    NCTM Conference in Minneapolis (no class)                         Take-home Problem Set

12 Nov    NCTM Conference in Minneapolis (no class)                                       ″

15 Nov    [12.5] Applications of Double Integrals                                 p 877, #1-21 odd

17 Nov    [12.6] Surface Area                                                                 p 881, #1-17 odd

18 Nov    [12.7] Triple Integrals                                                             p 890, #1-19 odd

19 Nov    [12.8] Triple Integrals in Cylindrical and Spherical Coords.  p 898, #1-25 odd

22 Nov    Lab #6

29 Nov    [12.9] Change of Variables in Multiple Integrals                    p 909, #1-11 odd

1 Dec       Group Practice Exam #4

2 Dec       EXAM #4

3 Dec       [13.1] Vector Fields                                                                p 922, #1-17 odd

6 Dec       [13.2] Line Integrals                                                                p 933, #1-15 odd

8 Dec       [13.3] The Fundamental Theorem for Line Integrals              p 943, #1-17 odd

9 Dec       Review …

10 Dec     Group Practice Final Exam

Final Exam: Friday, 17 Dec 2004, 9:50-11:50 am