67-273 CALCULUS III SPRING 2006
Section 001: 8:00-9:00 MTWF Swart 13
INSTRUCTOR: Zoubir Benzaid
OFFICE: Swart 238
PHONE: 424-7354 (O) 236-9257 (H)
OFFICE HOURS: MTWF: 10:30-1130 and MTW: 1:45-2:30 (And by appointment)
TEXT
CALCULUS: Concepts and Contexts by J. Stewart, Brooks/Cole, 2nd Edition, 2001..
I strongly recommend that you get the student solution manual (even if it is for the 3rd Edition)
CALCULATOR
TI-83+ (or perhaps a TI 84) Graphics Programmable Calculator.
If you have some other TI machine and know how to use it, great. However I will not be able to support it in class. The TI 89 or TI 92 (or similar calculator with symbolic capability) will not be allowed.
SOFTWARE
UWO has acquired a full site license for the Computer Algebra System Maple. This software can be accessed using any PC or Mac at any computer lab on campus. Maple is extremely user friendly and I expect you will be using it to complete your homework and assigned projects. I will be giving demonstrations of the software and assigning various Maple projects throughout the semester.
OBJECTIVES OF THE COURSE
- extends single variable calculus to higher dimensions; provides vocabulary for understanding fundamental equations of nature like weather, planetary motion, waves, heat, finance, epidemiology, or quantum mechanics.
- teaches important background needed for statistics, computer graphics, bioinformatics, etc;
- provides tools for describing curves, surfaces, solids and other geometrical objects in three dimensions;
- develops methods for solving optimization problems with and without constraints;
- prepares you for further study in other fields of mathematics and its applications;
- improves thinking skills, problem solving skills, visualization skills as well as computing skills
TOPICS
- Chapter 9: Vectors and Geometry of Space: Dot and Cross Products, Lines, Planes and Surfaces, Cylindrical and Spherical Coordinates.
- Chapter 10: Vector Functions: Space Curves, Calculus of Vector Functions, Arc Length and Curvature, Kinematics, Parametric Surfaces.
- Chapter 11: Partial Derivatives: Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximation, Chain Rule, Directional Derivatives and gradients, Optimization.
- Chapter 12: Multiple Integrals: Double Integrals, Iterated Integrals, Surface Area, Triple Integrals, Change of Variables in Multiple integrals, Applications.
- Chapter 13: Vector Fields: Line Integrals, Green's Theorem and if time permits we will also discuss Curl and Divergence, Surface Integrals, Stoke's Theorem and Divergence Theorem.
WEBSITE
I will maintain a website for this course at http://www.uwosh.edu/faculty_staff/benzaid. The site will contain the syllabus, homework assignments, practice tests and solutions, solutions to tests, solutions to selected homework problems, Maple worksheets, miscellaneous lecture notes and links to other interesting calculus sites.
EXAMS
There will be a series of three (3) one-hour exams and a comprehensive final examination. MAKE-UP TESTS will be given only in extraordinary circumstances. These written exams will count as 75% of your course grade. Tentative dates are
- Exam 1: 2/24
- Exam 2: 3/24
- Exam 3: 4/21
- Final Exam: 5/12
QUIZZES, HOMEWORK PROBLEMS, MAPLE PROJECTS and CLASS PRESENTATION OF HOMEWORK PROBLEMS
These will compose 25% of your grade. Make-up quizzes will not be given and late assignments will not be accepted.
HOMEWORK
Even numbered problems will be assigned from the book and collected every Monday. I will post the solutions on my website soon thereafter.
GRADING
A: [90,100]; AB: [88,90); B: [80, 88); BC: [78, 80); C: [68, 78); CD: [65,68); D: [56, 65); F: [0,56).
ATTENDANCE
You will be expected to attend classes regularly. I will be taking attendance daily and will penalize borderline students with an excessive number of absences (4 or more). Students are responsible for all material covered in class.
IMPORTANT COMMENTS
- Class participation is crucial to success in a math class. Please feel free to ask and answer questions. I will be doing the lecturing, but I expect all of you to actively participate in the learning process.
- Do not fall behind. As soon as I assign some homework problems, try a few of them the same day. To be successful in mathematics requires a consistent effort. Do not work in spurts or just cram before the exams. Reserve an hour or more everyday to reading the book and working problems. Give an honest effort and you will not be disappointed.
- Read the book and consult other books in the library. The following represent a recommended list of Calculus books:
- Anton, H: Calculus with Analytic Geometry
- Ash, C and Ash, R: The Calculus Tutoring Book
- Lax, P: Calculus with applications and computing
- Marsden & Weinstein: Calculus
- Simmons, G: Calculus with Analytic Geometry
- Stewart, J: Calculus
- Strang, G: Calculus
- Thomas & Finney: Calculus and Analytic Geometry
- Get to know each other and work in groups when completing the homework assignments.
| Read Sections | Homework Problems |
|---|---|
| 9.1: Vectors and the Geometry of Space | 6, 9, 16, 23, 24, 31, 36 |
| 9.2: Vectors | 6, 9, 16, 23, 26, 29, 32, 33, 34, 37 |
| 9.3: The Dot Product | 5, 14, 18, 26, 31, 33, 36, 38, 41, 43 |
| 9.4: The Cross Product | 1, 6, 15, 22, 27, 30, 32, 33 |
| 9.5: Equations of Lines and Planes | 3, 8, 17, 22, 27, 30, 38, 45, 51, 54 |
| 9.6: Functions and Surfaces | 4, 11, 15, 22, 24, 34 |
| 9.7: Cylindrical and Spherical Coordinates | 3, 6, 7, 10, 13, 18, 21, 23, 27, 32 |
| 10.1: Vector Functions and Space Curves | 5-10, 13, 14, 21, 24, 29 |
| 10.2: Derivatives and Integrals of Vector Functions | 3, 16, 20, 27, 30, 35, 43, 45, 47 |
| 10.3: Arc Length and Curvature | 3, 8, 12, 24, 32, 35, 45, 47 |
| 10.4: Motion in Space | 3, 12, 21, 25, 32, 35, 36 |
| 10.5: Parametric Surfaces | 2, 3, 5, 8, 11-16, 17, 22, 29, 32 |
| 11.1: Functions of Several Variables | 2, 7, 9, 15, 22, 25, 29, 31-36 |
| 11.2: Limits and Continuity | 5, 8, 13, 18, 25, 33, 35 |
| 11.3: Partial Derivatives | 3, 8, 13, 18, 27, 33, 38, 44, 46, 56, 59, 63, 66, 70, 79 |
| 11.4: Tangent Planes and Linear Approximations | 10, 13, 16, 19, 26, 31, 33, 40 |
| 11.5: The Chain Rule | 5, 8, 13, 20, 27, 30, 35, 39, 43, 44 |
| 11.6: Directional Derivatives and the Gradient Vector | 3, 5, 9, 12, 22, 28, 36, 43, 48, 51 |
| 11.7: Maximum and Minimum Values | 5, 14, 23, 26, 33, 37, 42 |
| 11.8: Lagrange Multipliers | 3, 12, 23, 37, 41, 42 |
| 12.1: Double Integrals over Rectangles | 3, 6, 9, 11, 12 |
| 12.2: Iterated Integrals | 3, 7, 8, 9, 12, 14, 17, 20, 25, 31 |
| 12.3: Double Integrals over General Regions | 3, 6, 7, 10, 14, 17, 19, 21, 24, 27, 29, 32, 35, 38, 39, 47, |
| 12.4: Double Integrals in Polar Coordinates | 3, 4, 8, 11, 14, 16, 19, 22, 24, 27, 32 |
| 12.5: Applications of Double Integrals | 3, 10, 13, 19, 22, 23 |
| 12.6: Surface Area | 3, 6, 9, 11, 14, 18, 21, 26 |
| 12.7: Triple Integrals | 3, 8, 11, 14, 16, 21, 24, 26, 30, 33, 38, 44 |
| 12.8: Triple Integrals in Cylindrical and Spherical Coordinates | 3, 7, 11, 14, 16, 19, 23, 26, 30 |
| 12.9: Change of Variables in Multiple Integrals | 3, 7, 10, 12, 15, 20, 22 |
| 13.1: Vector Fields | 3, 8, 11-14, 15-18, 21, 26, 29-32 |
| 13.2: Line Integrals | 3, 5, 12, 13, 17, 22, 25, 31, 34 |
| 13.3: The Fundamental Theorem for Line Integrals | 3, 6, 9, 14, 18, 27, 31, 33 |
| 13.4: Green's Theorem | 3, 6, 9, 12, 15, 19, 22 |
| 13.5: Curl and Divergence | 3, 6, 7, 10, 12, 16, 24, 29, 31, 32 |
| 13.6: Surface Integrals | 5, 8, 15, 19, 23, 33, 39, 41 |
| 13.7: Stokes' Theorem | 3, 6, 8, 14 |
| 13.8: The Divergence Theorem | 3, 6, 8, 11, 19 |