COURSE DESCRIPTION:
This course includes the following topics: multivariable calculus, including vectors; partial derivatives and their applications to maximum and minimum problems with and without constraints; line integrals; multiple integrals in rectangular and other coordinates; and Stokes' and Green's Theorems.
TEXT: CALCULUS, Eighth Edition
by Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards,
Houghton Mifflin, 2006.
PREREQUISITE: MAT 141
EQUIPMENT: Graphing Calculator, preferably TI-82 or TI-83
GRADING SCALE:
A 90 - 100 B 80 - 89 C 70 - 79 D 60 - 69 F Below 60
DEFINITIONS:
ABSENCE - Failure to be present for a scheduled meeting of the class or arriving for the class more than ten minutes after the scheduled time for the class to begin.
TARDY --- Arrival to class after the instructor has called the roll and before ten minutes past the time scheduled for the class to begin.
I. Absences are counted from the first day of classes.
II. Five absences are allowed for a class that meets three times per week and three absences are allowed for a class that meets two times per week.
III. Three tardies are considered as one absence. The student must meet with the instructor at the end of the class to which he has been late to have the absence changed to a tardy.
IV. There are no "excused" absences; all absences are counted, regardless of the reason for the absence.
V. A student missing class time by leaving early will also be counted absent.
Please note the following:
You are responsible for all material and announcements presented, whether you are present or absent.
Mathematics Department Airport: 822-3357 Beltline: 738-7689 Revised 2/14/2007
MAT 240 Course Objectives
Students should be able to:
1. Perform operations with vectors in space.
2. Represent lines, planes and surfaces in space using rectangular, cylindrical and spherical Coordinates.
3. Differentiate, integrate, and solve applied problems using vector-valued functions.
4. Find partial derivatives, differentials, directional derivatives and gradients for functions of several variables.
5. Determine extrema for functions of two variables.
6. Evaluate double and triple integrals.
7. Evaluate line integrals in vector fields.
8. Solve problems by identifying what information is available and relevant to the problem.
9. Solve problems by selecting or developing appropriate procedures and relationships.
10. Solve problems by correctly applying the methods selected to the information available.
11. Solve problems by verifying the validity and appropriateness of the solution.
A listing of major course objectives may be found at http//www.midlandstech.edu/math
MAT 240 ANALYTIC GEOMETRY AND CALCULUS III
Note: This outline is given for the regular Fall/Spring fourteen week semesters. The same material is covered in the summer term and the sessions classes, but in the appropriate fewer number of weeks: ten weeks for summer term, seven weeks for fall and spring sessions classes, and five weeks for summer session classes.
|
WEEK |
TOPIC |
TEXT REF. |
| 1 | Vectors and the geometry of Space | |
| Vectors in the Plane | 11.1 | |
| Space Coordinates and Vectors in Space | 11.2 | |
| 2 | The Dot Product of Two Vectors | 11.3 |
| The Cross Product of Two Vectors | 11.4 | |
| Lines and Planes in Space | 11.5 | |
| 3 | Surfaces in Space | 11.6 |
| Cylindrical and Spherical Coordinates | 11.7 | |
| 4 | TEST 1 | |
| Vector-Valued Functions | ||
| Vector-Valued Functions | 12.1 | |
| Differentiation and Integration of Vector-Valued Functions | 12.2 | |
| 5 | Velocity and Acceleration | 12.3 |
| Tangent Vectors and Normal Vectors | 12.4 | |
| 6 | Arc Length and Curvature | 12.5 |
| TEST 2 | ||
| Functions of Several Variables | ||
| Introduction to Functions of Several Variables | 13.1 | |
| 7 | Limits and Continuity | 13.2 |
| Partial Derivatives | 13.3 | |
| 8 | Differentials | 13.4 |
| Chain Rules for Functions of Several Variables | 13.5 | |
| Directional Derivatives and Gradients | 13.6 | |
| 9 | Tangent Planes and Normal Lines | 13.7 |
| Extrema of Functions of Two Variables | 13.8 | |
| 10 | Applications of Extrema of Functions of Two Variables | 13.9 |
| Lagrange Multipliers | 13.10 | |
| TEST 3 | ||
| 11 | Multiple Integration | |
| Iterated Integrals and Area in the Plane | 14.1 | |
| Double Integrals and Volume | 14.2 | |
| 12 | Change of Variables: Polar Coordinates | 14.3 |
| Surface Area | 14.5 | |
| Triple Integrals and Applications | 14.6 | |
| 13 | TEST 4 | |
| Vector Analysis | ||
| Vector Fields | 15.1 | |
| 14 | Line Integrals | 15.2 |
| Conservative Vector Fields and Independence of Path | 15.3 | |
| Green's Theorem | 15.4 | |
| Comprehensive Final Examination |