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Course Syllabus for MATH 301

VIRGINIA STATE UNIVERSITY
SCHOOL OF ENGINEERING, SCIENCE, & TECHNOLOGY
DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE & COMPUTER SCIENCE
MATH 301 - CALCULUS III - 3 sem. hours

COURSE SYLLABUS: FALL 2003


 

COURSE DESCRIPTION:

Mathematics 301 is the final course of a four semester sequence of Calculus for students majoring in Mathematics and the Natural Sciences.  The topics covered include : Vector-valued functions, Functions of several variables, Multiple integration, Introduction to vector analysis
 

COURSE PREREQUISITE: MATHEMATICS 300-CALCULUS III

COURSE TEXT: CALCULUS  by Larson, Hostetler and Edwards, Seventh edition, 2002, Houghton Mifflin Company
CALCULATOR: TI-83/TI-92/TI-92 Plus
 

TOPICS TO BE COVERED:

  1. Vector-Valued Functions
    • Vector-Valued Functions
    • Differentiation and Integration of Vector-Valued Functions
    • Velocity and Acceleration
    • Tangent Vectors and Normal Vectors
    • Arc Length and Curvature
  2. Functions of Several Variables
    • Introduction to Functions of Several Variables
    • Limit and Continuity
    • Partial Derivatives
    • Differentials
    • Chain Rules for Functions of Several Variables
    • Directional Derivatives and Gradients
    • Tangent Planes and Normal Lines
    • Extrema of Fuctions of Two Variables
    • Applications of Extrema of Fuctions of Two Variables
    • Lagrange Multipliers
  3. Multiple Integration
    • Iterated Integralsand Area in the Plane
    • Double Integrals and Volume
    • Change of Variables: Polar Coordinates
    • Center of Mass and Moments of Inertia
    • Surface Area
    • Triple Integrals and Applications
    • Triple Integrals in Cylindrical and Spherical Coordinates
    • Change of Variables: Jacobians
  4. Introduction to Vector Analysis
    • Vectors Fields
    • Line Integrals
    • Conservative Vector Fields and Independence of Path
    • Green's Theorem
    • Parametric Surfaces
    • Surface Integrals
    • Divergence Theorem
    • Stokes's Theorem

      •  

Chapters 11, 12, 13 and 14 from the textbook will be covered.

GRADING SYSTEM: The following components will determine the final grade.

1. Home Assignments - During each class period you will be assigned some problems from the textbook or from some other source. Sometimes the assignment will be collected and graded and other times one or two problems from the assignment will be chosen and students will be asked to do it in class. Total score from all home assignments will be 100 points.

2. Tests - Two one-hour tests. Each test will be worth 100 points. Test will be comprised of questions discussed in class, home assignments, solved examples in the text, and any other assigned problems. Tests will be announced in advance and student will have plenty of time to prepare for the tests.

3. Mid-term Examination - Mid-term examination will be conducted mid-way through the semester. It will include all the material covered upon to that time. It will be worth 100 points.

4. Final Examination - Final examination will be conducted at the end of the semester and it will be worth 200 points. It will include all the material covered during the semester.

Numerical Scores: The following numerical scores will be assigned to each components in the grade determination process,

                                                                          Points
                                     Tests                              200
                                     Home Assignments         100
                                     Mid-term                        100
                                     Final                               200
                                     Total                              600


               Letter Grade:       A: 90 - 100
                                             B: 80 - 89
                                             C: 70 - 79
                                             D: 60 - 69
                                             F: Below 60


BIBLIOGRAPHY

Anton, Howard. Calculus, 4th edition. New York: John Wiley & Sons, Inc., 1992.

Dolciani, Mary et.al. Modern Introductory Analysis. Boston: Houghton Mifflin, 1967.

Thomas/Finney. Calculus and Analytic Geometry. New York: Addision Wesley Pub. Co.

Kline, Morris. Mathematical Thought From Ancient to Modern Times. New York: Oxford University Press, 1972.

Stewart, James. Calculus. New York: Brooks/Cole Publishing Co.

The American Mathematical Monthly, vol. 87 (1980); vol. 93 (1986).