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MAT 309

I.  TITLE:      Calculus and Analytic Geometry III

II.  CATALOG DESCRIPTION:      A continuation of MAT 308.

III. PURPOSE:
Mathematics is the language of the sciences and is therefore naturally interdisciplinary.    The calculus, in particular, has played a major and fundamental role in many of the  advances made in the sciences, engineering, and technology; the calculus has also found  applications in business and economics.

MAT 309, the third course in the three-course introductory calculus sequence, is intended to introduce students to multivariate calculus.   In this course students will learn about   dot product and cross product and their many uses; in physics, for example, dot product can be used to compute work and cross product is used to express momentum of a particle and torque.   They will also study level curves and surfaces; an example is isothermal surfaces, which play a role in problems of heat conduction in a homogeneous body.  Students will learn about curvature and the tangential and normal components of acceleration as well as geometric and physical interpretations of partial derivatives.

Students who have had some calculus in high school may wish to complete the introductory calculus sequence, and they can benefit from doing so even if they are not mathematics or science majors.   Students completing this course will (1) engage in independent thought, expressing such thought orally in the classroom when presenting homework problems at the board as well as in writing on tests and quizzes; (2) understand the critical and scientific methodologies that mathematicians and scientists employ to discover mathematical truths; (3) learn to apply sound standards of critical analysis and evaluation to reach logical decisions; (4) gain an understanding of how applications of mathematics are important in the technological advances evident in our changing world; (5) be aware that, depending upon the level of mathematical literacy present in the educated population, technology may be used responsibly or irresponsibly; (6) achieve an  understanding of mathematical reasoning which will help prepare them for further study in their majors and provide a foundation for life-long learning.  These objectives correspond  to six of the eight characteristics of the MSU graduate.

IV. COURSE OBJECTIVES:
A. This course is intended to complete the student's introduction to the calculus, which stands as one of the truly monumental accomplishments of the human intellect.  This course focuses on the fundamental concepts of derivatives and integrals in n-dimensional space.

B. In order to apply the content of this course, the student should develop the analytical, logical thought processes which are required for problem-solving.
  The student should gain an understanding of and experience with optimization    methods (using the second-partials test and Lagrange multipliers) that are used
  throughout the sciences and engineering as well as in business and economics.

C. The student should gain an appreciation for the history of mathematics, with    particular attention to the contributions made by individual mathematicians from a   variety of backgrounds and nations.

V. CONTENT OUTLINE:
A. Vectors and surfaces
B. Vector-valued functions
C. Partial differentiation
D. Multiple integrals

VI. INSTRUCTIONAL ACTIVITIES:
A. This course is a thematic problem-solving course meant to help develop the   student's ability to logically and independently analyze and solve problems which   have been posed both in symbolic and in narrative form.  The use of projects and   group assignments promotes student engagement in and responsibility for learning;  group work may be evaluated on the basis of individual written reports on the   project/assignment.

B. The emphasis both in assignments and in testing is more on reasoning processes   than on computations, so this course requires a significant amount of writing and   critical thinking skills.   Instructors may require students to put homework solutions on the board and explain their work orally.  Students are encouraged, at the end of   each section, to identify a representative collection of problems from that section   and then write instructions (with complete sentences) about how to recognize each   type of problem, how to go about solving it, and why the method of solution works.

C. Use of the Mathematics Computer Laboratory is encouraged in student projects.

VII. FIELD AND CLINICAL EXPERIENCES:
Students may be assigned projects which require use of the mathematics computer  laboratory (Faculty Hall 109).

VIII. RESOURCES:
Scientific or graphing calculator
Mathematics Department Computer Laboratory: Faculty Hall 109
Instructor's office hours: as posted and by appointment

IX. GRADING PROCEDURES:
Performance on hour tests, homework sets/projects, pop quizzes, and the comprehensive  final examination will be considered in determining the course grade.   Students are  expected to demonstrate an understanding of the reasoning processes appropriate to  calculus as well as proficiency in basic computations; they are expected to know and  understand technical terminology, mathematical symbols, and key theorems and be able  to communicate this knowledge and understanding and apply these to solve problems.

hour tests (4)      56%
comprehensive final examination   28%
pop quizzes/homework/projects   16%

Grading Scale  (approximate):                       90  - 100                  A
                                                                    80  -   89                   B
                                                                    70  -   79                   C
                                                                    60  -   69                   D
                                                                    below 60                   E

No student may audit the course without the consent of the instructor.  Attendance and  participation are required for audit.

X. ATTENDANCE POLICY:
Class attendance is expected and is recorded.    Each student is responsible for all material covered and assignments made during missed class periods.   A student who has an excused absence from a test will be allowed to take a make-up test.

XI. ACADEMIC HONESTY POLICY:
Any instance of academic dishonesty, as determined by the instructor (in compliance with Board of Regents policy on Academic Integrity – Feb. 1975) will result in zero points for the assignment or a grade of “E” for the course.

XII. TEXT:  Current

XIII. PREREQUISITES:
MAT 308

Last updated February 14, 2000. Designed and maintained by Kyosung Koo