PELLISSIPPI STATE TECHNICAL COMMUNITY COLLEGE MASTER SYLLABUS
CALCULUS III MATH 2110 (formerly MTH 2410)
Class Hours:  4.0								Credit Hours:  4.0
Laboratory Hours:  0.0								Date Revised:  Fall 03
Catalog Course Description:
	Calculus of functions in two or more dimensions. Topics include solid analytic geometry,  partial differentiation, multiple integration, and selected topics in vector calculus.
Entry Level Standards:
	A thorough knowledge of algebraic, trigonometric, and beginning and intermediate calculus  functions is necessary for entrance to this course.
Prerequisite:  MATH 1920
Textbook(s) and Other Reference Materials Basic to the Course:
	Textbook: James Stewart. Multivariable Calculus Concepts and Contexts, Brooks/Cole Pub., 2001 Materials: A graphing calculator References: Earl Swokowski. Calculus with Analytic Geometry, 6th Edition. PWS-Kent Pub. Co., 1994. C. Henery Edwards & David Penney.  Multivariable Calculus with Analytic Geometry, 5th Edition. Prentice-Hall, Inc., 1998. Arnold Ostebee & Paul Zorn.  Multivariable Calculus. Saunders College Pub., 1997. William McCallum, Deborah Hughes-Hallett & Andrew Gleason.  Multivariable Calculus. John Wiley & Sons, Inc., 1997.
I. Week/Unit/Topic Basis:
	Week					Topic
	1					Three dimensional coordinate systems and vectors;  9.1-9.2
	2					Dot product, cross product and equations of lines and planes;  9.3-9.5
	3					Functions and surfaces;  cylindrical and spherical coordinates;  9.6-9.7
	4					Vector-valued functions: space curves, derivatives and integrals, arc length and curvature;  10.1-10.3
	5					Motion in space, parametric surfaces;  10.4-10.5
	6					Partial differentiation: functions of several variables, limits and continuity, partial derivatives; 11.1-11.3
	7					Tangent planes and linear approximations, the chain rule; 11.4-11.5
	8					Directional derivatives and the gradient vector, maximum and minimum values, Lagrange multipliers;  11.6-11.8
	9					Multiple integrals: double integrals, iterated integrals;  12.1-12.2
	10					Double integrals over general regions, double integrals in polar coordinates, applications of double integrals;  12.3-12.5
	11					Surface area, triple integrals;  12.6-12.7
	12					Triple integrals in cylindrical and spherical coordinates, change of variables in multiple integrals;  12.8-12.9
	13					Vector calculus: vector fields, line integrals, the fundamental theorem for line integrals;  13.1-13.3
	14					Green's theorem, curl and divergence, surface integrals;  13.4-13.6
	15					Stokes' Theorem, the divergence theorem;  13.7-13.8
	16					Final Exam
II. Course Objectives*:
	A.			Become familiarity with vector and solid analytic geometry. I,III,IV
	B.			Understand the concepts of vector-valued functions to suitable mathematical models. II,III
	C.			Be able to calculate partial derivatives and multiple integrals. III
	D.			Be able to work with partial derivatives and mulitiple integrals in application problems. II,III,V
	E.			Learn how to apply vector calculus. II,III,V
*Roman numerals after course objectives reference goals of the university parallel program.
III. Instructional Processes*:
Students will:
	1.				Use graphing calculators and/or computer software.  Technological Literacy Outcome
	2.				Solve real life problems such as using tangential and normal components of acceleration to justify banking curved roads, analyze the forces placed on beams, poles, etc. used in engineering constructions, calculate flux through simi-permeable membranes. Problem Solving and Decision Making Outcome, Numerical Literacy Outcome,  Transitional Strategy
	3.				Actively engage in student-led discussions and brainstorming sessions about the mathematical/physics based models inherent to the course.  Active Learning Strategies,  Transitional Strategies
	4.				Investigate and justify the engineering concepts contained in fields of statics and dynamics. Problem Solving and Decision Making Outcome, Numerical Literacy Outcome
*Strategies and outcomes listed after instructional processes reference Pellissippi State's goals for strengthening general education knowledge and skills, connecting coursework to experiences beyond the classroom, and encouraging students to take active and responsible roles in the educational process.
IV. Expectations for Student Performance*:
Upon successful completion of this course, the student should be able to:
	1.			Sketch vectors, use vector operations, find the magnitude of a vector, and find a unit vector in two-space and three space. A
	2.			Determine whether  two vectors are orthogonal; determine the angle between two vectors. A
	3.			Define the equations of lines and planes in three-space. A
	4.			Sketch the graph of rectangular, cylindrical, or spherical equations in three-space. A
	5.			Sketch the graph of vector valued functions and calculate the length of the curve. B
	6.			Differentiate and integrate vector valued functions. B
	7.			Find velocity, acceleration, and speed for a position vector. B
	8.			Find unit tangent and unit normal vectors and calculate curvature. B
	9.			Calculate tangential and normal components of acceleration. B
	10.			Find the limit of two variable functions. C
	11.			Determine the first and higher order partial derivatives. C
	12.			Use the chain rule to find partials derivatives and use partials to differentiate implicit functions. D
	13.			Find the gradient and directional derivative of a two-variable function. D
	14.			Find the equations for the tangent plane and the normal line to a surface and find the extrema of the surface. D
	15.			UseLagrange multipliers to find local extrema. D
	16.			Evaluate iterated integrals. C
	17.			Calculate areas, surface areas, and volumes using double integrals. D
	18.			Calculate volumes using triple integrals. D
	19.			Find mass, moments, center of mass and moments of inertia. D
	20.			Find the divergence and curl of vector fields. E
	21.			Evaluate line integrals. E
	22.			Determine if a line integral is independent of path and find a potential function for the vector function. E
	23.			Use Green's Theorem to evaluate a closed line integral. E
	24.			Evaluate surface integrals and calculate flux. E
	25.			Use the Divergence Theorem to calculate flux. E
*Letters after performance expectations reference the course objectives listed above.
V. Evaluation:
	A. Testing Procedures:
			Students are evaluated primarily on the basis of tests, quizzes, and homework. A minimum of 4 major tests is recommended. Computer applications or projects may constitute part of the final grade also.
	B. Laboratory Expectations:  None
	C. Field Work:  None
	D. Other Evaluation Methods:  None
	E. Grading Scale:
		93% - 100%   A      88 - 92        B+      83 - 87        B      78 - 82        C+      70 - 77        C      60 - 69        D      Below 60   F
VI. Policies:
	A. Attendance Policy:
		Pellissippi State Technical Community College expects students to attend all scheduled instructional activities. As a minimum, students in all courses must be present for at least 75 percent of their scheduled class and laboratory meetings in order to receive credit for the course. Individual departments/programs/disciplines, with the approval of the vice president of Academic and Student Affairs, may have requirements that are more stringent.
	B. Academic Dishonesty:
		Individual instructors must distribute their policy on academic dishonesty during the first week of class.