MAT 203 Calculus III

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PUEBLO COMMUNITY COLLEGE

COURSE SYLLABUS

1.

COURSE TITLE

Calculus III

PREFIX/NUMBER:

MAT 203

Credit Hours:

4

2.

PREREQUISITES:

Successful completion of MAT 202 with a C or better

3.

RESOURCES NEEDED:

TEXT:

Calculus, 7/e, James Stewart

ISBN: 9780538497817

SUPPLIES:

Paper, pencil, scientific calculator

4.

COURSE DESCRIPTION:

Completes the traditional subject matter of Calculus. Topics include vectors, vector-valued functions, and multivariable calculus including partial derivatives, multiple integrals, line integrals, and application.

5.

STANDARD COMPETENCIES:

A.

Solve problems involving curves defined parametrically which involves slope and are.

B.

Demonstrate vector arithmetic.

C.

Describe the difference between scalars and vectors geometrically and algebraically.

D.

Demonstrate the ability to work with vector valued functions. This includes limits, continuity, derivatives, and integrals.

E.

Solve problems involving velocity and acceleration.

F.

Solve problems involving unit tangent and unit perpendicular vector, the unit binomial vector, curvature and tangential and normal components of acceleration both in two space and three space.

G.

Demonstrate the ability to graph in three dimensions, and know the formulas of basic three dimensional objects such as spheres and planes.

H.

Work problems involving the dot and cross product.

I.

Demonstrate an understanding of the interpretation of these operations.

J.

Work problems of the line in three space both symmetrically and parametrically.

K.

Identify the six basic different surfaces in three dimensions. These surfaces are the ellipsoid, hyperboloid of one and two sheets, elliptic paraboloid, hyperbolic paraboloid, and elliptic cone.

L.

Relate problems in the rectangular coordinates to the cylindrical coordinates to the spherical coordinates.

M.

Apply the concept of the partial derivative.

N.

Understand the concept of differentiability and its relationship to the gradient. This includes working problems involving these concepts.

O.

Demonstrate an understanding of the directional derivative, level curves and level surfaces.

P.

Solve problems involving the chain rule for many variables.

Q.

Demonstrate the ability to work problems involving maxima and minima both with the second partials test and Lagrange’s method.

R.

Demonstrate the ability to work with the double and triple integral and understand applications. The student will also understand the use of the surface are integral.

S.

Demonstrate knowledge of vectors fields, the potential function, and the divergence and curl of a vector field.

T.

Show proficiency with line integral and independence of path.

U.

Demonstrate ability to do problems involving surface integrals.

V.

Demonstrate knowledge of the theorems of Green, Gauss, and Stokes and applying the theorems.

W.

Demonstrate a basic knowledge of linear algebra.

6.

COURSE OUTLINE:

13.0

Vectors and the geometry of space

13.1

Three Dimensional Coordinate Systems

13.2

Vectors

13.3

The Dot Product

13.4

The Cross Product

13.5

Equations of Lines and Planes

13.6

Cylinders and Quadratic Surfaces

14.0

Vector Functions

14.1

Vector Functions and Space Curves

14.2

Derivatives and Integrals of Vector Functions

14.3

Arc Length and Curvature

14.4

Motion in Space: Velocity and Acceleration

15.0

Partial Derivatives

15.1

Functions of Several Variables

15.2

Limits and Continuity

15.3

Partial Derivatives

15.4

Tangent Planes and Linear Approximations

15.5

The Chain Rule

15.6

Directional Derivatives and Gradient Vector

15.7

Maximum and Minimum Values

15.8

Lagrange Multipliers

16.0

Multiple Integrals

16.1

Double Integrals Over Rectangles

16.2

Iterated Integrals

16.3

Double Integrals Over General Regions

16.4

Triple Integrals

16.5

Triple Integrals in Cylindrical Coordinates

16.6

Triple Integrals in Spherical Coordinates

16.7

Change of Variables in Multiple Integrals

17.0

Vector Calculus

17.1

Vector Fields

17.2

Line Integrals

17.3

The Fundamental Theorem for Line Integrals

17.4

Green’s Theorem

17.5

Curl and Divergence

17.6

Parametric Surfaces and Their Areas

17.7

Surface Integrals

17.8

Stoke’s Theorem

17.9

The Convergence Theorem

17.10

Summary

7.

EVALUATION PROCEDURE:

Evaluation methods and procedures will be determined by the instructor. These may consist of, but are not limited to, quizzes, assignments, exams, individual and/or group projects.

Grading Scale:

90 – 100% - A

80 – 89% - B

70 – 79% - C

60 – 69% - D

0 – 59% - F

8.

SPECIAL REMARKS:

Homework:

Homework will be assigned and evaluated as determined by the instructor.

Cheating:

If cheating occurs, it will result in academic and possible disciplinary sanctions being taken against the student. The Academic Dishonesty Adjudication Process, as outlined in the Student Handbook, will be followed. Academic sanctions will include receiving a zero for the assignment or exam and any other sanctions determined by the instructor.

Attendance:

Attendance will be taken and students may be dropped when they have missed 20% of the total class time (12 hours). Missed exams will result in a zero unless prior arrangements have been made.

Conduct:

Professional and courteous behavior is expected at all times. Disruptive behavior is unacceptable in the classroom and may result in the student’s temporary or permanent removal from the course.

Assistance:

Help is available outside of the classroom from your instructor, in the Learning Center Math Lab, or the Pro Shop.

9.

ACADEMIC INTEGRITY:

The very nature of higher education requires that students adhere to accepted standards of academic integrity. Therefore, Pueblo Community College has adopted a policy of academic conduct as described in the Student Handbook. Violation of academic integrity may be defined to include the following: cheating, plagiarism, falsification and fabrication, abuse of academic materials, complicity in academic dishonesty, and personal misrepresentation. It is the student’s responsibility to be aware of the behaviors that constitute academic dishonesty. Sanctions for violating the standards of academic integrity may include warning, probation, suspension, and/or failure of the course or assignment at the discretion of the instructor. Cheating on any mathematics assignment or exam will result in a minimum sanction of receiving a zero for that assignment or exam. Additional sanctions may be included at the discretion of the instructor.

10.

ADA NOTICE:

Students who have a documented disability may be eligible to receive accommodations for this class. Please contact the Disabilities Resources Center at 549-3446 for further information.

1.	COURSE TITLE				Calculus III
	PREFIX/NUMBER:				MAT 203	Credit Hours:	4
2.	PREREQUISITES:				Successful completion of MAT 202 with a C or better
3.	RESOURCES NEEDED:
	TEXT:				Calculus, 7/e, James Stewart ISBN: 9780538497817
	SUPPLIES:				Paper, pencil, scientific calculator
4.	COURSE DESCRIPTION:				Completes the traditional subject matter of Calculus. Topics include vectors, vector-valued functions, and multivariable calculus including partial derivatives, multiple integrals, line integrals, and application.
5.	STANDARD COMPETENCIES:
	A.	Solve problems involving curves defined parametrically which involves slope and are.
	B.	Demonstrate vector arithmetic.
	C.	Describe the difference between scalars and vectors geometrically and algebraically.
	D.	Demonstrate the ability to work with vector valued functions. This includes limits, continuity, derivatives, and integrals.
	E.	Solve problems involving velocity and acceleration.
	F.	Solve problems involving unit tangent and unit perpendicular vector, the unit binomial vector, curvature and tangential and normal components of acceleration both in two space and three space.
	G.	Demonstrate the ability to graph in three dimensions, and know the formulas of basic three dimensional objects such as spheres and planes.
	H.	Work problems involving the dot and cross product.
	I.	Demonstrate an understanding of the interpretation of these operations.
	J.	Work problems of the line in three space both symmetrically and parametrically.
	K.	Identify the six basic different surfaces in three dimensions. These surfaces are the ellipsoid, hyperboloid of one and two sheets, elliptic paraboloid, hyperbolic paraboloid, and elliptic cone.
	L.	Relate problems in the rectangular coordinates to the cylindrical coordinates to the spherical coordinates.
	M.	Apply the concept of the partial derivative.
	N.	Understand the concept of differentiability and its relationship to the gradient. This includes working problems involving these concepts.
	O.	Demonstrate an understanding of the directional derivative, level curves and level surfaces.
	P.	Solve problems involving the chain rule for many variables.
	Q.	Demonstrate the ability to work problems involving maxima and minima both with the second partials test and Lagrange’s method.
	R.	Demonstrate the ability to work with the double and triple integral and understand applications. The student will also understand the use of the surface are integral.
	S.	Demonstrate knowledge of vectors fields, the potential function, and the divergence and curl of a vector field.
	T.	Show proficiency with line integral and independence of path.
	U.	Demonstrate ability to do problems involving surface integrals.
	V.	Demonstrate knowledge of the theorems of Green, Gauss, and Stokes and applying the theorems.
	W.	Demonstrate a basic knowledge of linear algebra.
6.	COURSE OUTLINE:
	13.0	Vectors and the geometry of space
		13.1	Three Dimensional Coordinate Systems
		13.2	Vectors
		13.3	The Dot Product
		13.4	The Cross Product
		13.5	Equations of Lines and Planes
		13.6	Cylinders and Quadratic Surfaces
	14.0	Vector Functions
		14.1	Vector Functions and Space Curves
		14.2	Derivatives and Integrals of Vector Functions
		14.3	Arc Length and Curvature
		14.4	Motion in Space: Velocity and Acceleration
	15.0	Partial Derivatives
		15.1	Functions of Several Variables
		15.2	Limits and Continuity
		15.3	Partial Derivatives
		15.4	Tangent Planes and Linear Approximations
		15.5	The Chain Rule
		15.6	Directional Derivatives and Gradient Vector
		15.7	Maximum and Minimum Values
		15.8	Lagrange Multipliers
	16.0	Multiple Integrals
		16.1	Double Integrals Over Rectangles
		16.2	Iterated Integrals
		16.3	Double Integrals Over General Regions
		16.4	Triple Integrals
		16.5	Triple Integrals in Cylindrical Coordinates
		16.6	Triple Integrals in Spherical Coordinates
		16.7	Change of Variables in Multiple Integrals
	17.0	Vector Calculus
		17.1	Vector Fields
		17.2	Line Integrals
		17.3	The Fundamental Theorem for Line Integrals
		17.4	Green’s Theorem
		17.5	Curl and Divergence
		17.6	Parametric Surfaces and Their Areas
		17.7	Surface Integrals
		17.8	Stoke’s Theorem
		17.9	The Convergence Theorem
		17.10	Summary
7.	EVALUATION PROCEDURE:
	Evaluation methods and procedures will be determined by the instructor. These may consist of, but are not limited to, quizzes, assignments, exams, individual and/or group projects.
	Grading Scale: 90 – 100% - A 80 – 89% - B 70 – 79% - C 60 – 69% - D 0 – 59% - F
8.	SPECIAL REMARKS:
	Homework:			Homework will be assigned and evaluated as determined by the instructor.
	Cheating:			If cheating occurs, it will result in academic and possible disciplinary sanctions being taken against the student. The Academic Dishonesty Adjudication Process, as outlined in the Student Handbook, will be followed. Academic sanctions will include receiving a zero for the assignment or exam and any other sanctions determined by the instructor.
	Attendance:			Attendance will be taken and students may be dropped when they have missed 20% of the total class time (12 hours). Missed exams will result in a zero unless prior arrangements have been made.
	Conduct:			Professional and courteous behavior is expected at all times. Disruptive behavior is unacceptable in the classroom and may result in the student’s temporary or permanent removal from the course.
	Assistance:			Help is available outside of the classroom from your instructor, in the Learning Center Math Lab, or the Pro Shop.
9.	ACADEMIC INTEGRITY:
	The very nature of higher education requires that students adhere to accepted standards of academic integrity. Therefore, Pueblo Community College has adopted a policy of academic conduct as described in the Student Handbook. Violation of academic integrity may be defined to include the following: cheating, plagiarism, falsification and fabrication, abuse of academic materials, complicity in academic dishonesty, and personal misrepresentation. It is the student’s responsibility to be aware of the behaviors that constitute academic dishonesty. Sanctions for violating the standards of academic integrity may include warning, probation, suspension, and/or failure of the course or assignment at the discretion of the instructor. Cheating on any mathematics assignment or exam will result in a minimum sanction of receiving a zero for that assignment or exam. Additional sanctions may be included at the discretion of the instructor.
10.	ADA NOTICE:
	Students who have a documented disability may be eligible to receive accommodations for this class. Please contact the Disabilities Resources Center at 549-3446 for further information.