MTH 277-VECTOR CALCULUS
I.
Course Description:
An introduction to vector-valued functions, functions of several variables, partial differentiation,
multiple integrals and vector analysis.
II.
Prerequisites:
MTH 173-174 ( Calculus with Analytic Geometry I-II) or equivalent.
III.
Introduction:
This course is designed to introduce the student to the concepts of vector-valued functions,
functions of several variables, partial derivatives, multiple integrals, and vector analysis.
IV. Instructional Materials:
Textbook:
Calculus, Eighth Edition, by Larson, Hostetler, and Edwards; 2006;
ISBN 0-618-50298-X; Houghton Mifflin Company
Supplementary:
Study and Solutions Guide, Volumes I and II, by Bruce H. Edwards;
ISBN 0-618-52791-5 & 0-618-52792-3
Calculus, 8E, Videotapes by Dana Mosely
Website (college.hmco.com)
Scientific Calculator
V. References:
Given as necessary.
2
Disability Services Policy:
Reasonable accommodations will be made for students with disabilities provided those students
have registered with the Office of Disability Services. Present your teacher with the
documentation.
TIDEWATER COMMUNITY COLLEGE
CLASSROOM AND LABORATORY
EMERGENCY PROCEDURES FOR FACULTY
In the event of a bomb threat, tornado, or fire, students and staff may be
asked to evacuate the building or move to a secure location within the
building.Evacuation routes for movement to an external location or to a
shelter within the building are posted at the front of the room.Students
should review the maps and make sure that the exit route and assembly
location for the building are clearly understood.If you have a disability
that may require assistance during an evacuation, please let your faculty
know at the end of the first class.
3
VI. Course Objectives:
The student must master the following concepts:
A.
Vectors and the geometry of space (Ch 11)
11.1*
11.2*
11.3*
11.4*
11.5
11.6
11.7
B.
Vector-valued functions (Ch 12)
12.1
12.2
12.3
12.4
12.5
C.
Vectors in the plane
Space coordinates and vectors in space
The dot product of two vectors
The cross product of two vectors in space
Lines and planes in space
Surfaces in space
Cylindrical and spherical coordinates
Vector-valued functions
Differentiation and integration of vector-valued functions
Velocity and acceleration
Tangent vectors and normal vectors
Arc length and curvature
Functions of several variables (Ch 13)
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.10
Introduction to functions of several variables
Limits and continuity
Partial derivatives
Differentials
Chain rules for functions of several variables
Directional derivatives and gradients
Tangent planes and normal lines
Extrema of functions of two variables
Lagrange multipliers
D. Multiple integration (Ch 14)
14.1
14.2
14.3
14.5
14.6
14.7
14.8
Iterated integrals and area in the plane
Double integrals and volume
Change of variables: polar coordinates
Surface area
Triple integrals and applications
Triple integrals in cylindrical and spherical coordinates
Change of variables: Jacobians
* Sections marked with an asterisk may not be included by all instructors.
4
E.
Vector Analysis (Ch 15)
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
VII.
Vector Fields
Line integrals
Conservative vector fields and independence of path
Green's theorem
Parametric surfaces
Surface integrals
Divergence theorem
Stoke's theorem
Suggested weekly outline for Fall and Spring semesters:
Week 1:
Week 2:
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9:
Week 10:
Week 11:
Week 12:
Week 13:
Week 14:
Week 15:
VIII.
11.1*,
11.4*,
11.7,
12.3,
13.1,
13.4,
13.7,
14.1,
14.3,
14.6,
14.8,
15.2,
15.4,
15.6,
15.8
11.2*,
11.5,
12.1,
12.4,
13.2,
13.5,
13.8,
14.2
14.5
14.7
15.1
15.3
15.5
15.7
11.3*
11.6
12.2
12.5
13.3
13.6
13.10
Suggested weekly outline for Summer semester:
Week 1:
Week 2:
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9:
Week 10:
11.1*,
11.5,
12.2,
13.1,
13.5,
13.10,
14.5,
15.1,
15.4,
15.7,
11.2*,
11.6,
12.3,
13.2,
13.6
14.1,
14.6,
15.2,
15.5,
15.8
11.3*,
11.7,
12.4,
13.3,
13.7,
14.2,
14.7,
15.3
15.6
11.4*
12.1
12.5
13.4
13.8,
14.3,
14.8
* Sections marked with an asterisk may not be included by all instructors.