THE COLLEGE OF THE BAHAMAS
Course Outline
Title: Calculus III
Abbreviation and Number: MATH281
AB Paper No.: 13-90
School: Mathematics, Physics and Technology
Department: Mathematics
Credits: 3
Course Sequence: ( ) Fall
( X ) Spring
(
( 3 ) Lecture
( ) Seminar
( ) Laboratory
(
Hours Per Week:
( ) Other
Pre-requisite(s): MATH271 or permission of Chair/Instructor
Co-requisite(s): None
) Fall and Spring
) Studio
(
) Kitchen
COURSE DESCRIPTION
This is the third in a three-course series in calculus. Students, with the aid of technology, study vector-valued and
several variable functions, partial differentiation and multiple integral.
SPECIFIC OBJECTIVES
Upon successful completion of this course, students will be able to
1) compute derivatives of vector-valued functions;
2) calculate integrals of vector-valued functions;
3) determine limits of functions of several variables;
4) analyze continuity and differentiability of functions of several variables;
5) apply Lagrange Multipliers to solve optimization problems;
6) evaluate double and triple integrals;
7) evaluate line and surface integrals;
8) apply Green’s, Stokes’ and Divergence Theorems to vector analysis; and
9) use a graphing calculator to analyze functions.
COURSE CONTENT
I.
Vector-Valued Functions
A. Arc Length in R3
B. Motion in Space
i. Position
ii. Velocity and Acceleration
C. Curvature
D. Tangent and Normal Vectors
E. Tangential and Normal Component of Acceleration
F. Parametric Surfaces
II.
Functions of Several Variables and Partial Differentiation
A. Limits and Continuity
B. Partial Derivatives
C. Tangent Planes and Linear Approximations
D. Product and Quotient Rules
E. Chain Rule
F. Implicit Differentiation
G. Gradient and Directional Derivative
H. Extrema
The College of The Bahamas
AB Paper No.: 13-90
Course Outline
Title: Calculus III
Abbreviation and Number: MATH281
I.
Optimization
i. Constrained
ii. Lagrange Multipliers
III.
Multiple Integrals
A. Double
i. Rectangular Coordinates
ii. Polar Coordinates
iii. Area, Volume and Centre of Mass
iv. Surface Area
B. Triple
i. Rectangular Coordinates
ii. Cylindrical Coordinates
iii. Spherical Coordinates
IV.
Vector Calculus
A. Vector Fields
B. Line Integrals
C. Independence of Path
D. Conservative Vector Fields
E. Green’s Theorem
F. Curl and Divergence
G. Surface Integrals
H. Divergence Theorem
I. Stokes’ Theorem
ASSESSMENT
Assignments.…………………….……. 15%
Quizzes.…………….………………….. 15%
In-Class Tests…….…………………… 30%
Final Examination.…………………….. 40%
Total……………………………………100%
REQUIRED RESOURCES
MyMathLab Access Code
TI – 83/84 Calculator
REQUIRED TEXT
Briggs, W., Cochran, L. (2011). Calculus: Early transcendentals (1st ed.). New Jersey: Upper Saddle River, Pearson.
SUPPLEMENTARY READINGS/MATERIALS
Hass, J., Wier, M., & Thomas, G. (2009). University calculus: Early transcendentals (2nd ed.). New Jersey: Upper
Saddle River, Pearson.
Larson, R., & Edwards, B. (2011). Calculus: Early transcendental functions (5th ed.). Boston: Brooks/Cole.
Smith, R. & Minton, R. (2012). Calculus: Early transcendental functions (4th ed.). New York: The McGraw-Hill
Companies.
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The College of The Bahamas
AB Paper No.: 13-90
Course Outline
Title: Calculus III
Abbreviation and Number: MATH281
JOURNALS
Educational Studies in Mathematics
For the Learning of Mathematics
International Journal of Mathematical Education in Science & Technology
Journal of Fractional Calculus and Applications
Mathematics in School
Mathematical Spectrum
WEBSITES
www.mymathlab.com (MyMathLab)
www.mathforum.org (Math Forum)
www.sosmath.com (Sosmath)
www.karlscalculus.org (Calculus Tutor)
www.analyzemath.com (Mathematics Tutorials)
www.tutorial.math.lamar.edu (Paul’s Online Calculus Notes)
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