SELF-PACED COURSE: FUNDAMENTALS OF ENGINEERING ANALYSIS
Course Director:
John Cavanaugh
Associate Professor
Bioengineering Center
818 W. Hancock
Phone: 313-577-3916
Fax: 313-577-8333
E-mail: cavanau@rrb.eng.wayne.edu
Web site: ttb.eng.wayne.edu/~cavanau/jmcweb.html
The syllabus and scheduled meetings will be placed on the web site.
Course Objective:
The purpose of this course is to cover the material in a college calculus sequence considered necessary by our program faculty to pursue a graduate degree in Biomedical Engineering.
Grading:
The course consists of four one credit units. Each unit will have one exam to test mastery of the material in that unit. An exam score of 75% or higher is necessary to pass a unit. You will have multiple chances to pass a unit and must pass that unit before taking the exam for the next unit. The grading will be as follows for each exam:
75-79 B-
80-84 B
84-88 B+
89-93 A-
94-100 A
Organization:
THE FOUR ONE CREDIT UNITS WILL COVER MATERIAL TAKEN DIRECTLY FROM THE CALCULUS SERIES VIDEOS BY Harold D. Shane, Professor of Mathematics at Baruch College, City University of New York.
Two sets of videos will be available. The sample
problems from the videos will be handed out to all students. You can elect
to study the material without use of the videos if you so choose. The exams
will be of the same format as the sample problems.
We will have 3-4 lectures covering engineering applications of differentiation and integration.
There is also tutoring available at the Math Tutoring Center
1198 Faculty Administration Building (FAB)
Phone 313-577-3195
Content:
UNIT #1 (Covering Calculus 1 video in its entirety)
EQUATIONS OF STRAIGHT LINES
FUNCTIONS
LIMITS
DERIVATIVES
GRAPHING
APPLICATIONS
UNIT #2 (Covering Calculus 2 video in its entirety)
SIMPLE INTEGRALS
APPLICATIONS OF INTEGRATION
LOGARITHMIC AND EXPONENTIAL FUNCTIONS
TRIGONOMETRIC FUNCTIONS
INVERSE TRIGONOMETRIC FUNCTIONS
METHODS OF INTEGRATION
UNIT #3
Note: This unit covers Parts 1, 2, and 5 of the Calculus 3 video. Parts 3 and 4 of the video are not required.
MISC APPLICATIONS:
Arc length
Area of a surface of revolution
Moments and centroids
Moments of inertia
Work
Fluid pressure
POLAR COORDINATES:
the polar coordinate system
SEQUENCES
UNIT #4 (Covering Calculus 4 video in its entirety except as noted below)
INFINITE SERIES
Evaluating a series
Testing for convergence and divergence with several tests
Power series
Taylor polynomial and series
Maclaurin polynomial and Maclaurin series not required.
VECTORS
In a plane
In space
Multiplication
Lines and planes in a space not required.
FUNCTIONS OF SEVERAL VARIABLES
Partial Derivatives
MULTIPLE INTEGRATION
Double Integrals
Triple Integrals