MATH 244 - MATHEMATICS FOR ENGINEERING & SCIENCE V
SECTION: 002 QUARTER: Winter 2004 TIME: 11:00-12:15
INSTRUCTOR: KANNO
CLASSROOM: GTM 317
OFFICE NUMBER: GTM 350
OFFICE HOURS: MWF 8:30-9:30, 12:30-1:30 TR 10:00-12:00
PHONE: 257-3329
E-MAIL: jkanno@LaTech.edu
WEB: www.latech.edu/~jkanno
PREREQUISITE: MATH 243
COREQUISITES: ENGR 221
COURSE GOALS: The student will become proficient in partial differentiation, multiple integration, and vector
calculus. This proficiency will be demonstrated by satisfactorily completing a series of exams and homework
assignments.
TEXTBOOKS: Calculus: Concepts and Contexts, by James Stewart
COURSE OUTLINE AND OBJECTIVES: Attached.
ATTENDANCE REGULATIONS: Class attendance is regarded as an obligation as well as a privilege. All
students are expected to attend regularly and punctually. Failure to do so may jeopardize a student’s scholastic
standing and may lead to suspension from the university.
HOMEWORK POLICY: Homework assignments will be made throughout the quarter. All homework assigned
during a particular class period will be due at the beginning of the next class period unless otherwise noted.
Homework assignments will not be accepted late. To take into account days when a student might be sick, the
two lowest homework scores will be dropped when computing the homework average.
GRAPHING CALCULATOR/COMPUTER ALGEBRA SYSTEM: A graphing calculator that does at least as
much as the TI-82 is required for the course. Its use on exams will be at the discretion of the instructor. The student
also needs to have access to Mathcad.
EXAMINATIONS: There will be three topical exams and a comprehensive final exam. If a student has to miss an
exam, he/she must notify the instructor prior to the exam either in person or by phone. An unexcused absence from
an exam will result in a zero on that exam. The exam dates are Wed. Jan. 7; Fri. Jan. 30; Mon. Feb. 16, and
Mon. Mar 1.
GRADE DETERMINATION POLICY: The grading scale will be: A = 90% - 100%; B = 80% - 89%; C = 70% 79%; D = 60% - 69%; F = 0% - 59%. The course grade will be calculated as follows:
Exams I-III
Homework Avg.
Final
Total
60%
10%
30%
100%
(20% each)
STUDENTS NEEDING SPECIAL ACCOMODATIONS & RETENTION OF GRADED MATERIALS:
Students needing testing or classroom accommodations based on a disability should discuss the need with the
instructor during the first week of class. In the event of a question regarding an exam grade or final grade, it will be
the responsibility of the student to retain and present graded materials which have been returned for student
possession.
Schedule of Classes MATH 244, Winter 2004
Day
W. 12/03
F. 12/05
M. 12/08
W. 12/10
F. 12/12
Topic
Homework
10.1 Vector Functions
10.2 Dervis. & Ints. Of Vector Functions
10.3 Arc Length & Curvature
10.3 Arc Length & Curvature
10.4 Motion in Space
M. 12/15
11.3 Partial Derivatives
p.710 # 1,4,5-10,12,13,19,21,24,26,29,32
p.716 # 2,3,7,10,12,17,22,23,29,30,31,43
p.723 # 1,3,6,7,10
p.723 # 13,17,24,27,30,49
p.733 # 1,4,7,12,13,16,17,25,27,29,32,34,35
p.776#2,3,7,8,11,17,22,23,24,33,38,42,47,51,53,56,60,62,
63,69,73
F. 12/19
M. 01/05/04
W. 01/07
F. 01/09
M. 01/12
11.4 Tangent Planes(Differentiability),
11.5 Chain Rule
11.6 Directional Derivatives
13.1 Vector Fields
Exam 1
13.2 Line Integrals
13.3 Fundamental Thm. For Line Ints
W. 01/14
11.4 Tan. Planes and Linear Approx.
F.
W.
F.
M.
W.
F.
M.
W.
F.
M.
W.
F.
M.
W.
F.
F.
10.5 Parametric Surfaces
12.6 Surface Area
13.4 Green's Theorem
13.5 Curl and Divergence.
13.6 Surface Integrals
Exam 2
13.6 Surface Integrals
13.7 Stokes' Theorem
12.7 Triple Integrals
12.8 Triple Integrals in Cylind. and Sphe.
12.9 Change of Vars. For Mult. Int.
13.8 Divergence Theorem
Exam 3
11.7 Maximum and Minimum Values
11.8 Lagrange Multiples
Review
W. 12/17
01/16
01/21
01/23
01/26
01/28
01/30
02/02
02/04
02/06
02/09
02/11
02/13
02/16
02/18
02/20
02/27
M. 03/01
Cumulative Final
* The text is Calculus, Concepts & Contexts by J. Stewart.
Additional problems will be assigned when needed.
p.796 # 2,5,8,10,13,17,18,31,32,34,39, 43
p.808 # 1,4,7,8,12,13,16,19,26,29,32
p.922 # 4,5,11-14,15-18,23,24,25,27, 29-33
p.934 # 13-17,19,22,24,28,34, 35,3,11
p.943 # 1,5,8,11,13,14,17,19,23,29,34
p.788 # 1,4,6,7,9,12,13,28,31,35,40
p.808 # 35,44,46
p.740 # 2,3,9,11-16,17,18,21,24,28, 30,32
p.881 # 2,3,6,7,8,15,16,19,22,26
p.951 # 1,4,9,10,15,17,19,20
p.958 # 2,5-8,12,13,15,17,20,28,33, 34
p.970 # 1,5,8,15,19,21,22,27,33,39,40
p.976 # 1,3,4,7,8,14,
p.890 # 2,3,6,8,11,17,25,30, 32,34,35,41,42
p.898 # 1,4,6,7,11,14,19,22,29,30,31,33
p.909 # 2-5,7,9,11,14,19,21
p.983 # 1-4,9,14,17,27,28
p.818 # 1,3-6,11,16,20,23,26, 31,40,42,43
p.827 # 1,3,4,9,16,19,24,36,39
Objectives for MATH 244, Engineering Mathematics V
By the end of the course the student will be able to
1. Calculate partial derivatives and gradients.
2. Apply the multivariate chain rule to calculate derivatives.
3. Interpret surface and contour plots to estimate partial derivatives, paths of steepest ascent or descent,
locations of extrema etc.
4. Classify a function of several variables as continuous, differentiable or neither at a point.
5. Calculate and classify the critical points of a function of several variables.
6. Model and solve constrained optimization problems using Lagrange multipliers.
7. Model a given curve as a parametric function of one variable.
8. Calculate the length of a parametric curve, the curvature at a point.
9. Calculate the velocity and the acceleration of a particle on a given path.
10. Determine which part of the acceleration of a particle increases the particle’s kinetic energy.
11. Calculate the limit of a parametric curve at a point.
12. Model a given surface or region as a parametric surface.
13. Calculate the area of a given parametric surface.
14. Calculate a double integral using the change-of-variable formula.
15. Interpret a vector field plot to estimate the value of a line integral in a vector field from a sketch of the
vector field and the path.
16. Calculate line integrals of scalar functions and of vector fields.
17. Determine if a given vector field is conservative.
18. Calculate the potential function of a conservative vector field.
19. Apply the fundamental theorem for line integrals to Calculate line integrals of conservative vector
fields.
20. Calculate the surface integral of scalar functions and of vector fields.
21. Apply Stokes’ Theorem to calculate surface integrals.
22. Apply Gauss’ Theorem (the Divergence Theorem) to calculate integrals over solids.
These topics can be found in Concepts: Sections 10.1-10.5, 11.3-11.8, 12.6-12.9, and 13.1-13.8.