Course alpha,
number, title
MTH 133—Calculus II
Required or elective
Required
Course (catalog)
description
Application of the integral and methods of integration, improper integrals, polar coordinates
and parametric curves, sequences and series, power series.
Prerequisite(s)
(MTH 132) or (MTH 152H)
Textbook(s)
and/or other
required material
Thomas’ Calculus Alternate Edition George B. Thomas Jr. and Ross L. Finney, Addison
Wesley, (2003)
Class/Lab schedule:
4 credit hours [3 lectures 1 recitation/week]
Topics covered
1.Volumes of solids, length of curves and work
2. Natural logarithm and its derivative
3. Inverse Function Theorem
4. Exponential function, its derivative and integral
5. Growth and decay
6. L’Hôpital’s rule and relative rates of growth
7. Inverse trigonometric functions and their derivatives
8. Hyperbolic functions
9. First order separable differential equations
10. Integration by parts
11. Partial fractions
12. Trigonometric substitutions
13. Use of tables and computers to find integrals
14. Improper integrals
15. Limits of sequences
16. Infinite series and the Geometric Series Theorem
17. The Integral Test
18. Comparison Tests
19. The Ratio Test and Absolute convergence
20. Power series and Taylor series
21. Binomial Series Theorem
22. Calculus of parametric equations
23. Polar coordinates and graphing polar equations
24. Integration in polar coordinates
Course learning
objectives
For the student to be able to:
1. understand applications of the definite integral
2. compute derivatives and integrals involving logarithmic, exponential and inverse
trigonometric functions
3. begin to understand differential equations as mathematical modeling
4. use advanced techniques of integration
5. compute limits of sequences
6. determine if an infinite series converges or diverges
7. express known functions as power series
8, express unknown functions as power series and find the radius of convergence of the
series
9. express curves as parametric equations and use the equations to compute properties of the
curve
10. Plot graphs of polar equations and compute areas of regions bounded by such graphs
Relationship of
course to XXX
program
The following measurement standard is used to evaluate the relationship between the course
outcomes and the educational-program outcomes:
3 = Strong Emphasis, 2 = Some Emphasis, 1 = Little or No Emphasis.
1
outcomes
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
an ability to apply knowledge of mathematics, science, and engineering—3
an ability to design and conduct experiments, as well as to analyze and interpret data—1
an ability to design a system, component, or process to meet desired needs—1
an ability to function on multi-disciplinary teams—1
an ability to identify, formulate, and solve engineering problems—1
an understanding of professional and ethical responsibility—1
an ability to communicate effectively—1
the broad education necessary to understand the impact of engineering solutions in a
global/societal context—1
a recognition of the need for and the ability to engage in life-long learning—1
a knowledge of contemporary issues—1
an ability to use the techniques, skills, and modern engineering tools necessary for
engineering practice—2
design, build, and test in mechanical systems area—1
design, build, and test in thermal/fluids area—1
application of advanced mathematics—1
capstone design experience—1
Contribution to
professional
component:
100% Mathematics and Basic Science
Person(s) who
prepared this
description
Professor Clifford E. Weil
Date of
Preparation
January 22, 2004
2