Course alpha, number, title
MTH 132 Calculus I
Required or elective
Required
Course (catalog) description
Limits, continuous functions, derivatives and their applications, Integrals and the fundamental theorem of calculus
Prerequisite(s)
(MTH 103 and MTH 114) or (MTH 116) or by Math Placement Exam score.
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:
3 credit hours [3 lectures/week]
Topics covered
1. Rate of change
2. Limits and rules for finding limits
3. Target vales and Formal definitions of limit
4. Extensions of the limit concept
5. Continuity
6. The derivative and rules of differentiation
7. Rate of change
8. Derivatives of trigonometric functions
9. The Chair Rule
10. Implicit differentiation and rational exponents
11. Related rates of change
12. Extreme values and the Mean Value Theorem
13. The first derivative test for local extreme values
14. Using the first and second derivative to graph
15. Limits at + and – infinity, asymptotes and dominate terms
16. Optimization
17. Linear approximation and Newton’s method
18. Indefinite integrals, simple differential equations and initial value problems
19. Integration by substitution
20. Summation and the Riemann integral
21. The Fundamental theorem of calculus.
22. Substitution
23. Areas between curves
Course learning
objectives
For the student to be able to:
1. Compute limits, derivatives, some indefinite and definite integrals
2. Apply derivatives to find rates of change, graph functions, and solve optimization prolems
3. Use definite integrals to solve simple initial value problems and find simple areas.
4. Acquire more mathematical maturity
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Relationship of
course to Mechanical
Engineering
program outcomes
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.
(a) an ability to apply knowledge of mathematics, science, and engineering—3
(b) an ability to design and conduct experiments, as well as to analyze and interpret data—1
(c) an ability to design a system, component, or process to meet desired needs—1
(d) an ability to function on multi-disciplinary teams—1
(e) an ability to identify, formulate, and solve engineering problems—1
(f) an understanding of professional and ethical responsibility—1
(g) an ability to communicate effectively—1
(h) the broad education necessary to understand the impact of engineering solutions in a
global/societal context—1
(i) a recognition of the need for and the ability to engage in life-long learning—1
(j) a knowledge of contemporary issues—1
(k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice—1
(l) design, build, and test in mechanical systems area—1
(m) design, build, and test in thermal/fluids area—1
(n) application of advanced mathematics—1
(o) capstone design experience—1
Contribution to pro- 100% Mathematics and Basic Science
fessional component:
Person(s) who prepared this description
Professor Clifford E. Weil
Date of
Preparation
January 22, 2004
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