MATH 140 (Calculus I)
Updated September 30, 2005
| DESCRIPTION |
Introduction to calculus, including functions, limits,
continuity,
derivatives and applications of the derivative, sketching of graphs of
functions, introduction to definite and indefinite integrals, and
calculation
of area. The course is especially recommended for science and
mathematics
majors. Credit will be granted for only one of the following:
MATH
140 or MATH 220. |
| PREREQUISITES |
Permission of the department based on 3 1/2 years of college
preparatory
mathematics (including trigonometry) and either a satisfactory score on
the mathematics placement examination or completion of Math 115 with a
grade of C or better. |
| TOPICS |
Chapter I. Functions
Brief review of major topics in precalculus
Chapter 2. Limits and Continuity
Limits, one sided and infinite limits
Tangent lines and velocity
Continuity, the Intermediate Value Theorem, and the
Bisection Method
Chapter 3. Derivatives
Derivatives, including the Chain Rule
Implicit differentiation
Related rates
Approximation of derivatives and the Newton-Raphson
method
Chapter 4. Applications of the Derivative
Maximum and minimum values, and the Maximum-Minimum
Theorem
Mean Value Theorem and its applications
Exponential growth and decay
Analysis of graphs of functions
Chapter 5. The Integral
Definite and indefinite integrals
The Fundamental Theorem of Calculus
Integration by substitution
Natural logarithmic function
Area
Chapter 10. Curves in the plane
Basic properties of parabolas, ellipses and
hyperbolas
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| TEXT |
Text(s)
typically used in this course.
Note: The course covers essentially all
of Chapters 2-5 of the 6th Edition of Ellis and Gulick, as well as
Section 10.3 and a very brief review of
precalculus from Chapter 1.
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