Math 173-Calculus with Analytic Geometry
I. Course Description:
A modern, unified course in analytic geometry and calculus
including functions, limits,
derivatives, differentials,indefinite integrals, definite integrals, and applications.
II. Prerequisites:
A satisfactory score on appropriate mathematics proficiency
examinations and four units of high
school mathematics including two units of algebra, one of
geometry, and one-half unit of
trigonometry or equivalent.
Math 166 or the sequence Math 163-164 satisfies these prerequisites.
III. Introduction:
This course is designed to serve as an introduction to
analytic geometry and calculus for students
majoring in mathematics,
engineering, computer science, and science.
IV. Instructional Materials:
Textbook: Calculus,
Eighth Edition, by Larson, Hostetler, and Edwards; 2006;
ISBN
0-618-50298-X; Houghton Mifflin Company
Supplementary: Study
and Solutions Guide, Volumes I and II,
by Bruce H. Edwards
ISBN
0-618-52791-5 & 0-618-52792-3
Calculus, 8E, Videotapes by Dana Mosely
Website
(college.hmco.com)
Scientific
Calculator
VI. Course Objectives:
The student must master the following concepts:
A. Limits and their
properties (Ch 1)
1.1 A preview of
calculus
1.2 Finding
limits graphically and numerically
1.3 Evaluating
limits analytically
1.4 Continuity
and one-sided limits
1.5 Infinite limits
B. Differentiation
(Ch 2)
2.1 The derivative
and the tangent line problem
2.2 Basic
differentiation rules and rates of change
2.3 The product
and quotient rules and higher-order derivatives
2.4 The chain
rule
2.5 Implicit
differentiation
2.6 Related rates
C. Applications of
differentiation (Ch 3)
3.1 Extrema on an
interval
3.2 Rolle's
theorem and the mean value theorem
3.3 Increasing
and decreasing functions and the first derivative test
3.4 Concavity and
the second derivative test
3.5 Limits at
infinity
3.6 A summary of
curve sketching
3.7 Optimization
problems
3.8
3.9 Differentials
D. Integration (Ch
4)
4.1
Antiderivatives and indefinite integration
4.2 Area
4.3 Riemann sums and
definite integrals
4.4 The
fundamental theorem of calculus
4.5 Integration
by substitution
4.6 Numerical
integration
E. Logarithmic,
exponential and other transcendental functions (Ch 5)
5.1 The natural
logarithmic function: differentiation
5.2 The natural
logarithmic function: integration
5.3 Inverse
functions
5.4 Exponential
functions: differentiation and integration
5.5 Bases other
than e and applications
5.6 Inverse
trigonometric functions: differentiation
5.7 Inverse
trigonometric functions: integration
5.8 Hyperbolic
functions
F. Applications of
integration (Ch 7)
7.1 Area of a
region between two curves
7.2 Volume: the
disc method
7.3 Volume: the shell method
7.4 Arc length and surfaces of revolution
VII. Suggested weekly outline for Fall and
Spring semesters:
Week 1: 1.1, 1.2,
1.3
Week 2: 1.4, 1.5,
T1
Week 3: 2.1, 2.2,
2.3
Week 4: 2.4, 2.5,
2.6, T2
Week 5: 3.1, 3.2,
3.3
Week 6: 3.4, 3.5,
3.6
Week 7: 3.7, 3.8,
3.9, T3
Week 8: 4.1, 4.2,
4.3
Week 9: 4.4, 4.5,
4.6, T4
Week 10: 5.1, 5.2
Week 11: 5.3, 5.4
Week 12: 5.5, 5.6
Week 13: 5.7, 5.8,
T5
Week 14: 7.1, 7.2
Week 15: 7.3, 7.4,
T6