COURSE OUTLINE
MAT 141 ANALYTIC GEOMETRY AND CALCULUS II
4.0 Credit Hours
COURSE
DESCRIPTION: This course
includes the following topics: continuation
of calculus of one variable, including analytic geometry, techniques of
integration, volumes by integration and other
applications; infinite series, including
TEXT: CALCULUS, Eighth Edition by
Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards Houghton Mifflin, 2006
PREREQUISITE: MAT 140
EQUIPMENT: Graphing Calculator, preferably TI-83 or
TI-83+
GRADING
SCALE:
A 90 – 100 B 80 – 89 C 70 – 79 D 60 – 69 F Below 60
MATHEMATICS
DEPARTMENT ATTENDANCE REQUIREMENTS
DEFINITIONS:
ABSENCE - Failure to be present for a scheduled
meeting of the class or arriving for the class more than ten minutes after the
scheduled time for the class to begin.
TARDY --- Arrival to class after the instructor
has called the roll and before ten minutes past the time scheduled for the
class to begin.
I. Absences are counted from the first day of
classes.
II. Five absences are allowed for a class that
meets three times per week and three absences are allowed for a class that
meets two times per week.
III. Three tardies are
considered as one absence. The student must meet with the instructor at the end
of the class to which he has been late to have the absence changed to a tardy.
IV. There are no "excused" absences; all
absences are counted, regardless of the reason for the absence.
V. A student missing class time by leaving early
will also be counted absent.
Please note: You are responsible for all material and announcements presented,
whether you are present or absent.
Mathematics
Department Airport: 822-3357 Beltline:
738-7689 Revised 2/27/2007
MAT 141 COURSE OBJECTIVES
Students should be able to:
1. Calculate areas, volumes, and arc
lengths using integration.
2. Integrate functions using
techniques, which include: integration by parts, trigonometric integrals,
trigonometric substitution, partial fractions, and a table of integrals.
3. Establish power series
representations of functions and use the appropriate convergence test to study
the behavior of series.
4. Graph and write equations for
conic sections.
5. Represent functions in polar
coordinates.
6. Use derivatives in finding
tangents and in curve sketching in polar coordinates.
7. Find area and arc length for polar
curves.
8. Solve problems by identifying
what information is available and relevant to the problem.
9. Solve problems by selecting or
developing appropriate procedures and relationships.
10. Solve problems by correctly
applying the methods selected to the information available.
11. Solve problems by verifying the
validity and appropriateness of the solution.
MAT 141 ANALYTIC GEOMETRY AND CALCULUS II
Note: This outline is given for the
regular Fall/Spring fourteen week semesters. The same material is covered in
the summer term and the sessions classes, but in the
appropriate fewer number of weeks: ten weeks for summer term, seven weeks for
fall and spring sessions classes, and five weeks for summer session classes.
|
WEEK |
TOPIC |
SECTION |
|
1 |
Logarithmic, Exponential, and Other
Transcendental Functions |
|
|
|
Inverse Trigonometric Functions:
Differentiation |
5.6 |
|
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Inverse Trigonometric Functions:
Integrations |
5.7 |
|
|
Hyperbolic Functions |
5.8 |
|
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|
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|
2 |
Differential Equations |
|
|
|
Slope Fields and Euler’s Method |
6.1 |
|
|
Differential Equations: Growth and decay |
6.2 |
|
|
Separation of Variable and the Logistic
Equation |
6.3 |
|
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|
|
3 |
First-Order Linear Differential Equations |
6.4 |
|
|
TEST 1 |
|
|
|
Integration Techniques, L’Hôpital’s
Rule, and Improper Integrals |
|
|
|
Basic Integration Techniques |
8.1 |
|
|
|
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|
4 |
Integration by Parts |
8.2 |
|
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Trigonometric Integrals |
8.3 |
|
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Trigonometric Substitution |
8.4 |
|
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|
5 |
Partial Fractions |
8.5 |
|
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Integration by Tables and Other
Integration Techniques |
8.6 |
|
|
Indeterminate Forms and L’Hôpital’s Rule |
8.7 |
|
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|
6 |
Improper Integrals |
|
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TEST 2 |
|
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7 |
Infinite Series |
|
|
|
Sequences |
9.1 |
|
|
Series and Convergence |
9.2 |
|
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The Integral test and p-Series |
9.3 |
|
|
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|
8 |
Comparisons of Series |
9.4 |
|
|
Alternating Series |
9.5 |
|
|
The Ratio and Root Tests |
9.6 |
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|
9 |
TEST 3 |
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9.7 |
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10 |
Power Series |
9.8 |
|
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Representation of Functions by Power
Series |
9.9 |
|
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Taylor and Maclaurin
Series |
9.10 |
|
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|
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|
11 |
Conics, Parametric Equations, and Polar
Coordinates |
|
|
|
Conics and Calculus |
10.1 |
|
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TEST 4 |
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|
12 |
Plane Curves and Parametric Equations |
10.2 |
|
|
Parametric Equations and Calculus |
10.3 |
|
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Polar Coordinates and Polar Graphs |
10.4 |
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|
13 |
Area and Arc Length in Polar Coordinates |
10.5 |
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Polar Equations for Conics and Kepler’s Lawa |
10.6 |
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14 |
TEST 5 |
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Comprehensive
Final Examination |
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