MAT 112 Calculus 2
TENTATIVE COURSE OUTLINE
Catalog Description:
A
continuation of MAT111. This is the second course in the standard
integrated calculus sequence. Topics
include definitions of the indefinite and definite integrals of algebraic,
logarithmic, exponential, and trigonometric functions, techniques and
applications of integration, improper integrals; infinite sequences and series;
analytic geometry and polar coordinates.
Prerequisites: MAT111 with minimum C grade
Required Materials:
Text: Calculus
Howard
Anton, 7^{th} edition
A graphing
calculator is required. TI – 83 or 86 will be used by
the instructor and is therefore strongly recommended for the student
Instructor: Richard Porter
Email:
porterr@mcc.ecu
Web Page:
http://www.mcc.edu/~porterr
Office: LA
114 Extension
3826
Office Hours: See Web Page
Grading:
Quizzes and Homework: 40%
Midterm: 20%
Final: 40%
Grade
Scale:
90%100%........A
80%89.5%.......B
70%79.5%.......C
60%69.5%.......D
<59.5%.............F
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6.1,6.2 
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6.2,6.3 
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6.3,6.4 
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6.4,6.5 
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6.6,6.7 
6 

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6.8,6.9 
7 

M 
Review 
8 

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7.17.3 
9 

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7.47.6 
10 

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7.7,7.8 
11 

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8.1,8.2 
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8.3,8.4 
13 

M 
8.5 
14 

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8.6 
15 

M 
8.7,8.8 
16 

W 
Review 
17 

M 
Midterm 
18 

W 
10.1,10.2 
19 

M 
10.3 
20 

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10.4,10.5 
21 

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10.6 
22 

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10.7 
23 

M 
10.8 
24 

W 
10.9 
25 

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10.1 
26 

W 
Review 
27 

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11.1,11.2 
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11.3,11.4 
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11.5,11.6 
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W 
Review 
UNIT I (Chapter 6) Integration
Classes 16
1. Associate the process of integration
with finding the area under a curve.
2. Find the infinite integral for
polynomial, trigonometric, logarithmic and exponential function by reversing
the derivative formulas.
3. Use a u – substitution to find an indefinite
integral and when given conditions evaluate the constant of integration.
4.
Interpret
and use the properties of sigma notation to evaluate sigma notated problems.
5.
Use the
left end point, right end point, and mid point approximations and the
properties of limit to determine exact areas under a curve.
6.
Use the
theorems and properties to evaluate and rewrite definite integrals.
7.
State
and use the First Fundamental Theorem of Calculus, the Mean Value Theorem for
Integrals, and the Second Fundamental Theorem of Calculus.
8.
Use
integration techniques to determine velocity and position functions when given
an acceleration function, and to find the average value of a continuous
function over a closed interval.
9.
Use u – substitution to rewrite the
integrals and redefine its bounds to evaluate composite function integrals.
10.
Define
the natural logarithm as an integral and use the definition and the properties
of limits to aid in evaluating limits of exponential and logarithmic functions.
UNIT II (Chapter 7) Applications of the Definite
Integral
Classes 710
1. Find the area bounded
by several functions using x or y as the independent variable of
integration.
2. Find the volume
generated by revolving an area bounded by several functions about the x axis or y axis by using the diskwasher or cylindrical shells methods.
3.
Use
integrals to find the length of a plane curve.
4. Use integrals to find
the surface of revolution.
5. Define the hyperbolic
functions and their inverses.
6. Find derivatives and integrals
involving the hyperbolic functions and their inverses.
UNIT III (Chapter 8) Principles of Integral Evaluation
Classes 1117
1. Apply the appropriate
integration formulas previously presented in this course.
2. Recognize when to use
and perform integration by parts as many times as needed to evaluate an
integral.
3. Use trigonometric identities to
integrate powers of trigonometric functions.
4. Use trigonometric substitution where
applicable to evaluate integrals.
5. Use partial fraction
decomposition when needed to integrate rational functions.
6. Use integral tables to
evaluate integrals.
7. Use the trapezoid rule
or Simpson’s rule to approximate definite integrals.
8. Determine whether an integral is
improper, and if so, determine if it converges or diverges and be able to find
what it converges to if it converges.
UNIT IV (Chapter 10)
Infinite Series (18 lecture hours)
Classes 1826
1. Define an infinite
sequence, write several of its terms, write its general term and determine
whether it converges to a limit or diverges.
2. Use the difference,
ratio or derivative method to determine if a sequence is eventually monotonic
or neither, if sequence is bounded and if it is bounded its limit.
3. For a given infinite series determine which convergence test
(divergence test, integral test, comparison test, limit comparison test, ratio
test, root test, alternating series test) to use to
determine absolute convergence, conditional convergence or divergence, apply
the test and if possible determine the limit.
4. Write an nth degree Maclaurin
or
5. Find the radius of
convergence and interval of convergence for a given power series.
6. Use the Remainder
Estimation Theorem to estimate the error in using a polynomial of nth degree to approximate a function.
7. Perform algebraic and calculus
manipulations of power series.
UNIT V (Chapter 11) Analytic
Geometry in Calculus
Classes 2730
1. For given points or
equations in rectangular form convert them to polar form and vice versa.
2. Graph equations and
points using the polar coordinate system and polar symmetry tests.
3. Determine the polar
equation for a given graph.
4. Find slopes of tangent lines, equations
of tangent lines and length of parametric and polar curves.
5. Find areas of regions
that are bounded by polar curves.
6. Find vertices, foci,
centers, asymptotes, directrix, where applicable of
conic sections given in rectangular form and use this information to solve
application problems.
7. For a given polar
equation of a conic section find its eccentricity, foci, the
distance from the pole to the directrix or vertices
in order to graph the conic section.
8. Find the polar equation of a conic
section for given conditions.
It is essential that the
student, throughout the semester, devote at least eight hours per week in
homework effort.