Math 1272 (Calculus II)
What to Review for the Final Exam
Spring 2010
Section headings in boldface will be important to review;
those in plain face will not
be covered on the exam
.
7.1
Integration by Parts
7.2
Trigonometric Integrals
7.3
Trigonometric Substitution
7.4
Integration of Rational Functions by Partial Fractions
7.5
Strategy for Integration
7.6
Integration Using Tables
7.7
Approximate Integration
 know how to set up a numerical integration by the
Midpoint Rule, Trapezoid Rule, and Simpson’s Rule
7.8
Improper Integrals
8.1
Arc Length
8.2
Area of a Surface of Revolution
8.3
Applications
9.1
Modeling with Differential Equations
9.2
Direction Fields and Euler’s Method
9.3
Separable Differential Equations
10.1
Curves Defined by Parametric Equations
10.2
Calculus with Parametric Curves
10.3
Polar Coordinates
10.4
Areas and Lengths in Polar Coordinates
11.1
Sequences
11.2
Series
11.3
The Integral Test and Estimates of Sums
11.4
The Comparison Tests
11.5
Alternating Series
11.6
Absolute Convergence and the Ratio and Root Tests
11.7
Strategy for Testing Series
11.8
Power Series
11.9
Representations of Functions as Power Series
11.10 Taylor and Maclaurin Series
 know how to produce them; know the Maclaurin
series for
1/(1
−
x) ,
e
x
, sin x , cos x , tan
−
1
x , (1 + x)
k
11.11 Applications
 know how to write a Taylor polynomial
12.1
Threedimensional Coordinate Systems
 rectangular coordinates only
12.2
Vectors
12.3
The Dot Product
12.4
The Cross Product
12.5
Equations of Lines and Planes
13.1
Vector Functions and Space Curves
13.2
Derivatives and Integrals of Vector Functions
13.3
Arc Length and Curvature
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View Full DocumentMath 1272 (Calculus II)
Representative Final Examination Topics
This is a list of the topics upon which final exam problems (or parts of problems) have
been based, grouped roughly according to the frequency with which they have appeared,
as found from surveying the exams from Spring 2005, Fall 2005, Fall 2007, Spring/Fall
2008, Spring and Fall 2009.
You should
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 Spring '08
 WILSON
 Calculus, Derivative, Maclaurin Series, Taylor Series

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