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PENN STATE UNIVERSITY
ABINGTON COLLEGE
MATHEMATICS DEPARTMENT
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MATH 141
Catalog Description:CALCULUS WITH ANALYTIC GEOMETRY II (4) Derivatives, integrals, applications, sequences and series, analytic geometry, polar coordinates, partial derivatives.
Prerequisite: Math 140 or 140A
Text: Calculus, third edition, Stewart, Brooks/Cole Publishing Co.
TOPICS
CHAPTER 6 INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE
TRIGONOMETRIC FUNCTIONS
(6.1 to 6.4 may be reviewed if desired)
6.6 Inverse Trigonometric Functions
6.8 Indeterminate Forms and L'Hospital's Rule
CHAPTER 7 TECHNIQUES OF INTEGRATION
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitutions
7.4 Integration of Rational Functions by Partial Fractions
7.5 Rationalizing Substitutions
7.6 Strategy for Integration
7.7 Using Tables of Integrals (OPTIONAL)
7.8 Approximate Integration
7.9 Improper Integrals
CHAPTER 8 FURTHER APPLICATIONS OF INTEGRATION (OPTIONAL)
8.2 Arc Length
8.3 Surface Area
8.4 Moments and Centers of Mass
CHAPTER 9 PARAMETRIC EQUATIONS AND POLAR COORDINATES
9.1 Curves Defined by Parametric Equations
9.2 Tangents and Areas
9.4 Polar Coordinates
9.5 Areas and Lengths in Polar Coordinates (LENGTHS OPTIONAL)
9.6 Conic Sections
9.7 Conic Sections in Polar Coordinates (OPTIONAL)
CHAPTER 10 INFINITE SEQUENCES AND SERIES
10.1 Sequences
10.2 Series
10.3 The Integral Test
10.4 The Comparison Tests
10.5 Alternating Series
10.6 Absolute Convergence and the Ration and Root Tests
10.7 Strategy for Testing Series
10.8 Power Series
10.9 Representation of Functions as Power Series
10.10 Taylor and Maclaurin series
10.11 The Binomial Series
10.12 Applications of Taylor Polynomials
CHAPTER 11 THREE DIMENSIONAL ANALYTIC GEOMETRY AND VECTORS
11.1 Three-Dimensional Coordinate Systems
11.6 Quadric Surfaces
CHAPTER 12 PARTIAL DERIVATIVES
12.1 Functions of Several Variables12.2 Limits and Continuity (lightly)
12.3 Partial Derivatives12.5 The Chain Rule
The Mathematics Department requires that the instructor must
adhere to the syllabus