MATH 141
COURSE DESCRIPTION: Calculus and Analytic Geometry II (4:4:0)
Derivatives, integrals, applications; sequences and series;
analytic geometry; polar coordinates. Students may take only one
course for credit from among MATH 141 and 141B. During
Spring and Fall semesters, the course is offered in 60 fifty
minute lectures, four per week; in the summer session it is
offered in 40 seventy-five minute lectures, five per week.
PREREQUISITE: MATH 140, 140A or 140B. Students who do not
meet the prerequisite and who do not drop the course will be
dis-enrolled.
TOPICS
INVERSE FUNCTIONS
Inverse Functions
The Natural Logarithmic Function
The Natural Exponential Function
General Logarithmic and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions
Hyperbolic Functions
Indeterminate Forms and l'Hospital's Rule
TECHNIQUES OF INTEGRATION
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions
Rationalizing Substitutions
Strategy for Integration
Using Tables of Integrals and Computer Algebra Systems
Approximate Integration
Improper Integrals
FURTHER APPLICATIONS OF INTEGRATION
Differential Equations
Arc Length
PARAMETRIC EQUATIONS AND POLAR COORDINATES
Curves Defined by Parametric Equations
Polar Coordinates
Lengths in Polar Coordinates
INFINITE SEQUENCES AND SERIES
Integral Test and Estimation of Sums
Comparison Tests
Alternating Series
Absolute Convergence and the Ratio and Root Tests
Strategy for Testing Series
Power Series
Taylor and Macluarin Series
Applications of Taylor Polynomials
(6/97)