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MATH 41

COURSE DESCRIPTION: (GQ) Trigonometry and Analytic Geometry
(3:3:0) Straight lines: circles; functions and graphs; graphs of
polynomial and rational functions; exponential and logarithmic
functions; trigonometry; conic sections.

PREREQUISITES: Math 21 or satisfactory performance on the
mathematics proficiency examination.

TOPICS

FUNCTIONS AND GRAPHS
Graphs and Symmetry
Equations of Lines
The Definition of a Function
The Graphs of a Function
Techniques in Graphing
Methods of Combining Functions
Inverse Functions

POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO OPTIMIZATION
Linear Functions
Applied Functions: Setting up Equations
Maximum and Minimum Problems
Polynomial Functions
Graphs of Rational Functions

EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Exponential Functions
The Exponential Function y = e^x
Logarithmic Functions
Properties of Logarithms
Applications

TRIGONOMETRIC FUNCTIONS OF ANGLES
Trigonometric Functions of Acute Angles
Right-Triangle Applications
Trigonometric Functions of General Angles
Algebra and the Trigonometric Functions
The Law of Sines and the Law of Cosines

TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS
Trigonometric Functions of Real Numbers
Graphs of the Sine and Cosine Functions
Graphs of the Tangent and the Reciprocal Functions
Identities
Trigonometric Equations
The Inverse of Trigonometric Functions

ANALYTIC GEOMETRY
The Parabola
The Ellipse
The Hyperbola
Polar Coordinates

ROOTS OF POLYNOMIAL EQUATIONS
Division of Polynomials
The Remainder Theorem and the Factor Theorem
The Fundamental Theorem of Algebra
Rational and Irrational Roots
Conjugate Roots and Descartes's Rule of Signs

8/13/92

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