4 Credit Course
Offered in Lecture Format
Prerequisite required  (MATH 1910)

SYLLABUS

I. LOGARITHMIC AND EXPONENTIAL FUNCTIONS

A. The integral definition of ln(x)
B. e^x as the inverse of ln(x)
C. Basic derivatives and integrals
D. Logarithmic differentiation
E. Functions involving bases other than e
F. Some limits equal to e

II. TRIGONOMETRIC FUNCTIONS AND THEIR INVERSES

A. Derivatives of trigonometric functions
B. Basic integrals involving trigonometric functions
C. Inverse trigonometric functions
        1. Definitions and graphs
        2. Derivatives
        3. Integrals

III. HYPERBOLIC FUNCTIONS

A. Definitions
B. Graphs
C. Basic derivatives
D. Basic integrals
*E. Inverses

IV. MORE ON INTEGRATION

A. Integration by parts
B. The partial fractions technique
C. Using tables of integrals
D. Numerical integration
        1. The trapezoidal rule
        2. Simpson's rule

V. MORE INVOLVED LIMITS

A. Indeterminate forms
B. L'Hospital's rule
        1. Direct application of the rule
        2. Situations involving indirect application of the rule

VI. IMPROPER INTEGRALS

A. The infinity type
B. The closed interval type
C. Problems of mixed type

VII. INFINITE SERIES

A. Sequences and convergence
B. Infinite series defined
C. Geometric series
D. P-series
E. Some tests for series with positive terms
F. The alternating series test
G. Absolute and conditional convergence
H. Power series
I.     Taylor expansions

VIII. POLAR COORDINATES

A. Definition; conversions to and from rectangular coordinates
B. Polar graphs
C. Finding points of intersection of polar graphs
D. Finding areas in polar coordinates

IX. PARAMETRIC EQUATIONS IN THE PLANE

A. Elimination of parameter; graphing
B. Finding slopes of tangent lines
C. Arclength

*Optional

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