MATH 115B (Pre-Calculus)
| DESCRIPTION |
MATH 115B combines precalculus and calculus topics; the
sequence MATH
115B-140B covers the material of MATH 115-140 in a more integrated
fashion
by virtue of a somewhat different ordering of topics. For purposes of
credit
and prerequisites, MATH 115B is the same as MATH 115, and MATH 140B is
the same as MATH 140. A student who goes from MATH 115B to MATH 140
will
be better prepared for calculus topics than a MATH 115 student, but may
have to do some additional preparation on a few topics such as triangle
trigonometry. The functions studied in Math 115B include polynomials
and
exponential, logarithmic and trigonometric functions. Calculus topics
include
limits; derivatives of polynomials and exponential, logarithmic and
trigonometric
functions; and applications of the derivative in graphing.
For further information on MATH 115B, contact Dr. Frances Gulick at ffg@math.umd.edu
|
| PREREQUISITES |
Satisfactory score on Math Department placement exam,
completion of
the appropriate module of MATH 003, or completion of Math 113.
|
| TOPICS |
Algebra
Functions
Inequalities,
Domains
Function
graphs
Transformations
Calculus
Limits
Tangent lines
(lines)
(Absolute
value inequalities)
Limit
theorems, including
Squeezing Theorem and Substitution Rule
One-sided
limits
Infinite
limits
Continuity
The derivative
Differentiable
functions
Mean Value
Theorem
Applications
of MVT
Concavity
Power
functions
(Combinations
of
functions)
Derivatives of
combinations
Critical
numbers
and extreme values
(Quadratic
functions)
Precalculus/calculus
Polynomials
Exponential functions
Graphs
Derivative of
e^x
and e^{f(x)}
Logarithm functions
Definition as
inverse
of exponential function
Graphs
Logarithm
laws
Derivative of
ln(x)
and ln(f(x))
Trigonometry
Unit circle,
terminal
points, reference numbers
Circle/Trig.
functions
Sinusoidal
graphs
The other trig
graphs
Trig identitities
(quotient,
Pythagorean,period,negative number)
Sine and cosine
sum
and difference, double-angle identities
Trig
derivatives
(A graphing calculator such as the TI- 83, is required for
Math 115B.
It is used in exploring the graphs of functions and equations and in
solving
problems.
|
| TEXT |
Text(s)
typically used in this course |
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