Math 32 Home
Departmental Course Syllabus
Exam Solutions
Topics Outline
Practice Problems
Exam I
Modeling
Differential Equations
Seperation of Variables
Euler's Method
Population Models
Exponential Growth
Logistic Growth
The Coalition Model
Methods of integration
substitution
integration by parts
using tables
partial fractions
The First and Second Fundamental Theorems of Calculus
Definite Integrals, Area, Average and Total Change of Functions
Approximating Definite Integrals
Right and Left Riemann Sums
Exam II
Approximating Definite Integrals
The Midpoint Rule
The Trapezoid Rule
Simpson's Rule
Improper Integrals
limits going to infinity
limits to points where integrand is not defined
Volumes by slicing
Work
Probability
Events
Random Variables
Expected Values
Series
partial sums, geometric series
the n
th
term test
the harmonic series
the sum of x
-p
for 0<p<=1 and p>1
convergence tests
the comparison test
the ratio test
the integral test
Exam III
Probability and Distribution Functions
density functions
mean, median
cumulative probability distribution functions
normal distributions
mean, standard deviation
Taylor Approximations
linear approximation
second, third, n
th
order Taylor polynomials
convergence of Taylor series
Series, part II
Alternating Series; The Alternating Series Test
Absolute Convergence
The Extended Ratio Test
Convergence of Power Series
Taylor Series and intervals of convergence
Fourier Series
Oscillations
Complex numbers
real and imaginary parts
polar notation
Euler's identity
second order differential equations
simple harmonic motion s''+(k/m)s=0
damped harmonic motion s''+(a/m)s'+(k/m)s=0
general solutions to second order linear differential equations with constant coefficients
characteristic equations
Series Solutions to Differential Equations
solutions expressed as Taylor series about a point
predator-prey model and phase planes
systems of first order differential equations
phase planes
trajectories
equilibrium points
SIR model and phase planes
phase plane analysis
nullclines
analyzing trajectories in regions defined by nullclines
equilibrium points and nullclines
applications to the SIR model