| Problem Set 1 |
Series. Geometric series. Applications of
geometric series (e.g. mortgage calculations).
Infinite series. Convergence tests. Setting up series
to model situations. |
|
Area under a curve. Integral notation. Interpreting
the meaning of an area under a curve. Calculating the
area under a curve using a graphing calculator.
Calculating the area under a curve using geometric
figures. Calculating the area under a curve using
antiderivatives. Calculating antiderivatives via
short-cut rules. Checking to see if a given function
is an antiderivative or not. Application of integrals:
Average Value. |
| Problem Set 3 |
Trigonometry. Using right-angle triangle
definitions of sine, cosine and tangent to model
situations. Finding formulas for periodic function.
Derivatives and
integrals of trigonometric functions. Solving equations
involving sine and cosine. Inverse trigonometric functions.
Derivatives and integrals involving inverse trigonometric
functions. |
| Problem Set 4 |
Differential equations. Locating and classifying
equilibrium solutions. Sketching slope fields. Using a
slope field to sketch the graph of a function. Euler's
method. Deciding whether estimates from Euler's method
are over- or under-estimates. Verifying symbolic solutions
for differential equations. Finding symbolic solutions
using the technique of Separation of Variables.
Symbolic solution of the Logistic Equation. |
| Problem Set 5 |
This is just a few additional problems for people
who have already completed everything on Problem sets
1-4. The problems included here are on u-substitution,
formulating and solving differential equations
(Separation of Variables) and volumes of revolution. |