The links are to Paul's Notes, the section numbers refer to Boyce and DiPrima (10th edition).
WeBWorK set 1
Precalculus essentials
Differentiation essentials
Worksheet 1, meet your neighbors, is on paper and you will turn it in for attendance.
WeBWorK set 2
Introduction to WeBWorK, Classifying DEs.
Definitions from Paul's notes (section 1.1, 1.2,
1.3 in Boyce and DiPrima).
direction fields (section 1.1)
Worksheet on Classification of DEs,
with solutions.
Worksheet 2.
Here are the scanned solutions to the
first page of the worksheet,
and to the second page.
WeBWorK set 3
separable 1st order ODEs (section 2.2)
Interval of Validity,
or interval of existence, of solutions. (section 2.4)
Definitions of General Solution and Interval of Existence.
Worksheet 4.
Here are the scanned solutions.
Memorize these solutions and do NOT use separation of variables:
Assume \(k\) and \(y_0\) are constants.
The general solution to \(\frac{dy}{dx} = ky\) is \(y = C e^{kx}\).
The solution to the IVP \(\frac{dy}{dx} = ky, \ y(0) = y_0\) is
\(y = y_0 e^{kx}\).
Worksheet 5.
Here are the scanned solutions.
WeBWorK set 4
Linear 1st order ODEs
(section 2.1)
Recipe to solve any first order linear ODE for y(x).
Here’s the recipe for y(t).
Worksheet 6.
Here are the scanned solutions.
Worksheet 7.
Here are the scanned solutions.
WeBWorK set 5
1st order modeling (section 2.3).
Solving dy/dt = k(y-A) by inspection.
Group work for Tuesday, January 28, worth 5 class points.
Here are the scanned solutions.
Second day on modeling: Worksheet 9 on Modeling.
Here is a compact version
of worksheet 9, for projection during class.
Here are the scanned solutions to worksheet 9.
Here is a full page solution to problem 3, taken from solutions to an old exam.
WeBWorK set 6
Autonomous Equations and
Equilibrium Solutions
(section 2.5).
Euler's method (Section 2.7).
Worksheet 10.
Here are the scanned solutions.
Here is a derivation of the solution
to the logistic equation which is given to you in set 6, problem 5.
Most textbooks do separation of variables, with partial fractions to do the \(P\) integral. Gross!
The Final Exam is scheduled for
Tuesday, May 7, 12:30-2:30, in our usual classroom.