These notes are provided in the form of .doc and/or .pdf files which the student
can access with MicroSoft Word or Acrobat Reader. The latter is freely available from
the Adobe website. A notation (Information) following the hyperlink indicates that the
material is posted for the student's information only and will not be explicitly tested
on
exams, etc. If you have trouble accessing any of these files, please check with the instructor.
Current Math 4245 Notes
These are shown with a 2009 posting date, indicating they are officially posted for the present course.
Lecture of Tuesday, August 25, 2009.
Solution of Equations
Posted August 24, 2009.
Suggested exercises in the "QuickCheck Exercises" section at
the end
of these notes should be worked and
put in your notebook.
Key to "QuickCheck" Exercises #1 (Opens with MS Word).
Lecture of Thursday, August 27,2009.
Introduction to First Order Equations
Posted September 1, 2009.
Key to "QuickCheck" Exercises #2
Lecture of Tuesday, September 1, 2009.
Linear First Order Equations
Posted September 1, 2009.
Lecture of Thursday, September 4, 2009.
Separable First Order Equations
Posted September 2, 2009.
Key to "QuickCheck" Exercises #3 (Opens with MS Word).
Lecture of Tuesday, September 8, 2009.
Existence and Uniqueness of Solutions
Posted September 8, 2009.
Lecture of Tuesday, September 15, 2009.
Numerical Approximation of Solutions MicroSoft Word file.
Posted September 15, 2009.
Lecture of Thursday, September 17.
Second Order Differential Equations
Posted September 17, 2009.
Lecture of Thursday, September 24.
Repeated Real Roots; Reduction of Order
Posted September 24, 2009. Note the QuickCheck exercises.
Key to "QuickCheck" Exercises (Opens with MS Word).
Lecture of Tuesday, September 29, 2009.
Complex Roots of the Characteristic Equation
Posted September 29, 2009.
Lecture of Thursday, October 1, 2009.
Inhomogeneous Second Order Equations
Posted October 7, 2009.
Lecture of Tuesday, October 8, 2009.
Variation of Parameters; More on Inhomogeneous Second Order Equations
The second topic, treated on pages 6-10, will not be covered directly in class.
Posted October 7, 2009.
Informational Material; will not be tested directly.
Using Complex Numbers (Review)
Posted October 7, 2009.
Oscillatory force, page 1.
Oscillatory force, page 2.
Oscillatory force, page 3.
Oscillatory force, page 4.
Oscillatory force, page 5.
Posted October 7, 2009.
Lecture of Thursday, October 8, 2009.
n-th Order Homogeneous Equations.
Posted October 8, 2009.
Lecture of Tuesday, October 13, 2009.
Laplace Transform; Introduction
Laplace Transform; Computation
Posted October 15, 2009.
Lecture of Thursday, October 15, 2009.
Laplace Transform; Specific Properties
Posted October 15, 2009.
Laplace Solution of Initial Value Problems
Posted October 20, 2009.
More on Initial Value Problems
Posted October 20, 2009.
Key to Laplace transform problems. (MSWord file.)
Lecture of Tuesday, October 20, 2009
Distributions; Impulses
Posted October 20, 2009
The Convolution Operation
Posted October 20, 2009.
Lecture of Thursday, October 22, 2009.
Convolution Applications
Posted October 20, 2009.
Lecture of Tuesday, October 27, 2009.
n-th Order Inhomogeneous Equations
Posted November 7, 2009. See "QuickCheck Exercises" at end of file.
Key to Suggested Exercises, p. 1
Key to Suggested Exercises, p. 2
Key to Suggested Exercises, p. 3
Key to Suggested Exercises, p. 4
Key to Suggested Exercises, p. 5
Lecture of Thursday, October 29, 2009.
Systems of Differential Equations
Posted April 2, 2007.
Lecture of Thursday, October 29, 2009.
Linear Systems of Differential Equations
Posted November 7, 2009. Last page modified April 10.
Lecture of Tuesday, November 3, 2009.
Constant Coefficient Linear Systems
Posted November 7, 2009.
Lecture of Tuesday, November 10, 2009.
Linear Systems with Complex Eigenvalues
Posted November 18, 2009.
Lecture of Thursday, November 12, 2009.
Inhomogeneous Linear Systems
Posted November 18, 2009.
Lecture of Tuesday, November 17, 2009.
Equilibrium Points; Stability, I.
Posted November 18, 2009.
Lecture of Thursday, November 19, 2009.
Equilibrium Points; Stability, II.
Posted November 19, 2009.
Old Math 4245 Notes.
These, shown with a posting date earlier than 2009, are not yet officially posted for the present course.
Lecture of Thursday, March 29
Suggested Exercises: K&J; p. 220,221: 1-21 odd; pp. 235-237, all odd;
p. 245, 246, 1-17 odd; pp. 263,264, 1-27 odd.
Informational Material
Vectors, I (Review)
Vectors, II (Review)
Vectors, III (Review)
