Applied Harmonic Analysis: An Introduction to Signal Processing
MATH 416

Fall 2005
FINAL EXAM MATH 414 FALL 2004
For this test, you may use our text (Brauer and Nohel) and one page of notes
(you can use both sides). In your proofs and explanations, you do not need to
reprove results you can cite in the text.
1. Judge each of the followi
Applied Harmonic Analysis: An Introduction to Signal Processing
MATH 416

Fall 2005
EXAM 2MATH 414FALL 2004
Possible points are in parentheses.
1. (a) (10) State the Gronwall Inequality. Include all assumptions and conclusions.
(b) (10) State our fundamental existence and uniqueness theorem for linear dierential equations. Include all as
Applied Harmonic Analysis: An Introduction to Signal Processing
MATH 416

Fall 2005
EXAM 1MATH 414FALL 2004
No books, notes, calculators or electronic devices.
1. (a) (10 pts) State the existence and uniqueness theorem for a dierential equation
of the form y = A(t)y . Include hypotheses.
(b) (10 pts) State the existence and uniqueness th