MATH 416 Midterm: MATH414 BOYLE-M FALL2004 0101 MID EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 416
• Professor: All

Document Summary

No books, notes, calculators or electronic devices: (a) (10 pts) state the existence and uniqueness theorem for a di erential equation of the form y = a(t)y. Include hypotheses. (b) (10 pts) state the existence and uniqueness theorem for a di erential equation of the form y = f (t, y). Include hypotheses: (30 points) for each of the following choices of a, compute a fundamental matrix of solutions for the di erential equation y = ay, and draw the phase portrait of the system. 5 3(cid:19) (i) a = (cid:18) 6 2. Justify your answer: (20 pts) consider the scalar de x x 4x = 0. Discuss the behavior of the solutions (t) as t + . Justify your answer: true or false (15 points), no argument required. (a) if || || denotes a norm on rn and g is a continuous function from [0, 1] into rn, then ||r 1.