2.1: 1,2
2.2: 1–4
2.3: 1–3
Homework Solutions Part 1 (encrypted)
Chapter 3
3.1: 1–5
Chapter 4
4.1: 1,2
4.2: 1,3
4.3: 1,2
4.4: 1,2,7,9
Chapter 5
5.2: 1,2,4 [on #4 the factorization is wrong. The last factor is (x2 –9) ]
Homework Solutions Parts 2,3 & 4 (encrypted)
5.3: 1,2,3
5.4: 1,2
Homework Solutions Part 5 (encrypted)
Chapter 6
6.1: 1
6.2: 1 (Use a bounding function, not dr/dt),2,5–7
Homework Solutions Part 6 (encrypted)
Note that Exercise 6.2.2 is the same as 6.2.3: If you want an extra problem try this one:
Consider the system of differential equations:
dx/dt = 3x + 2y - x(x2+y2)
dy/dt = -x + y - y(x2+y2)
a) Classify the fixed point at the origin.
b) Show that (0,0) is the only fixed point.
c) Calculate r (dr/dt) in terms of x and y.
d) Show that dr/dt is positive for small r and negative for large r. Hint: To show that the quadratic
terms are positive definite (positive for all (x,y)≠ (0,0) ), either complete the square or use the test for the minimum of a function.
e) Prove that the system has a periodic orbit.
6.4: 1,2
6.5: 1
6.6: 1,3
Handout on a rigorous approach to the divergence of a vector field
Homework Solutions Part 7 (encrypted)
All Homework Solutions (encrypted)
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Chapter 7
7.1: 2
7.2: 1
