Math 246: Recommended Problems from the Textbook

These problems will be similar to problems of the exams and the final exam. But they will not be collected or graded. Note that partial solutions to the problems are in the back of the textbook.

Section 1.1 (Introduction), p.8

1-4

Section 2.1 (Linear Equations), p. 38

only find the general solution: 1, 2, 6, 10
13, 14, 16, 18

Section 2.2 (Separable Equations), p. 45

1,2,3,4,9,10,13,21

Section 2.3 (Modeling with First Order Equations), p. 57:

1,3,5,29,30

Section 2.4 (Differences between Linear and Nonlinear Equations, p. 72

1,3,22

Section 2.5 (Autonomous Equations and Population Dynamics), p. 84

3,4,5,10,11,20

Section 2.6 (Exact Equations and Integrating Factors), p. 95

2,3,7,13,19

Section 2.7, 8.1, 8.2, 8.3, 8.6 (Numerical Methods)

problems

Section 3.1 (Homogeneous Equations with Constant Coefficients), p. 136

1,5,8,9,10

Section 3.4 (Complex Roots), p.158

7,9,12,17,21

Section 3.5 (Repeated Roots), p. 166

1,11,12,13,14

Section 3.6 (Method of Undetermined Coefficients), p. 178

1, 3, 6,7; only (a) for: 19,20,23

Section 3.7 (Variation of Parameters), p. 183

5,7,10

Section 3.8 (Mechanical and Electrical Vibrations), p. 197

1, 5, 11, 17
Note: weight is the force with which mass is pulled by earth's gravity. It is related to the mass m by w = m g , where g = 9.80665 m s^-2 = 32.174 ft s^-2.
``mass stretches spring a distance d'' means that spring constant is k = w/d = m g/d

Section 6.2 (Solution of IVP using the Laplace Transform), p. 307

11, 12, 22; 21, 23

Section 6.3 (Step Functions), p. 314

1, 2, 7, 8, 11,16, 18

Section 6.4 (Discontinuous Forcing Functions), p. 321

1, 5, 9, 10

Section 6.5 (Impulse Funcions), p. 328

1,4,5

Section 7.5 (Homogeneous Systems of First Order Linear Equation), p. 381

2, 3, 5, 7

Section 7.6 (Complex Eigenvalues), p. 390

1, 4, 6

Section 7.8 (Repeated Eigenvalues), p. 407

1, 2

Section 9.1 (The Phase Plane: Linear Systems), p. 468

do parts (a), (b), (c) in all problems: 1, 2, 5, 7, 10, 11

Section 9.3 (Almost Linear Systems), p. 487

(do parts (a), (b), (c) in all problems, sketch a phase portrait close to each critical point): 5, 6, 7, 8, 10, 12

Tobias von Petersdorff , tvp@math.umd.edu