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.10

1-6

Section 2.1 (Linear equations), p. 23

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

Section 2.3 (Separable equations), p. 38:

1, 2, 3, 5, 6, 9, 10, 13, 14
7, 21, 22

Section 2.5 (Modeling with Linear Equations), p. 54:

1, 2, 3, 23, 24, 28

Section 2.6 (Population Dynamics and Related Problems), p. 69:

3, 4, 10

Section 2.8 (Exact Equations and Integrating Factors), p. 88:

2, 3, 7, 13, 19

Section 2.10 (Misc. Problems), p. 94:

1, 3, 5, 6, 8, 17, 20, 22

Section 8 (Numerical Methods)

problems

Section 3.1 (Homogeneous Equations with Constant Coefficients), p. 128

1, 5, 8, 9, 10

Section 3.4 (Complex Roots), p. 150

7, 9, 12, 17, 21

Section 3.5 (Repeated Roots), p. 159

1, 11, 12, 13, 14

Section 3.6 (Method of Undetermined Coefficients), p. 171

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

Section 3.7 (Variation of Parameters), p. 177

5, 7, 10

Section 3.8 (Mechanical and Electrical Vibrations), p. 190

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 k = w/d = m g/d

Section 3.9 (Forced Vibrations), p. 198

5, 7

Section 6.2 (Solution of IVP using the Laplace Transform), p. 303

(you can use Matlab for the inverse transform) 11, 21, 22, 23

Section 6.3 (Step Functions), p. 311

(do all these problems by hand without Matlab): 2, 7, 8, 16, 18

Section 6.4 (Discontinuous Forcing Functions), p. 318

(you can use Matlab for the inverse transform): 1, 5, 9

Section 6.5 (Impulse Funcions), p. 324

(you can use Matlab for the inverse transform): 1, 4, 5

Section 7.5 (Systems of First Order Linear Equation), p. 378

(in all problems, find the general solution and sketch a phase portrait): 2, 3, 5, 7

Section 7.6 (Complex Eigenvalues), p. 387

(in all problems, find the general solution and sketch a phase portrait): 1, 4, 6

Section 7.7 (Repeated Eigenvalues), p. 396

(in all problems, find the general solution and sketch a phase portrait): 2, 3

Section 9.1 (The Phase Plane: Linear Systems), p. 469

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

Section 9.3 (Almost Linear Systems), p. 488

(do parts (a), (b), (c) in all problems): 5, 6, 10, 12

Tobias von Petersdorff , tvp@math.umd.edu