MATH-2400 Introduction to Differential Equations.

Problems for Homework Assignments

TEXT: W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Eighth Edition, Wiley, 2005.

READING: Please keep in mind that reading mathematical texts requires a serious, active work with paper and pen to make sure that you understand and can use the techniques. Also, try to look the material over ahead of the time it is presented in the lectures.

PROBLEMS TO BE HANDED IN (in case homework is collected): these problems are listed in boldface. You are welcome to consult the text and notes and discuss the problems with other people. However, the solutions should be yours. If you have difficulties with these problems you might consider the Practice Problems (see below) first. Quizzes will be based on these problems.

PRACTICE PROBLEMS: All the problems on the list (except for those to be handed in) have solutions posted. Since the solutions are listed according to the 7th edition of the book, in the list below the 7th edition problems’ numbers are given in square brackets [if they are different form the ones for the current 8th edition]. In order to succeed in the course (and on the tests) you have to learn how to solve these problems. The best strategy would be first to give them an honest try, without consulting the book, if it doesn't work enlist the book's help, and only after that try the solutions set.

Section

Problems

Comments on Reading

1.1

4,6

Glance over 1.2

1.3

1,2,7,18; 4,5,8

Graphs in 1.3-2.2 are easy; try to do them by hand. You can use DEplot from Maple.

2.1

4, 18,20, 30[28]; 3, 9(a,c)

 

2.2

2, 11, 22; 11, 21

 

2.3

3,7[6],9,16[18]; 4, 8[7](a,b)

Skip Example 4. First write down a differential equation.

2.4

 

Optional, but very important for understanding theory

2.5

3, 10,15; 1, 2, 11

 

3.1

1, 12,21; 15, 23

 

3.2

3,8; 14, 15, 22

 

3.3

13; 4, 9, 14(a)

Skip Abel’s theorem but pay a special attention to the summary on p.157 and the discussion following that summary.

3.4

10, 18; 1-6, 22

 

3.5

2, 16, 28; 12, 18

No reduction of order

3.6

4, 9,10, 15; 3, 13

Skip the proof pp 182-183

3.7

3, 5

 

3.8

2, 9; 3, 5, 13

 

3.9

2, 6, 8, 11, 17; 5,10

 

7.1

3; 2, 5

Pay a special attention to Example 1.

7.2

22,24; 21(c,d), 23

A summary of matrices is online (course page).

7.3

6,7,15,16,23,24; 5, 17-18

 

7.4

2,4,5,6

A very important theory

7.5

3,7, 24; 15, 26, 27

 

7.6

3, 9,13,16; 10, 15, [26optional]

 

9.1

1,2,4,5,6,7,17

Important review of linear systems; skip Case 3(b).

9.2

1,4,7,8,11,13

 

9.3

2, 6; 7(a-d, use Maple worksheet systems for part d), 10 (a-c)

Up to damped pendulum p. 508. The process of obtaining a linear system (p. 506) is especially important.

9.4

3, 4, 5, 17[12]; 2 (use Maple worksheet systems)

 

10.1

2, 4, 14,16

 

10.2

1-10, 22; 20(a,b)

 

10.3

1,2,3,5,7,10

 

10.4

1-6; 17,18, 22 [Sketch the graphs]

 

10.5

2,5,7,18; 3, 8, 11

 

10.6

3, 4, 7, 11,13; 1,8,9 [skip part (c), in (d) determine the limiting value alone], 13  [skip part (c)]

 

10.7

1, 2, 6, 7, 12, 13

Last 2 problems explain, what kind of waves the solutions are.