Lecture Dates

Sections in Textbook

Homework Problems

Deadlines for Homework

Wednesday 10/24

7.5

9, 11, 12, 14

(cont'd)

Due on Wednesday 10/31.

Thursday 10/25 x-hour

No class on Friday 10/26

Homecoming weekend

7.6

3(a), 5(a), 7

(8^th edition: only solve and express in terms of real-valued functions in problems 3, 5)

Monday 10/29

7.8

2(c), 3(c), 5

(8^th edition: only solve the system in problems 2, 3)

Due on Wednesday 11/7.

Wednesday 10/31

7.8

10.1

1, 5, 10, 14

Friday 11/2

10.5

3, 5

10.7, 10.B

Monday 11/5

10.7

Solve #1(a,b) using the method of D'Alembert (discussed in class; a sketch can be found in Problems 13, 14, 16 and 20 in Section 10.7).

Due on Monday 11/12.

Same numbers in the 8^th edition.

Wednesday 11/7

10.7

Solve #1(a) using Fourier series.

10.2

14, 15

Thursday 11/8 x-hour

No class on Friday 11/9

10.3

6

10.4

16, 17

10.5

9, 10

Monday 11/12

No class on Wednesday 11/14

Pre-examination break 11/14-11/15

10.6

9(a)

This assignment will not be collected or graded, but similar problems may appear on the final.

10.7

5(a)

Lecture Dates

Sections in Textbook

Homework Problems

Deadlines for Homework

Monday 09/10

1.1

#7. Write down a differential equation of the form dy/dt=ay+b whose all solutions approach y=3 as t→∞.

#12. Draw a direction field for y'=-y(5-y). Based on the direction field, determine the behavior of y as t→∞. If this behavior depends on the initial value of y at t=0, describe this dependency.

Due on Wednesday 9/19

1.3

Wednesday 9/12

1.2

#8. Consider a population p of field mice that grows at a rate proportional to the current population, so that dp/dt=rp.

(a) Find the rate constant r if the population doubles in 30 days.

(b) Find r if the population doubles in N days.

2.1

Friday 9/14

1.3 (cont'd)

#12. Verify that y₁(t)=t^-2 and y₂(t)=t^-2lnt are solutions of t²y''+5ty'+4y=0 for t>0.

2.1 (cont'dite)

#15. Find the solution of the initial value problem ty'+2y=t²-t+1, y(1)=1/2, for t>0.

#17. Find the solution of the initial value problem y'-2y=e^2t, y(0)=2.

#33. Show that if a and λ are positive constants, and b is any real number, then every solution of the equation y'+ay=be^-λt has the property that y→0 as t→∞.

Hint. Consider the cases a=λ and a≠λ separately.

2.2

#3. Solve the equation y'+y²sinx=0.

#8. Solve the equation dy/dx=x²/(1+y²).

Monday 9/17

2.4

#3. Without solving the initial value problem y'+(tant)y=sint, y(π)=0, determine an interval in which the solution is certain to exist.

#14. Solve the initial value problem y'=2ty², y(0)=y₀, and determine how the interval in which the solution exists depends on the initial value y₀.

#25. Let y=y₁(t) be a solution of y'+p(t)y=0 and let y=y₂(t) be a solution of y'+p(t)y=g(t). Show that y=y₁(t)+y₂(t) is also a solution of the latter equation.

#33. Solve the initial value problem y'+p(t)y=0, y(0)=1, where p(t)=2 for 0≤t≤1 and p(t)=1 for t>1.

Due on Wednesday 9/26.

All problem numbers also work for the 8^th edition.

Wednesday 9/19

2.4 (cont'd)

2.3

Thursday 9/20

x-hour

2.3 (cont'd)

2, 4 and 8(a,b)

Friday 9/21

2.5

We draw the entire graph and phase line, in contrast to the first quadrant / positive ray figures in the book.

3, 13 and 15(a)

2.4 (cont'd)

28

Monday 9/24

2.6

2, 14, 28

Due on Wednesday 10/3.

Same problem numbers in the corresponding sections in the 8^th edition.

Wednesday 9/26

2.6

24, and the following problem:

#24α. Use #24 to solve the equation (3y²+4xy)+(4xy+3x²)y'=0.

3.1

11, 12

4.1, 4.2

Thursday 9/27

x-hour

3.3: Complex Roots (=3.4 in the 8^th edition)

1, 5, 11, 19

Friday 9/28

3.4: Repeated Roots (=3.5 in the 8^th edition)

2, 13, 14, 23, 25

Monday 10/1

3.5, 3.8 (=3.6, 3.9 in the 8^th edition)

Due on Wednesday 10/10

Lecture Dates

Sections in Textbook

Homework Problems

Deadlines for Homework

Monday 10/1

3.5, 3.8 (=3.6, 3.9 in the 8^th edition)

Due on Wednesday 10/10.

Same problem numbers in the corresponding sections in the 8^th edition.

Wednesday 10/3

3.5: Undetermined Coefficients (=3.6 in the 8^th edition)

1, 2, 13, 14, 16, 18, 19(a)

3.8 (=3.9 in the 8^th edition)

Friday 10/5

3.7: Vibrations (=3.8 in the 8^th edition)

6

3.8: Forced Vibrations (=3.9 in the 8^th edition)

9, 11

Monday 10/8

3.8: Forced Vibrations (=3.9 in the 8^th edition)

Due on Wednesday 10/17.

7.3

3

Wednesday 10/10

7.3

8, 29 (=7, 28 in the 8^th edition)

In #29 don't assume anything about det A.

Thursday 10/11

x-hour

4.1

8

Friday 10/12

3.2

11

4.1

2, 6

7.1

5, 9

7.4

5

Monday 10/15

4.2

2, 13, 14, 23, 25

Due on Wednesday 10/24.

7.4

Wednesday 10/17

3.2

23, 27 (22, 26 in the 8^th edition)

7.4

6

Thursday 10/18

x-hour

3.2 (3.3 in the 8^th edition)

35, 39 (=21, 25 in the 8^th edition)

Friday 10/19

3.2

19

3.6 (=3.7 in the 8^th edition)

10, 15

Monday 10/22

7.3

19, 25 (=18, 24 in the 8^th edition)

Due on Wednesday 10/31.