M 427K Advanced Calculus for
applications, I
Unique# 58865 - Fall 2008
Homework assignments from 8th
edition textbook
First assignment: Due Wednesday September 10
Linear equations:
From the ODE with Matlab manual: page 43: 1, 2, 3, 4, 5, 6, 7, 9.
From the textbook: Chapter 2 -- Section 1:
1, 3, 5, 6, 10, 11
(for part a) draw the directional fields using Matlab-"dfield6
" program.)
13, 16, 17, 21, 22 and
24 (Draw the Directional fields using Matlab-"dfield6" program and draw
the computed solution using Matlab-"plot"
function)
28, 34 and 36 (do not use Matlab).
Homework 2-- Due: Monday September 22
Separable ODEs : Chapter 2 -- Section 2 (page 47):
3, 6, 7, 10, 12, 19,
(you may use "dfield" and "plot")
22, 23, 25, 27.
Differences between linear and non-linear ODEs: Chapter 2
-- Section 4 (page
75):
1, 4,
6, 8, 9, 13, 14, 15, 25, 26, 28, 29.
Homework
3: Due: Wednesday October 1
Autonomous Equations and population
dynamics: Chapter 2- Section 5
From Matlab Manual, page 45: 16, 17, 18, 19, 23,
24, 25.
From the textbook: 3, 4, 5, 7, 8, 9, 18, 20, 22. (Use
"dfield7" and "plot" as needed)
Homework
4: Due: Wednesday October 8
Exact equations: Section 6:
page 99: 1, 2, 8, 9, 16, 20, 21, 25, 27, 29.
Homework “Not Due”
From Miscellaneous problems on pages
127-127: Optional, but make sure you workout as many problems as you need.
Not Due
Homework
5: New Due Date for both written
and Matlab graphics part: Thursday October 16
Chapter
3: Second order equations
Section 1 - page 142: 3, 5, 7, 10,11, 13, 17, 19.
NOTE: For problems
10,11,13,19, 30 and 31, write the equations as a first order system of ODEs. Then use `pplane6' from MATLAB to graph the phase diagram
and to plot the solution. For the use of `pplane6' consult ODEs
using MATLAB, chapter 7, pages 93 to 100.
New
Due date:
both written and Matlab graphics part due on Thursday October 16
Homework 6: Due:
Wednesday October 22
Section 2. page 151: 2, 3, 5, 8, 11, 13, 15, 17.
Section 3. page 158: 1, 4, 6, 15, 17, 18
Homework 7: Due:
Wednesday October 29
Section 4. page 164 : 1-4, 7, 8, 11, 12, 15, 17, 19, 21,
27, 29, 39, 40.
For problems 17, 19,
21, write the equations as a first order system. Then use `pplane6' from MATLAB
to graph the phase diagram and to plot the solution
Homework 8: Due:
Wednesday November 5
Section
5. page 172: 2, 5, 8, 11, 12, 15, 23, 25, 30,
38, 39.
For problems 11, 12 and 15 write the equations as a first order system. Then
use `pplane5' from MATLAB to graph the phase diagram and to plot the solution.
Section 6. page 184: 7, 8, 9, 10, 11, 12, 17, 18.
NOTE: pplane6 will not work on problems 17 and 18, since we can not add a
right hand side to the pplane6 format.
Homework 9: Due:
Wednesday November 12
Section
7. page 190: 2, 5,
10, 13, 15.
Section
8. page 203: 3, 6, 26. (for problems 3
and 6 use `pplane6' and `plot' to check you answers)
Section
9. page 214: 5, 7, 9. (Use `ODE45-oscillator hand out'
and `plot' to check you answers)
Homework 10: Due: Monday
November 24
Chapter 5
: Solving ODEs by series
solutions
Section
1. page 249:
9, 11, 12, 13, 14, 15, 17, 18, 23, 24.
Section
2. page 254: 2, 5, 6, 15,
16, 21
Homework 11: Not Due (but this material is included for the final exam)
Chapter 7
: linear systems of ODE’s
Section 2. page
372: 1, 3, 9, 21, 22, 23
Section 3. page 383: 14, 15, 17, 18, 19 28,
Section 5: page 398: 1, 3 , 6, 15, 16