Chapter 9 Differential Equations - abbymath.comabbymath.com/Classes/CalculusC/Chapter9.pdf ·...
Transcript of Chapter 9 Differential Equations - abbymath.comabbymath.com/Classes/CalculusC/Chapter9.pdf ·...
Chapter 9Differential Equations
9-2 Direction Fields and Euler’s Method9-3 Separable Equations3-8 Exponential Growth and Decay9-4 The Logistic Equation9-5 First-Order Linear Differential Equations
The following notes are for the Calculus C (SDSU Math 151)classes I teach at Torrey Pines High School. I wrote andmodified these notes over several semesters. Theexplanations are my own; however, I borrowed severalexamples and diagrams from the textbooks* my classes usedwhile I taught the course. Over time, I have changed someexamples and have forgotten which ones came from whichsources. Also, I have chosen to keep the notes in my ownhandwriting rather than type to maintain their informalityand to avoid the tedious task of typing so many formulas,equations, and diagrams. These notes are free for use by mycurrent and former students. If other calculus students andteachers find these notes useful, I would be happy to knowthat my work was helpful. - Abby Brown
* , 6th & 4th editions, James Stewart, ©2007 & 1999Brooks/Cole Publishing Company, ISBN 0-495-01166-5 & 0-534-36298-2.(Chapter, section, page, and formula numbers refer to the 6th edition of this text.)
, 5th edition, Roland E. Larson, Robert P. Hostetler, & Bruce H. Edwards,
Calculus: Early Transcendentals
*Calculus ©1994D. C. Heath and Company, ISBN 0-669-35335-3.
SDUHSD
Abby Brown
Calculus II/CSDSU Math 151
www.abbymath.comSan Diego, CA
Note: You will need a calculator for most of thesenotes. On a test, the numbers will be nice enoughthat you won’t need a calculator.
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 1 of 14
2 1 1 2x
2
1
1
2
y
4 3 2 1 1 2 3 4x
4
3
2
1
1
2
3
4
y
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 2 of 14
4 3 2 1 1 2 3 4x
1
1
2
3
4
5
6
7
8
y
4 3 2 1 1 2 3 4x
1
2
3
4
y
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 3 of 14
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 4 of 14
0.2 0.4 0.6 0.8 1.0 1.2 1.4x
1.0
1.5
2.0
2.5
3.0
3.5y
h 1
h 0.5
h 0.25h 0.2
h 0.1
h 0.05h 0.02
Step Size Euler Estimate y 3
1.000 1.50000
0.500 1.28333
0.400 1.24360
0.200 1.16823
0.100 1.13269
0.050 1.11546
0.010 1.10195
0.005 1.10028
0.001 1.09895
n x y
0 1.0 0.00000
1 1.1 0.10000
2 1.2 0.19091
3 1.3 0.27424
4 1.4 0.35117
5 1.5 0.42259
6 1.6 0.48926
7 1.7 0.55176
8 1.8 0.61058
9 1.9 0.66614
10 2.0 0.71877
11 2.1 0.76877
12 2.2 0.81639
13 2.3 0.86184
14 2.4 0.90532
15 2.5 0.94699
16 2.6 0.98699
17 2.7 1.02545
18 2.8 1.06249
19 2.9 1.09820
20 3.0 1.13269
Step Size Euler Estimate y 1
1.000 2.0000000
0.500 2.5000000
0.250 2.8828125
0.200 2.9766400
0.100 3.1874849
0.050 3.3065954
0.020 3.3831761
0.010 3.4096277
0.005 3.4230342
0.001 3.4338479
3 2 1 1 2 3x
3
2
1
1
2
y
1 2 3 4x
1.0
0.5
0.5
1.0
1.5
y
e
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 5 of 14
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 6 of 14
4 2 2 4
4
2
2
4 2 2 4
4
2
2
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 7 of 14
4 2 2x
4
2
2
y
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 8 of 14
4 2 2 4
4
2
2
4
4 2 2 4
4
2
2
4
4 2 2 4
4
2
2
4
4 2 2 4
4
2
2
4
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 9 of 14
1 2 3 40.5 1.5 2.5 3.5Day
50
100
150
200
250
300
25
75
125
175
225
275
P
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 10 of 14
10 20 30 40 50 60 70 80 90 100t
100200300400500600700800900
100011001200
P
10 20 30 40 50 60 70 80 90 100t
100200300400500600700800900
100011001200
P
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 11 of 14
20 40 60 80t
200
400
600
800
1000
P
h 20h 10
h 1
Step Size Euler Estimate P 40 Euler Estimate P 80
20 539 1032
10 647 997
5 695 991
1 725 986
0.1 731 985
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 12 of 14
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 13 of 14
Name: ___________________________________ www.abbymath.com - Ch. 9
Page 14 of 14