Integration and differential equations
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Integrationanddifferential
equations
R.S.Johnson
Downloadfreebooksat
R.S. Johnson
Integration and diferential equations
2
Download free eBooks at bookboon.com
Integration and diferential equations
© 2012 R.S. Johnson & bookboon.com
ISBN 978-87-7681-970-5
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Download free eBooks at bookboon.com
Integration and diferential equations
Contents
Contents
Part I
Preface to these two texts
8
An introduction to the standard methods of elementary integration
9
List of Integrals
10
Preface
11
1
Introduction and Background
12
1.1
he Riemann integral
12
1.2
he fundamental theorem of calculus
17
1.4
heorems on integration
19
1.5
Standard integrals
23
1.6
Integration by parts
26
1.7
Improper integrals
32
1.8
Non-uniqueness of representation
35
Exercises 1
36
2
he integration of rational functions
38
2.1
Improper fractions
38
2.2
Linear denominator, Q(x)
39
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Integration and diferential equations
Contents
2.3
Quadratic denominator, Q(x)
41
2.4
Cubic denominator, Q(x)
44
Exercises 2
48
3
he integration of trigonometric functions
49
3.1
Simple products
49
3.2
Powers of sin and cos
50
3.3
Rational functions of sin and cos
54
Exercises 3
56
Answers
58
he integration of ordinary diferential equations
60
List of Equations
61
Preface
62
1
What is a diferential equation ?
63
1.1
he nature and solution of diferential equations
63
1.2
Classiication of ODEs
63
1.3
Overview of the equations to be discussed
65
Part II
360°
thinking
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