Integration and differential equations

Integration and differential equations Download free books at... Johnson Integration and diferential equations Download free eBooks at bookboon.com... Integration and diferential equatio

Integration and differential equations

Download free books at

R.S Johnson

Integration and diferential equations

Download free eBooks at bookboon.com

Integration and diferential equations

© 2012 R.S Johnson & bookboon.com

ISBN 978-87-7681-970-5

Download free eBooks at bookboon.com

Integration and diferential equations

4

Contents

Contents

Preface to these two texts 8

Part I An introduction to the standard methods of elementary integration 9

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

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

5

Contents

2.3 Quadratic denominator, Q(x) 41

2.4 Cubic denominator, Q(x) 44

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

Part II he integration of ordinary diferential equations 60

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

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