An edition of Integration and differential equations
(2013)
Integration and differential equations
by R. S. Johnson
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Integration involves ideas, with associated techniques, that are familiar from school mathematics; mastering this branch of mathematics is an essential requirement before moving to more sophisticated concepts and applications.
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Publish Date
2013
Publisher
Bookboon
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Book Details
Table of Contents
Sisältö
Introduction and Background
The Riemann integral
The fundamental theorem of calculus
Theorems on integration
Standard integrals
Integration by parts
Improper integrals
Non-uniqueness of representation
Exercises 1
The integration of rational functions
Improper fractions
Linear denominator, Q(x)
Quadratic denominator, Q(x)
Cubic denominator, Q(x)
Exercises 2
The integration of trigonometric functions
Simple products
Powers of sin and cos
Rational functions of sin and cos
Exercises 3
Answers
Part II The integration of ordinary differential equations
List of Equations
Preface
What is a differential equation ?
The nature and solution of differential equations
Classification of ODEs
Overview of the equations to be discussed
First order ODEs: standard results
Separable equations
Homogeneous equations
The general linear equation
First order ODEs: special equations
The Bernoulli equation
The Clairaut equation
The Riccati equation
Exact differentials
Missing variables
Second order ODEs
Constant coefficient equations
The Euler equation
Reduction of order
Variation of parameters
Finding particular integrals directly
Missing variables
Exercises 4
More general aspects of ODEs
Interchanging x and y
Singular solutions
Uniqueness
Exercises 5
Answers
Index
Edition Identifiers
Work Identifiers
Links outside Open Library
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History
- Created November 3, 2015
- 4 revisions
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| August 22, 2020 | Edited by ISBNbot2 | normalize ISBN |
| November 3, 2015 | Edited by Alice Kirk | Edited without comment. |
| November 3, 2015 | Edited by Alice Kirk | Added new cover |
| November 3, 2015 | Created by Alice Kirk | Added new book. |