EBooks.com, 2012. – 122 p.Contents
Preface to these two texts Part I An introduction to the standard methods of elementary integration List of Integrals Preface
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
The integration of rational functions
Improper fractions
Linear denominator, Q(x)
Quadratic denominator, Q(x)
Cubic denominator, Q(x) Exercises
The integration of trigonometric functions
Simple products
Powers of sin and cos
Rational functions of sin and cos Exercises
Answers
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
More general aspects of ODEs
nterchanging x and y
Singular solutions
Uniqueness Exercises
Answers
Index
