# Download Integration and differential equations by R S Johnson

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### Download Integration and differential equations by R S Johnson

### Table of Content:

- 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 andy
- Singular solutions
- Uniqueness
- Exercises 5
- Answers
- Index

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