Integration and differential equations
Publisher: Bookboon
Published: 2013
ISBN-13: 9788776819705
Table of contents: title: Introduction and Background; title: The Riemann integral; title: The fundamental theorem of calculus; title: Theorems on integration; title: Standard integrals; title: Integration by parts; title: Improper integrals; title: Non-uniqueness of representation; title: Exercises 1; title: The integration of rational functions; title: Improper fractions; title: Linear denominator, Q(x); title: Quadratic denominator, Q(x); title: Cubic denominator, Q(x); title: Exercises 2; title: The integration of trigonometric functions; title: Simple products; title: Powers of sin and cos; title: Rational functions of sin and cos; title: Exercises 3; title: Answers; title: Part II The integration of ordinary differential equations; title: List of Equations; title: Preface; title: What is a differential equation ?; title: The nature and solution of differential equations; title: Classification of ODEs; title: Overview of the equations to be discussed; title: First order ODEs: standard results; title: Separable equations; title: Homogeneous equations; title: The general linear equation; title: First order ODEs: special equations; title: The Bernoulli equation; title: The Clairaut equation; title: The Riccati equation; title: Exact differentials; title: Missing variables; title: Second order ODEs; title: Constant coefficient equations; title: The Euler equation; title: Reduction of order; title: Variation of parameters; title: Finding particular integrals directly; title: Missing variables; title: Exercises 4; title: More general aspects of ODEs; title: Interchanging x and y; title: Singular solutions; title: Uniqueness; title: Exercises 5; title: Answers; title: Index