Integration and differential equations
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776819705
Table of contents: title: Content; title: 1. Introduction and Background; title: 1.1. The Riemann integral; title: 1.2. The fundamental theorem of calculus; title: 1.3. Theorems on integration; title: 1.4. Standard integrals; title: 1.5. Integration by parts; title: 1.6. Improper integrals; title: 1.7. Non-uniqueness of representation; title: 1.8. Exercises 1; title: 2. The integration of rational functions; title: 2.1. Improper fractions; title: 2.2. Linear denominator, Q(x); title: 2.3. Quadratic denominator, Q(x); title: 2.4. Cubic denominator, Q(x); title: 2.5. Exercises 2; title: 3. The integration of trigonometric functions; title: 3.1. Simple products; title: 3.2. Powers of sin and cos; title: 3.3. Rational functions of sin and cos; title: 3.4. Exercises 3; title: 3.5. Answers; title: 4. Part II The integration of ordinary differential equations; title: 5. List of Equations; title: 6. Preface; title: 7. What is a differential equation ?; title: 7.1. The nature and solution of differential equations; title: 7.2. Classification of ODEs; title: 7.3. Overview of the equations to be discussed; title: 8. First order ODEs: standard results; title: 8.1. Separable equations; title: 8.2. Homogeneous equations; title: 8.3. The general linear equation; title: 9. First order ODEs: special equations; title: 9.1. The Bernoulli equation; title: 9.2. The Clairaut equation; title: 9.3. The Riccati equation; title: 9.4. Exact differentials; title: 9.5. Missing variables; title: 10. Second order ODEs; title: 10.1. Constant coefficient equations; title: 10.2. The Euler equation; title: 10.3. Reduction of order; title: 10.4. Variation of parameters; title: 10.5. Finding particular integrals directly; title: 10.6. Missing variables; title: 10.7. Exercises 4; title: 11. More general aspects of ODEs; title: 11.1. Interchanging x and y; title: 11.2. Singular solutions; title: 11.3. Uniqueness; title: 11.4. Exercises 5; title: 11.5. Answers; title: 11.6. Index