Sequences and Power Series
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776812393
Table of contents: title: Content; title: 1. Repetition of important formulæ; title: 1.1. Decomposition; title: 1.2. Trigonometric formulæ; title: 1.3. Notations and conventions; title: 1.4. Standard power series; title: 1.5. Power like standard series3; title: 1.6. Recognition of power like series; title: 1.7. Exponential like standard series; title: 1.8. Recognition of exponential like series; title: 1.9. Integration of trigonometric polynomials; title: 1.10. Use of pocket calculators; title: 2. Real sequences, folklore; title: 2.1. Rules of magnitude; title: 2.2. Square roots etc.; title: 2.3. Taylor’s formula; title: 2.4. Standard sequences; title: 3. Practical methods for sequences; title: 3.1. Sequences; title: 3.2. Iterative sequences; title: 3.3. Sequences of functions; title: 4. General series; methods in problems; title: 4.1. Denition; title: 4.2. Rules of calculus; title: 4.3. Change of index; title: 4.4. A general advice; title: 4.5. Elementary standard series; title: 4.6. Types of Convergence; title: 4.7. An elaboration on the ow diagram; title: 4.8. Convergence tests; title: 4.9. Series of functions; title: 5. Power series; methods in solution of problems; title: 5.1. Standard power series; title: 5.2. The structure of standard series; title: 5.3. Convergence of power series; title: 5.4. Review of some important theorems; title: 5.5. Sum by termwise differentiation or integration; title: 5.6. The method of power series; title: 5.7. Recursion formulæ and difference equations; title: 5.8. Second order differential equations (straight tips); title: 5.9. Differential equation of second order; title: 6. Formulæ; title: 6.1. Squares etc.; title: 6.2. Powers etc.; title: 6.3. Differentiation; title: 6.4. Special derivatives; title: 6.5. Integration; title: 6.6. Special antiderivatives; title: 6.7. Trigonometric formulæ; title: 6.8. Hyperbolic formulæ; title: 6.9. Complex transformation formulæ; title: 6.10. Taylor expansions; title: 6.11. Magnitudes of functions