Sequences and Power Series

A book with 'Guidelines for Solutions of Problems'. The book is in English.

1. Decomposition
2. Trigonometric formulæ
3. Notations and conventions
4. Standard power series
5. Power like standard series3
6. Recognition of power like series
7. Exponential like standard series
8. Recognition of exponential like series
9. Integration of trigonometric polynomials
10. Use of pocket calculators

1. Rules of magnitude
2. Square roots etc.
3. Taylor’s formula
4. Standard sequences

1. Sequences
2. Iterative sequences
3. Sequences of functions

1. Denition
2. Rules of calculus
3. Change of index
4. A general advice
5. Elementary standard series
6. Types of Convergence
7. An elaboration on the ow diagram
8. Convergence tests
9. Series of functions

1. Standard power series
2. The structure of standard series
3. Convergence of power series
4. Review of some important theorems
5. Sum by termwise differentiation or integration
6. The method of power series
7. Recursion formulæ and difference equations
8. Second order differential equations (straight tips)
9. Differential equation of second order

1. Squares etc.
2. Powers etc.
3. Differentiation
4. Special derivatives
5. Integration
6. Special antiderivatives
7. Trigonometric formulæ
8. Hyperbolic formulæ
9. Complex transformation formulæ
10. Taylor expansions
11. Magnitudes of functions