Power Series from a Computational Point of View

Inhaltsverzeichnis

• 1. Taylor Polynomials.
• 2. Exponentials, Sines, and Cosines.
• 3. The Geometric Sum.
• 4. Combinations of Taylor Polynomials.
• 5. Complex Taylor Polynomials.
• Problems.
• 2. Sequences and Series.
• 1. Sequences of Real Numbers.
• 2. Sequences of Complex Numbers and Vectors.
• 3. Series of Real and Complex Numbers.
• 4. Picard’s Theorem on Differential Equations.
• 5. Power Series.
• 6. Analytic Functions.
• 7. Preview.
• 3. Power Series and Complex Differentiability.
• 1. Paths in the Complex Plane C.
• 2. Path Integrals.
• 3. Cauchy’s Integral Theorem.
• 4. Cauchy’s Integral Formula and Inequalities.
• 4. Local Analytic Functions.
• 1. Logarithms.
• 2. Local Solutions to Analytic Equations.
• 3. Analytic Linear Differential Equations.
• 5. Analytic Continuation.
• 1. Analytic Continuation Along Paths.
• 2. The Monodromy Theorem.
• 3. Cauchy’s Integral Formula and Theorem.