1. Taylor Polynomials. - 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. - Problems. - 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. - Problems. - 4. Local Analytic Functions. - 1. Logarithms. - 2. Local Solutions to Analytic Equations. - 3. Analytic Linear Differential Equations. - Problems. - 5. Analytic Continuation. - 1. Analytic Continuation Along Paths. - 2. The Monodromy Theorem. - 3. Cauchy's Integral Formula and Theorem. - Problems. Language: English