§4.1. Derivatives of Complex-Valued Functions of §4.2. Definite Integrals of Functions w §4.3. Paths §4.4. Path Integrals §4.5. Examples §4.6. Upper Bounds for Integrals §4.7. Primitive Functions §4.8. Examples §4.9. Cauchy Integral Theorem §4.10. Proof of Cauchy Integral Theorem §4.11. Extended Cauchy Integral Theorem §4.12. Cauchy Integral Formula §4.13. Derivatives of Analytic Functions §4.14. Liouville’s Theorem §4.15. Maximum Modulus Principle

§5.1. Convergence of Series §5.2. Taylor Series §5.3. Examples §5.4. Laurent Series §5.5. Examples §5.6. Absolute and Uniform Convergence of Power Series §5.7. Continuity of Sums of Power Series §5.8. Integration and Differentiation of Power Series §5.9. Uniqueness of Series Representations §5.10. Multiplication and Division of Power Series

§6.1. Residues §6.2. Cauchy’s Residue Theorem §6.3. Using a Single Residue §6.4. The Three Types of Isolated Singular Points §6.5. Residues at Poles §6.6. Examples §6.7. Zeros of Analytic Functions §6.8. Uniquely Determined Analytic Functions §6.9. Zeros and Poles §6.10. Behavior of f Near Isolated Singular Points §6.11. Reflection Principle

§7.1. Evaluation of Improper Integrals §7.2. Examples §7.3. Improper Integrals From Fourier Analysis §7.4. Jordan’s Lemma §7.5. Indented Paths §7.6. An Indentation Around a Branch Point §7.7. Definite Integrals Involving Sine and Cosine §7.8. Argument Principle §7.9. Rouche’s Theorem

§8.1. Conformal mappings §8.2. Unilateral Functions §8.3. Local Inverses §8.4. Affine Transformations §8.5. The Transformation = /1 zw §8.6. Mappings by /1 z §8.7. Fractional Linear Transformations §8.8. Cross Ratios §8.9. Mappings of the Upper Half Plane

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