Main menu: Home | Syllabus | Calendar | Homework | Vocabulary |

Course Calendar

Note:   This calendar is approximate and is subject to revision during the term.
• Week 1 (August 7- August 11)       Sections 1 - 18
• The Algebra of Complex Numbers.
• The Geometry of Complex Numbers.
• The Operations of Conjugation and Absolute Value, and Their Relationships with Sums and Products.
• Polar Form and Exponential Form.
• Roots of Complex Numbers.
• Regions in the Complex Plane.
• Functions of a Complex Variable.
• Limits. Theorems on Limits.
• Limits Involving Infinity. Riemann Sphere.
• Continuity. Basic Properties of Continuous Functions.
• Week 2 (August 14- August 18)       Sections 19 - 39
• Differentiation. Basic Properties of and Formulas for Differentiation.
• Cauchy-Riemann Equations.
• Analytic Functions. Singular points.
• Harmonic Functions. Harmonic Conjugates.
• The Complex Exponential Function.
• The Complex Trigonometric Functions.
• Hyperbolic Functions.
• The Complex Logarithm. Branch Cuts. Logarithmic Identities.
• The Power Function.
• Week 3 (August 21- August 25)       Sections 41 - 59
• Calculus of Complex Functions of a Real Variable.
• Arcs, Simple Closed Curves, and Contours.
• Contour Integrals. Upper Bounds for Moduli of Contour Integrals.
• Antiderivatives and Independence of Path.
• Cauchy-Goursat Theorem. Simply Connected and Multiply Connected Domains. Principle of Deformation of Paths.
• Cauchy Integral Formula. Generalized Cauchy Integral Formula.
• Liouville's Theorem and the Fundamental Theorem of Algebra.
• Maximum Modulus Principle.
• Week 4 (August 28- September 1)       Sections 60 - 72
• The Basics of Sequences and Series.
• Taylor Series Representation of Analytic Functions. Maclaurin Series.
• Laurent Series.
• Uniform Convergence. Continuity of Power Series. Analyticity of Power Series.
• Week 5 (September 4- September 8)       Sections 73 - 78
• Multiplication and Division of Power Series.
• Isolated Singular Points and Residues.
• Cauchy's Residue Theorem.
• Classification of Isolated Singularities.