This is a complete set of Maple lessons for an undergraduate course in Complex Analysis or Complex Variables. Each lesson develops the theory behind its topic and provides numerous worked examples. All principles are illustrated with Maple graphics, including conformal maps, contour plots and fractals. These 68 lessons were developed by Dr. John Mathews of the California State University Fullerton as part of his book, Complex Analysis: for Mathematics & Engineering, 4th Ed, 2001, co-authored with Dr. Russell Howell of Westmont College. Download the entire course Preview or download individual lessons below

	Chapter 1 Complex Numbers Section 1.1 The Origin of Complex Numbers preview download Section 1.2 The Algebra of Complex Numbers preview download Section 1.3 The Geometry of Complex Numbers preview download Section 1.4 The Geometry of Complex Numbers 2 preview download Section 1.5 The Algebra of Complex Numbers, Revisited preview download Section 1.6 The Topology of Complex Numbers preview download Chapter 2 Complex Functions Section 2.1 Functions of a Complex Variable preview download Section 2.2 Transformations and Linear Mappings preview download Section 2.3 The Mappings z^n and z^(1/n) preview download Section 2.4 Limits and Continuity preview download Section 2.5 Branches of Functions preview download Section 2.6 The Reciprocal Transformation preview download Chapter 3 Analytic and Harmonic Functions Section 3.1 Differentiable Functions preview download Section 3.2 The Cauchy-Riemann Equations preview download Section 3.3 Harmonic Functions preview download Chapter 4 Sequences, Series, and Julia and Mandelbrot Sets Section 4.1 Sequences and Series preview download Section 4.2 Julia and Mandelbrot Sets preview download Section 4.3 Geometric Series and Convergence Theorems preview download Section 4.4 Power Series Functions preview download Chapter 5 Elementary Functions Section 5.1 The Complex Exponential Function preview download Section 5.2 Branches of the Complex Logarithm preview download Section 5.3 Complex Exponents preview download Section 5.4 Trigonometric and Hyperbolic Functions preview download Section 5.5 Inverse Trigonometric and Hyperbolic Functions preview download Chapter 6 Complex Integration Section 6.1 Complex Integrals preview download Section 6.2 Contours and Contour Integrals preview download Section 6.3 The Cauchy-Goursat Theorem preview download Section 6.4 The Fundamental Theorems of Integration preview download Section 6.5 Integral Representations for Analytic Functions preview download Section 6.6 The Theorems of Morera and Liouville and Some Applications preview download Chapter 7 Taylor and Laurent Series Section 7.1 Uniform Convergence preview download Section 7.2 Taylor Series Representations preview download Section 7.3 Laurent Series Representations preview download Section 7.4 Singularities, Zeros and Poles preview download Section 7.5 Applications of Taylor and Laurent Series preview download Chapter 8 Residue Theory Section 8.1 The Residue Theorem preview download Section 8.2 Calculation of Residues preview download Section 8.3 Trigonometric Integrals preview download Section 8.4 Improper Integrals of Rational Functions preview download Section 8.5 Improper Integrals of Trigonometric Functions preview download Section 8.6 Indented Contour Integrals preview download Section 8.7 Integrands with Branch Points preview download Section 8.8 The Argument Principle and Rouche's Theorem preview download Chapter 9 Conformal Mapping Section 9.1 Basic Properties of Conformal Mappings preview download Section 9.2 Bilinear Transformations preview download Section 9.3 Mapping Involving Elementary Functions preview download Section 9.4 Mapping Involving Trigonometric Functions preview download Chapter 10 Applications of Harmonic Functions Section 10.1 Preliminaries preview download Section 10.2 Invariance of Laplace's Equation and the Dirichlet Problem preview download Section 10.3 Poisson's Integral for the Upper Half-Plane preview download Section 10.4 Two-Dimensional Mathematical Models preview download Section 10.5 Steady State Temperatures preview download Section 10.6 Two Dimensional Electrostatics preview download Section 10.7 Two-Dimensional Fluid Flow preview download Section 10.8 The Joukowski Airfoil preview download Section 10.9 Schwarz-Christoffel Transformation preview download Section 10.10 Images of a Fluid Flow preview download Section 10.11 Sources and Sinks preview download Chapter 11 Fourier Series and the Laplace Transform Section 11.1 Fourier Series preview download Section 11.2 The Dirichlet Problem for the Section Disk preview download Section 11.3 Vibrations in Mechanical Systems preview download Section 11.4 The Fourier Transform preview download Section 11.5 The Laplace Transform preview download Section 11.6 Laplace Transforms of Derivatives and Integrals preview download Section 11.7 Shifting Theorems and the Step Function preview download Section 11.8 Exercises for Multiplication and Division by t preview download Section 11.9 Inverting the Laplace Transform preview download Section 11.10 Convolution preview download