Calculus Revisited: Calculus of Complex Variables, Differential Equations, and Linear Algebra MIT

 Education
This course gives an introduction to Complex Variables, Ordinary Differential Equations and Linear Algebra.

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Part I: Complex Variables, Lecture 1: The Complex Numbers
Herb Gross explains the need to define complex numbers. He defines the structure of the system of complex numbers including addition, subtraction, multiplication, division, powers and roots and shows that the system is closed under all these operations.

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Part I: Complex Variables, Lecture 2: Functions of a Complex Variable
Professor Herb Gross discusses functions of a complex variable, limits, derivatives and the CauchyRiemann conditions. Functions of a complex variable that are differentiable everywhere are called analytic functions.

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Part I: Complex Variables, Lecture 3: Conformal Mappings
Herb Gross defines and explains what is meant by a conformal mapping.

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Part I: Complex Variables, Lecture 4: Sequences and Series
Herb Gross defines complex valued functions by means of power series expansions. He shows us how the amazing identity of DeMoivre is derived.

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Part I: Complex Variables, Lecture 5: Integrating Complex Functions
Herb Gross generalizes the definition of the integral of a realvalued function of a real variable to the integral of a complexvalued function of a complex variable and examines the ramifications of this generalization.

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Part II: Differential Equations, Lecture 1: The Concept of a General Solution
Herb Gross defines and illustrates the different types of solutions of a differential equation: General solutions, particular solutions and singular solutions.