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

Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra (Res.18-008, MIT OCW). This consists of 20 video lectures given by Professor Herbert Gross, providing an introduction to Complex Variables, Ordinary Differential Equations and Linear Algebra. Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. (from ocw.mit.edu)

Part I, 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.


Go to the Course Home or watch other lectures:

Part I - Complex Variables (5)
Part I, Lecture 1 - The Complex Numbers
Part I, Lecture 2 - Functions of a Complex Variable
Part I, Lecture 3 - Conformal Mappings
Part I, Lecture 4 - Sequences and Series
Part I, Lecture 5 - Integrating Complex Functions
Part II - Differential Equations (7)
Part II, Lecture 1 - The Concept of a General Solution
Part II, Lecture 2 - Linear Differential Equations
Part II, Lecture 3 - Solving the Linear Equations L(y) = 0; Constant Coefficients
Part II, Lecture 4 - Undetermined Coefficients
Part II, Lecture 5 - Variations of Parameters
Part II, Lecture 6 - Power Series Solutions
Part II, Lecture 7 - Laplace Transforms
Part III - Linear Algebra (8)
Part III, Lecture 1 - Vector Spaces
Part III, Lecture 2 - Spanning Vectors
Part III, Lecture 3 - Constructing Bases
Part III, Lecture 4 - Linear Transformations
Part III, Lecture 5 - Determinants
Part III, Lecture 6 - Eigenvectors
Part III, Lecture 7 - Dot Products
Part III, Lecture 8 - Orthogonal Functions