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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 III, Lecture 8 - Orthogonal Functions

Herb Gross defines and illustrates the Fourier representation of a piecewise continuous function.


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