Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra (Res.18-008, MIT OCW) | Mathematics

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)

The Complex Numbers

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

References

Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra
Instructor: Professor Herbert Gross. Lecture Notes. Assignments and Solutions. This course gives an introduction to Complex Variables, Ordinary Differential Equations and Linear Algebra.