Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra (Res.18-008, MIT OCW): Part I - Complex Variables: Lecture 1

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 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.

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