# infocobuild

## 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 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