Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra (Res.18-008, MIT OCW): Part III - Linear Algebra: Lecture 7

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 7 - Dot Products

Herb Gross axiomatically defines the dot product as the map of ordered pairs of vectors into the real numbers. Using this definition, Herb next defines and shows how and why to find an orthonormal basis.

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