Study Materials | Calculus Revisited: Complex Variables, …
Supplementary Notes for Complex Variables, Differential Equations, and Linear Algebra. Prerequisite materials, detailed proofs, and deeper treatments of selected topics. Invented Number Systems (PDF - 2.9MB) Development of the Complex Numbers (PDF - 1.1MB) Linear Independance (PDF - 3.0MB) Some Notes on Differential Operators (PDF - 4.0MB)
Calculus Revisited: Complex Variables, Differential Equations, and ...
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. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course.
The study of complex variables is both beautiful from a purely mathematical point of view, and provides a powerful tool for solving a wide array of problems arising in applications.
We discussed elementary linear algebra and differential equations, basic complex variables, and some multi-variable calculus. The students took two diagnostic exams on these
Lecture 1: The Complex Numbers | Calculus Revisited: Complex Variables ...
Track Description: 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.
A complex variable is simply a variable whose possible values are allowed to reside in the complex numbers. We’re using the classic text by Churchill and Brown:
Calculus Revisited: Calculus of Complex Variables, Differential ...
Jan 9, 2012 · This course gives an introduction to Complex Variables, Ordinary Differential Equations and Linear Algebra. View the complete course at: http://ocw.mit.edu/RES18-008F11
MIT Calculus Revisited: Calculus of Complex Variables - YouTube
Jul 2, 2014 · This course gives an introduction to Complex Variables, Ordinary Differential Equations and Linear Algebra. View the complete course at: http://ocw.mit.edu/R...
Part III: Linear Algebra | Calculus Revisited: Complex Variables ...
In essence, linear algebra allows us to extend the concept of dimension beyond the usual 1-, 2- and 3-dimensional spaces. More specifically, we define the dimension of an equation to be the number of independent variables it contains, For example if f(x 1 ,x 2 ,x 3 ,x 4 ) and x 1 ,x 2 ,x 3 and x 4 are independent variables then the domain of f ...
Complex Values and Linear Algebra - Mathematics Stack Exchange
Yes: linear algebra works over any field, in particular over the complex numbers. If your variables and coefficients are complex numbers, but the equations are linear on the unknowns, then the usual methods of complex numbers work, exactly as they do over the real numbers.