Mastering Differential Equations: The Visual Method

Offered By: The Great Courses Plus

Tags

Differential Equations Courses Linear Algebra Courses Chaos Theory Courses Bifurcations Courses Nonlinear Dynamics Courses Oscillators Courses

Course Description

Overview

Embark on an amazing mathematical journey in 24 intellectually stimulating and visually engaging half hour lectures.

Syllabus

By This Professor
01: What Is a Differential Equation?
02: A Limited-Growth Population Model
03: Classification of Equilibrium Points
04: Bifurcations-Drastic Changes in Solutions
05: Methods for Finding Explicit Solutions
06: How Computers Solve Differential Equations
07: Systems of Equations-A Predator-Prey System
08: Second-Order Equations-The Mass-Spring System
09: Damped and Undamped Harmonic Oscillators
10: Beating Modes and Resonance of Oscillators
11: Linear Systems of Differential Equations
12: An Excursion into Linear Algebra
13: Visualizing Complex and Zero Eigenvalues
14: Summarizing All Possible Linear Solutions
15: Nonlinear Systems Viewed Globally-Nullclines
16: Nonlinear Systems near Equilibria-Linearization
17: Bifurcations in a Competing Species Model
18: Limit Cycles and Oscillations in Chemistry
19: All Sorts of Nonlinear Pendulums
20: Periodic Forcing and How Chaos Occurs
21: Understanding Chaos with Iterated Functions
22: Periods and Ordering of Iterated Functions
23: Chaotic Itineraries in a Space of All Sequences
24: Conquering Chaos-Mandelbrot and Julia Sets

Taught by

Robert L. Devaney

Related Courses

Nonlinear Dynamics: Mathematical and Computational Approaches
Santa Fe Institute via Complexity Explorer Nonlinear Dynamics 1: Geometry of Chaos
Georgia Institute of Technology via Independent Underactuated Robotics
Massachusetts Institute of Technology via edX Introduction to Nonlinear Dynamics
Indian Institute of Technology Madras via Swayam Biological Engineering: Cellular Design Principles
Purdue University via edX