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Mastering Differential Equations: The Visual Method (DVD & GUIDEBOOK SET)
Professor Robert L. Devaney is Professor of Mathematics at Boston University, where he has taught for more than 30 years. An expert in dynamical systems, he has delivered more than 1400 invited lectures to audiences around the world. His awards include the Director's Award for Distinguished Teaching Scholars from the National Science Foundation and the Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching from the Mathematical Association of America
24 lectures/30 minutes per lecture
DISC 1
1 What Is a Differential Equation?
2 A Limited-Growth Population Model
Classification of Equilibrium Points
4 Bifurcations-Drastic Changes in Solutions
5 Methods for Finding Explicit Solutions
6 How Computers Solve Differential Equations
DISC 2
7 Systems of Equations-A Predator-Prey System
8 Second-Order Equations-The Mass-Spring System
9 Damped
and Undamped Harmonic Oscillators
10 Beating Modes and Resonance of Oscillators
11 Linear Systems of Differential Equations
12 An Excursion into Linear Algebra
DISC 3
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
DISC 4
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