Videos:

• Arclength
• The volume of a body of rotation I.
• The volume of a body of rotation II.
• The lateral surface of a body of rotation
• Polar coordinates, Riemann sphere
• Complex sequences
• Taylor series
• The Riemann surface of z³
• The Riemann surface of e^z
• The Riemann surface of sinz
• Predator-prey models

Dynamical systems playlist:

• 1. Introduction
• 1.1. Fundamental notions
• 1.2. Stability
• 2. Linear equations, linearization
• 2.1. Two real eigenvalues
• 2.2. Complex conjugate pair of eigenvalues
• 2.3. Linearization
• 3. Auxiliary functions
• 3.1. First integral
• 3.1+ Derivative with respect to a system of equations
• 3.2. Lyapunov function
• 3.2+ Definit functions
• 3.3. Auxilliary function for instability
• 4. The Lotka-Volterra system
• 5. The mathematical pendulum
• 6. Bifurcations
• 6.1. Saddle-node bifurcation
• 6.2. Transcritical bifurcation
• 6.3. Pitchfork bifurcation
• 6.4. Hopf bifurcation