Back To MATH7501 Home

Unit 7: Derivatives, Optimisation and basic ODEs
Unit Outline:
7.1: Derivative definition and meaning
Course Reader:
The paradox of the derivative (3Blue1Brown):
Derivatives... What? (mathbff):
The Smoothest Ride (Vihart):
The Case for Hovercars (Vihart):
Derivatives and Mathematica (lyrnmath):
7.2: Working with derivatives
Course Reader:
Derivative formulas through geometry (3Blue1Brown):
Visualizing the chain rule and product rule (3Blue1Brown):
Derivatives of exponentials (3Blue1Brown):
Derivative using log properties (Khan Academy):
Derivatives... How? (mathbff)
The Chain Rule... How? (mathbff):
What is L'Hospital's rule? (Krista King):
Mean value theorem (Khan Academy):
7.3: Smoothness
Course Reader:
Differentiability implies continuity (Khan Academy):
7.4: Optimization
Course Reader:
Optimization - Calculus (Krista King):
QQQQ

Under construction

Finding Local Maximums/Minimums - Second Derivative Test (PatrickJMT):
Multivariable maxima and minima (Khan Academy - Grant Sanderson):
Optimization with Calculus (Khan Academy):
7.5: Basic Ordinary Differential Equations
Course Reader:
What are differential equations? (Krista King):
Differential equation introduction (Khan Academy):
Solving Separable First Order Differential Equations (PatrickJMT):