lecture02: revision (extrema of surfaces, Taylor's theorem, the chain rule, ...)

Topics covered

• Extrema of functions of one variable
• Classification of extrema
• Functions of $n$ variables
• 2D example 1
• 2D example 2
• 2D example 3
• The Chain rule
• Chain Rule for more variables
• A graphical example
• Chain Rule Derivation
• Chain Rule special case
• Taylor's theorem in 2D
• Taylor's theorem in N-D
• Maxima of N variables
• Quadratic forms
• Notes on maxima and minima
• Calculus of variations
• Functionals
• Integral functionals
• Some simple cases
• Crude Brachystochrone
• Notation