Differential Calculus Notes For Mathematics 100 and 180

Overview & Synopsis

The contents include, The basics, Limits, Derivatives, Applications
of derivatives, Numbers, Sets, Other important sets, Functions, Parsing
formulas, Inverse functions, Another limit and computing velocity, The limit of
a function, Calculating limits with limit laws, Continuity, Revisiting tangent
lines, Interpretations of the derivative, Proofs of the arithmetic of
derivatives, Derivatives of Exponential Functions, Derivatives of trigonometric
functions, The natural logarithm, Implicit Differentiation, Inverse
Trigonometric Functions, The Mean Value Theorem, Higher order derivatives,
Velocity and acceleration, Related rates, Optimisation, Sketching graphs,
Introduction to antiderivatives, Carbon dating, Population growth, Some
examples, Further examples, The error in the Taylor polynomial approximations,
Local and global maxima and minima, Finding global maxima and minima,
Symmetries, A checklist for sketching, Sketching examples, Standard examples,
Variations.