Differential calculus and rates of change

Mathematics for Materials and Design

The full set of notes for this topic is here. All materials on this topic can be downloaded here.

Sessions:

1. Revision of differentiation of functions of one variable (see sessions 11-14 in this course for a slower-paced look at this topic)
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction.
     • Product rule.
     • Chain rule.
     • Rates of change and higher-order derivatives.
     • Stationary points and extreme values.


2. Introduction to partial differentiation
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction.
     • Partial differentiation example I.
     • Partial differentiation example II.
     • Higher-order partial derivatives.
     • Higher-order partial derivatives example.
     • Example 1 from the slides.
     • Example 2 from the slides.
     • Example 3 from the slides.
     • Example 4 from the slides.
     • Example 5 from the slides.


3. Applications of partial differention
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction and propagation of uncertainty.
     • Propagation of uncertainty - example I.
     • Propagation of uncertainty - example II.
     • Propagation of uncertainty - example III.
     • Rates of change of multivariate functions.
     • Multivariate rates of change - example I.
     • Multivariate rates of change - example II.