1) Introduction and Motivation Flashcards
1
Q
How are ordinary differentiation and partial differentiation of functions denoted and distinguished
A
- Ordinary differentiation - du/dx
- Partial differentiation - ∂u/∂x and ∂u/∂y
2
Q
What is the Chain Rule for Functions of Multiple Variables
A
3
Q
What is the Chain Rule for Coordinate Transformations
A
4
Q
What is the Taylor Series expansion for a function around the point a
A
5
Q
What is the Wave Equation
A
6
Q
What is the unstead Heat Equation
A
7
Q
What is Laplace’s Equation
A
8
Q
Summarise the derivation of the damped wave equation
A
9
Q
Summarise the derivation of the unstead heat equation
A
10
Q
What are the limitations of using a one-dimensional heat model for a heated spoon
A
- Model assumes insulation at the top and bottom of the spoon, simplifying the actual conditions
- The spoon is surrounded by air at a constant room temperature, making it a three-dimensional heat transfer problem
- Model Justification: This model can still provide a reasonable approximation of the temperature distribution near the middle of the spoon
