MAT 1236 Calculus III Section 14.5 The Chain Rule
HW.. WebAssign 14.5 Quiz: 14.5
Preview The Chain Rule for multivariable functions Look only at how to memorize the formulas Why the formulas actually work depends on 14.4 which we do not cover.
The Doppler Effect
1 variable Vs 2 variables
The Chain Rule
The Chain Rule: Case 1
Example 1 Find
The Chain Rule: Case 2
Example 2 Find
Other Cases Similar
Example 3 Find in terms of partial derivatives in x and y (i.e. ) Note that the function f is not given explicitly.
Example 4 (Implicit Differentiation) Suppose y is a function in x and is given implicitly by the equation What is the relationship between
Example 4 (Implicit Differentiation) Suppose y is a function in x and is given implicitly by the equation What is the relationship between
Example 4 (Implicit Differentiation) Suppose y is a function in x and is given implicitly by the equation
Example 4 (Implicit Differentiation) Suppose y is a function in x and is given implicitly by the equation Show that
Where to use? (If time permitted) Taken from MAT 3724 Applied Analysis (Mathematical Physics)
Wave Equation: Set Up Assumptions:
Thought Experiment
What would you expect to happen?
Thought Experiment
Modeling Wave Propagation in a String
Solution: d’Alembert’s Formula