12.3 - Solution of the Heat Equation by Separation of Variables
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What does the assumption \( u(x,t) = X(x) T(t) \) represent?
💡 Hint: Think about how we can break the problem into simpler parts.
Name one type of boundary condition we could apply.
💡 Hint: What specifies temperature at the boundaries?
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the method of separation of variables aim to do?
💡 Hint: Think about the word 'separation'.
True or False: The solution to the heat equation can include both sine and cosine functions.
💡 Hint: Recall how we solved the spatial part.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Given a rod of length \( L \) with heat starting at a linear distribution, derive the temperature at later times using separation of variables.
💡 Hint: Begin with writing the equation and identify the boundaries.
How would the solution change if we modified the boundary condition to Neumann conditions?
💡 Hint: Consider how heat flux will reflect in the function behavior.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.