Oxford Calculus - Heat Equation Derivation

Derive the Heat Equation from physical principles in this 25-minute video lecture by University of Oxford mathematician Dr Tom Crawford. Begin with a one-dimensional cylindrical rod and calculate the change in internal energy for a small section using Liebniz Rule. Learn how to equate this to the difference between heat flux in and out of the segment. Discover the process of deriving the first equation relating temperature to heat flux by dividing both sides by h and taking the limit as h approaches zero. Apply Fourier's Law to rewrite the equation solely in terms of temperature. Explore the extension of the Heat Equation to 2D and 3D scenarios. Access a free worksheet to test your understanding and utilize the Maple Calculator App for checking your work. Gain insights into one of the first partial differential equations studied by undergraduate mathematics students.