Essential Mathematics

Lesson 0: Some general instructions

Lesson 1: Functions1 Quiz

Lesson 2: Derivatives1 Topic

Lesson 3: Vector and Vector operations1 Quiz

Lesson 4: Integrals1 Quiz

Lesson 5: Matrix (Linear Algebra)

Lesson 6: Vector Differential Calculus: Grad, Div, Curl

Lesson 7: Vector Integral Calculus: Gauss theorem, Greens and Stokes

Lesson 8: Tensors and Tensor Notation1 Quiz

Lesson 9: Complex Numbers1 Quiz

Lesson 10: ODEs and its solution1 Quiz

Lesson 11: PDEs and its solution1 Quiz

Lesson 13: Taylor Series1 Quiz

Lesson 14: Fourier Series and FFT1 Quiz

Lesson 15: Numerical Differentiation1 Quiz

Lesson 16: Numerical Integration1 Quiz

Lesson 17: Probability and PDF1 Quiz

Lesson 18: Statistics and Regression1 Quiz
Programming unsteady problem Copy
In this video, you will learn how to solve unsteady problems using the FTCS scheme by programming it. You will also understand the importance of stability criteria and how to choose the time step size.
Assignment: Lesson 11
1. Program FTCS scheme for 1D unsteady heat conduction equation ( if possible try to make your own program and don’t copy the one discussed here). Use boundary conditions as Tbase =300 C, Ttip= 50C, and initial temperature as 30 C. Study the effect of grid size and time step size and prepare a neat report explaining it.
2. This is an optional question but will be good to practice. Try the same problem (problem 1 above) with an implicit scheme (Crank Nicolsen) and compare the result with an explicit scheme and give general comments on stability in the report.
[Upload all the assignments of module 3 as a single PDF file here]