# [APMA 3102] applied mathematics II (PDE)

- Departments: Applied Physics and Applied Mathematics
- Professors: Adam Sobel and Michael Tippett

Professor Tippett is not one of the best professors I had nor one of the worst. PDE is a very challenging class for someone who first takes it. The textbook chosen for this class is not good at explaining the materials, and Professor Tippett did it even worse. It is very hard to follow him during lectures because he did not give students a big picture of what they are studying, and he constantly makes mistakes during derivation. (Constant mistakes during derivation are very dangerous for students who first learn PDE. Students ended up thinking themselves even though they were right.)

I learned most of the materials from watching youtube videos and trying to figure my way out in the hard-to-understand textbook.

#### Workload:

The workload is not that much. To be honest, I doubt most students can keep up with heavy workload based on what they learned from the class.

Wow this class is such a blast. I have some exposure to partial differential equations through my research in computer science but this class clears up a lot of topics I haven't been able to understand previously. The materials covered in the class provide just enough motivation for me to go on and explore more aspects of PDE that I will encounter in my career. This class is an example of how an engineering class at Columbia should be -- perfect topics, perfect professor, the right combination of intuition, theory, and practical problem solving.

Adam Sobel is one of the best math teacher I have ever had at Columbia. He is clear, concise, and considerate. Every time we start a new topic he always states the motivation of the topic so we get the idea of why things are derived the way they are. Every time we hit some giant and unthinkable formulae (which arise from Fourier Series, Rayleigh Quotient, or Green's function), he would pause and make sure that we don't just see a bunch of garbage on the board but some profound and meaningful formulae that can be explained with intuition. At the end of the day I always walk out of the class having understood something interesting, but that only makes me craving for more. Man, I have always wondered, why this guy is so good at making me understanding things, I mean complicated things like Green's function, so easily? No doubt, he has been working with these equations for decades, and he has seen real-world problems that PDE models can be applied, in atmospheric science. Who else would be more perfect to teach a class like this, besides a professor who knows the topic so well and balanced, theoretically and practically, and is capable of explaining things so clear like a mirror?

The textbook we used is 4th / 5th edition Haberman. Really really good book. The book alone already provides great examples and great insights about several problems in PDE. Very recommended.

The class does come with a price (besides your tuition). The exam will be hard, and I mean it can be really hard. You will wonder why that one question is even asked, and how you could even start answering it. This is because Sobel wants you to understand things not only practically but also intuitively. Therefore, some questions in the exam will only be solved if you have solid qualitative understanding of the material. I personally think that the quality of the class as a whole far outweighs the fact that the exam can be very challenging though.

No matter where you come from, if you are interested in PDE, don't miss your chance to take the class with him. It will be totally worth of your time and effort.

#### Workload:

9 problem sets. Somewhere between 1 - 2 weeks each.

1 midterm

1 final

## Directory Data

Dept/Subj | Directory Course | Professor | Year | Semester | Time | Section |
---|---|---|---|---|---|---|

APAM / APMA | APAM APMA E3102: Applied Mathematics II: Pde's: Applied Mathematics II | Adam Sobel | 2013 | Spring | TR / 4:10- 5:25 PM | 1 |

APAM / APMA | APAM APMA E3102: Applied Mathematics II: Pde's: Applied Mathematics II | Adam Sobel | 2012 | Spring | TR / 4:10- 5:25 PM | 1 |

APAM / APMA | APAM APMA E3102: Applied Mathematics II: Pde's: Applied Mathematics II | Ian Langmore | 2011 | Spring | TR / 11:00-12:15 PM | 1 |

APAM / APMA | APAM APMA E3102: Applied Mathematics II: Pde's: Applied Mathematics II | Ian Langmore | 2010 | Spring | TR / 11:00-12:15 PM | 1 |

APAM / APMA | APAM APMA E3102: Applied Mathematics II: Pde's: Applied Mathematics II | Matias Courdurier | 2009 | Spring | TR / 11:00-12:15 PM | 1 |