## COURSE DESCRIPTION

**The two primary goals of many pure and applied scientific
disciplines can be summarized as follows: i) formulate/devise a
collection of mathematical laws (i.e., equations) that model the
phenomena of interest; ii) analyze solutions to these equations in
order to extract information and make predictions. The end result of i)
is often a system of partial differential equations (PDEs).
Thus, ii) often entails the analysis of a system of PDEs. This course
will provide an application-motivated introduction to some fundamental
aspects of both i) and ii). **

**In order to provide a broad overview of PDEs, our investigation of
i) will touch upon a diverse array of equations including a) the Laplace and Poisson equations of electrostatics; b) the diffusion equation, which models e.g. the spreading out of heat energy and chemical diffusion processes; c) the SchrÃ¶dinger equation, which governs the evolution of quantum-mechanical wave functions; d) the wave equation, which models e.g. the propagation of sound waves in the linear acoustical approximation; e) the Maxwell equations of electrodynamics; and other topics as time permits.**

**In our introduction to ii), we will study three important classes of
PDEs that differ markedly in their qualitative and quantitative
properties: elliptic, diffusive, and hyperbolic. In each case, we will
discuss some fundamental analytical tools that will allow us to probe
the nature of the corresponding solutions. **

**Prerequisites:** **18.100; and one of 18.06, 18.700, or 18.701**

**Textbook: ****Partial Differential Equations in Action**** by Sandro Salsa (3rd Edition)**

## RECENT UPDATE

**[02.07.2017]** **Welcome to the start of the semester! Our first lecture falls on this date.**

**[02.10.2017]**** Problem Set #1 has been posted**.

**[02.15.2017]**** Problem Set #2 has been posted**.

**[02.22.2017]**** Problem Set #3 has been posted. Solutions to Problem Set #1 have been posted.**

**[03.1.2017]**** Problem Set #4 has been posted**.

**[03.15.2017]**** Problem Set #5 has been posted**. **Solutions to Problem Set #2 have been posted.**

**[03.21.2017]**** Solutions to Problem Set #3 have been posted.**

**[03.22.2017]**** Problem Set #6 has been posted**.

**[03.23.2017]**** Solutions to Problem Set #4 have been posted.**

**[03.24.2017]**** Practice Midterm and Formula Sheet have been posted (click on the "Exams" link at the top).**

**[03.24.2017]**** Note: Your midterm will take place in class on Thursday April 6.**

**[04.03.2017]**** Solutions to the Practice Midterm have been posted (click on the "Exams" link at the top).**

**[04.06.2017]**** Solutions to Problem Set #5 have been posted.**

**[04.12.2017]**** Problem Set #7 has been posted**.

**[04.20.2017]**** Problem Set #8 has been posted**. ** Solutions to Problem Set #6 have been posted.**

**[04.26.2017]**** Problem Set #9 has been posted**.

**[04.27.2017]**** Solutions to Problem Set #7 have been posted.**

**[05.03.2017]**** Problem Set #10 (the last one!) has been posted**.

**[05.04.2017]**** Solutions to Problem Set #8 have been posted.**

**[05.06.2017]**** Solutions to the in-class Midterm have been posted.**

**[05.11.2017]**** Solutions to Problem Set #9 have been posted.**

**[05.15.2017]**** Practice final exam with solutions has been posted.**

**[05.17.2017]**** Solutions to Problem Set #10 have been posted.**