### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

### Course Overview

This year, 2.035 focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

### Prerequisites

18.02, 18.03, or permission of instructor.

### Course Outline

#### Linear Algebra: (8 classes)

- Linear vector spaces
- Euclidean vector spaces
- Linear transformations
- Cartesian tensors

#### Calculus of Variations: (6 classes)

- First variation
- Second variation
- Variational principles in mechanics
- Approximate solutions

### Grading

ACTIVITES | PERCENTAGES |
---|---|

Midterm | 40% |

Final exam | 60% |

### Midterm Exam

Part 1: In-class. You can use your own handwritten class notes only.

Part 2: Take home. You can use Knowles and your own handwritten class notes only.

### Final Exam

The final exam will be entirely take home. All problems will be on calculus of variations. There will be 6 problems of which you can work any 5. You should not devote more than 2 hours on any one problem.