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.


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


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.