|
Course Outline
Text
Strang, Gilbert. Introduction to Applied Mathematics. Wellesley-Cambridge Press. (Table of Contents)
Exams
The exams are tentatively scheduled for Sessions 15, 27 and 39. They are in the normal class and class hour and are OPEN BOOK AND NOTES. There is NO FINAL exam.
Grades
Problem Sets (9): 34%
Exams (3): 66%.
Problem Sets
Exercises in bold in the Problem Sets are especially important and typically present some additional insight on the subject. Any changes to problem sets and due dates will be announced in class and on the course web page. Working together is allowed in problem sets. However, you must write up your results individually and indicate the names of your collaborators. Use of existing solutions is not allowed.
I. Applied Linear Algebra
1. Gaussian elimination and pivots
2. Factorization A = LU and positive definite matrices
3. Positive definite matrices: 2 × 2 (Omit: detailed proof for n × n)
4. Least squares: ATA
5. Systems of springs and masses
II. Equilibrium Equations: Discrete Case
6. Fundamental equations of equilibrium
7. Electrical networks: AT CA (Omit: RLC circuit and Loop currents)
8. Structures in equilibrium: determinate or indeterminate
9. Instability: rigid motion and mechanism
10. Review of Lectures 1–9
11. Minimizing with constraints: Lagrange multipliers (Omit: Projections)
12. Duality. Energy and co-energy
13. Weighted least squares
14. Review for Exam 1
15. EXAM 1: Chapters 1 and 2
III. Equilibrium Equations: Continuous Case
16. Equilibrium of an elastic bar
17. Sturm-Liouville problem, boundary layers and delta function
18. Equilibrium of an elastic beam (Omit: Spline approximations)
19. Potential flow, Stokes and divergence theorems
20. Green's theorem, boundary conditions and Poisson's equation
21. Calculus of variations: introduction (Omit: Complementary minimum principle)
22. Calculus of variations: examples (Omit: Lagrangians and Hamilton's equation)
23. Line integrals, potentials, curl and gradient in 3D (Omit: Electricity and magnetism)
24. Vector calculus and curvilinear coordinate systems
25. Fluid mechanics
26. Review for Exam 2
27. EXAM 2: Chapter 3
IV. Fourier Series and Transforms
28. Fourier coeffiients
29. Sine and cosine series, Parseval’s formula
30. Fourier solution to Laplace equation and convergence
31. Orthogonal functions; Bessel functions
32. Discrete Fourier series and the n roots of unity
33. Convolution rule and signal processing
34. Constant-diagonal matrices
35. Fourier transforms: Plancherel’s formula and uncertainty principle
36. Transform rules (Omit: Integral equations)
37. Solutions of ODE’s and Green’s function
38. Review for Exam 3
39. EXAM 3: Chapter 4
|