## Fall 2018 - Scientific Computing I

Updated 11/20/2018. Final Exam Main references__Principles of scientific computing__, Bindel, Goodman here.__Numerical optimization__, Nocedal, Wright here.__Afternotes in Numerical Analysis__, Stewart here.__Lecture notes on ODEs__, Strain here.

__Numerical Computing with IEEE Floating Point Arithmetic__by M. Overton Available online here__Numerical analysis__by T. Sauer,- David Bindel's class page

- 08/28
__Sources of error__Chpt 2 from Bindel, Goodman here, - 08/30
__Sources of error__Chpt 2 from Bindel, Goodman. - HW1
- 09/04
__Linear Algebra I__Chpt 4 from Bindel, Goodman.
Vector spaces, Matrices and linear transformations.
- HW2
- 09/06
__Linear Algebra I__Chpt 4 from Bindel, Goodman.
Adjoint operators, vector and matrix norms,eigenvalue problem.
- 09/11
__Linear Algebra I__Chpt 4 from Bindel, Goodman.
Eigenvalue problem, Differentiation and perturbation theory, variational principles.
- 09/13
__Lecture moved to 09/11__Software and coding principles.
Discussion of a Plane Wave problem to illustrate.
- 09/18
__Linear Algebra I__Chpt 4 from Bindel, Goodman.
Variational principles for symmetric eigenvalue problems, least squares, singular values and principal components.
- HW3
- 09/20
__Linear Algebra I__Chpt 4 from Bindel, Goodman.
Singular value decomposition, condition number.
- 09/25
__Linear Algebra II__Chpt 5 from Bindel, Goodman.
Gauss elimination, LU decomposition.
- HW4
- 09/27
__Linear Algebra II__Chpt 5 from Bindel, Goodman.
Choleski factorization, Least squares and QR factorization.
- 10/02
__Nonlinear equations__Chpt 11 from Nocedal, Wright.
Comments on software. Newton's method.
- 2nd UPDATED HW5
- 10/04
__Nonlinear equations__Chpt 11 from Nocedal, Wright.
Inexact Newton methods and Broyden's method.
- 10/09
__Nonlinear equations__Chpt 11 from Nocedal, Wright.
Tensor methods, a hybrid method (From Lecture 5 in the Afternotes).
Merit functions, line search methods.
- HW6, see Bisection function, Hybrid method function.
- 10/11
__Nonlinear equations__Chpt 11 from Nocedal, Wright.
Trust regions, Continuation/homotopy methods.
- 10/16
__Fundamentals of unconstrained optimization__Chpt 2 from Nocedal, Wright. - HW7
- 10/18
__Line search methods__Chpt 3 from Nocedal, Wright. - 10/23
__Line search methods__Chpt 3 from Nocedal, Wright. - HW8
- 10/25
__Trust-region methods__Chpt 4 from Nocedal, Wright. - 10/30
__Trust-region methods__Chpt 4 from Nocedal, Wright. - HW9 and codes.
- 11/01
__Conjugate Gradient methods__Chpt 5 from Nocedal, Wright.
Conjugate direction method. Basic properties of the CG method.
- 11/06
__Conjugate Gradient methods__Chpt 5 from Nocedal, Wright.
Practical CG method. Rate of convergence. Preconditioning.
- No HW
- 11/08
__Odrinary Differential Equations__ - 11/13
__Odrinary Differential Equations__ - 11/15
__Odrinary Differential Equations__ - 11/20
__Conjugate Gradient methods__Chpt 5 from Nocedal, Wright.
Practical precontinioners. Nonlinear CG methods.
- HW10

## Teaching at UMD

- 2018 Spring Introduction to Numerical Analysis (Undergrad). Material posted on ELMS-Canvas Here, some details here.

## Teaching at NYU

- Analysis Section 003 (Spring 2016).
- Calculus 3 Section 004 (Fall 2015).
- Math for Econ 1 Section 001 (Spring 2015).
- Calculus 1 Section 046 (Fall 2014).

## Teaching activities at UPMC - Paris 6