| Class | Date | Topic | Section(s)
|
| 1
| Mo, Jan 28
| Introduction
| 1.1
|
| 2
| We, Jan 30
| Linear algebra review: vector spaces and linear maps.
| 2.1, 2.2
|
| 3
| Fr, Feb 1
| Linear algebra review: linear systems.
| 2.3
|
| 4
| Mo, Feb 4
| Gaussian elimination and LU factorization.
| 2.5
|
| 5
| We, Feb 6
| Introduction to Matlab.
|
|
| 6
| Fr, Feb 8
| Pivoting in LU factorization.
| 2.5
|
| 7
| Mo, Feb 11
| Matrix norms.
| 2.4
|
| 8
| We, Feb 13
| Matrix norms. Introduction to iterative methods.
| 2.4, 2.6
|
| 9
| Fr, Feb 15
| Iterative metods: the Jacobi method.
| 2.6
|
| 10
| Mo, Feb 18
| Iterative metods: the Jacobi and Gauss-Seidel methods.
| 2.6
|
| 11
| We, Feb 20
| Nonlinear equations (root finding): the bisection method.
| 8.1
|
| 12
| Fr, Feb 22
| Nonlinear equations (root finding): the contraction principle.
| 8.1
|
| 13
| Mo, Feb 25
| Nonlinear equations (root finding): the fixed-point method.
| 8.1
|
| 14
| We, Feb 27
|
|
|
review
| 15
| Fr, Feb 29
| first midterm exam
|
|
| 16
| Mo, Mar 3
| Nonlinear equations (root finding): Newton's method.
| 8.1
|
| 17
| We, Mar 5
| Nonlinear equations (root finding): error estimation for Newton's method.
| 8.1 and notes
|
| 18
| Fr, Mar 7
| Nonlinear systems: contractions in higher dimensions.
| 8.2
|
| 19
| Mo, Mar 10
| TBA
|
|
| 20
| We, Mar 12
| Nonlinear systems: fixed point method revisited.
| 8.2
|
| 21
| Fr, Mar 14
| Nonlinear systems: Newton's method.
| 8.2
|
| 22
| Mo, Mar 24
| Taylor's formula.
| notes (read also 5.2)
|
| 23
| We, Mar 26
| Polynomial interpolation.
| notes (read also 5.2)
|
| 24
| Fr, Mar 28
| Lagrange form of interpolation polynomial.
| 5.3
|
| 25
| Mo, Mar 31
| Newton interpolation.
| 5.4
|
| 26
| We, Apr 2
| Error estimation for polynomial interpolation.
| 5.5
|
| 27
| Fr, Apr 4
| Error estimation for polynomial interpolation. Convergence and divergence.
| 5.5
|
| 28
| Mo, Apr 7
| Continuous piecewise polynomial interpolation.
| notes
|
| 29
| We, Apr 9
| review
|
|
| 30
| Fr, Apr 11
| second midterm exam
|
|
| 31
| Mo, Apr 14
| Hermite (differentiable) piecewise polynomial interpolation.
| 12.2
|
| 32
| We, Apr 16
| Spline interpolation.
| 12.1
|
| 33
| Fr, Apr 18
| Numerical derivatives.
| 6.1
|
| 34
| Mo, Apr 21
| Higher-order numerical derivatives.
| 6.2
|
| 35
| We, Apr 23
| Multipoint first-order numerical derivatives.
| 6.3
|
| 36
| Fr, Apr 25
| Numerical integration (I)
| 6.5
|
| 37
| Mo, Apr 28
| Numerical integration (I)
| 6.6
|
| 38
| We, Apr 30
| Numerical solution of ordinary differential equations.
| 9.1
|
| 39
| Fr, May 2
| Single-step and Runge-Kutta methods
| 9.2
|
| 40
| Mo, May 5
| TBA
|
|
| 41
| We, May 7
| TBA
|
|
| 42
| Fr, May 9
| TBA
|
|
| 43
| Mo, May 12
| TBA
|
|
|
| MO, MAY 19 (10:30 AM-12:30 PM)
| FINAL EXAM
| note special date and time
|