This is a site for Courant's undergraduate course in Numerical Analysis.

**Instructor**: Charles Puelz

**Location and Time**: Tues and Thurs, 11-1215pm, CIWW 201

**Office hours**: Tues, 4-5pm and Thurs, 2-3pm, CIWW 905

**TA**: Tristan Goodwill. Session is held **Friday, 11 - 1215pm, CIWW 517**

**Grader**: Runxi Bai

**Syllabus**: syllabus.pdf

We will be working mainly from the book *An Introduction to Numerical Analysis* by Suli and Mayers. Also, have a look at Trefethen and Bau’s book: *Numerical Linear Algebra*.

I’ll post pdfs of my notes, along with some sample Matlab codes. Some of the codes are from Georg Stadler… thanks!

**1/29**:*sections 1.1, 1.2.*nonlinear equations, fixed point iteration. simple_iteration.pdf.**1/31**:*sections 1.2, 1.3.*fixed point convergence. contractions_and_convergence.pdf, fixed_point_convergence.m**2/5**:*section 1.3.*review of Cauchy and convergent sequences. convergence_and_stability.pdf.**2/7**:*sections 1.3, 1.4.*stability and Newton’s method. stability_and_Newtons.pdf.**2/12**:*sections 1.4, 1.5.*Newton’s and secant method. Newton_and_secant.pdf, parabola_fixed_point.m, Newton_example.m.**2/14**:*sections 1.4, 1.5, 2.1.*finish Newton’s and secant method and start Gaussian elimination. secant_and_Gaussian_elim.pdf**2/19**:*sections 1.6, 2.1, 2.2.*bisection and Gaussian elimination. bisection_and_Gaussian_elim.pdf**2/21**:*sections 2.2, 2.3.*LU factorization. LU_factorization.pdf**2/26**: Computer arithmetic. Computer_arithmetic.pdf**2/28**:*sections 2.3, 2.4*LU with pivoting. LU_with_pivoting.pdf**3/5**:*section 2.7*intro to normed vector spaces. intro_to_norms.pdf**3/7**:*section 2.7*condition numbers. condition_number.pdf**3/12**:*section 2.7*condition numbers continued.**3/14**:*section 2.8*least squares. intro_to_least_squares.pdf**3/26**:*section 2.8, 5.1, 5.2.*also see Trefethen and Bau’s book referenced above. least squares and eigenvalues. least_squares_and_eigenvalues.pdf**4/2**:*section 5.1, 5.2.*Gerschgorin and power method. See also lecture 27 in Trefethen and Bau. power_method.pdf, gerschgorin.m**4/4**:*section 5.5.*QR factorization with Householder reflectors. QR_with_Householder.pdf**4/9**: QR factorization with Givens rotations and intro to Lagrange interpolation. QR_with_Givens.pdf**4/11**:*sections 6.1, 6.2.*Lagrange interpolation. Lagrange_interp.pdf**4/16**:*sections 6.3, 6.4.*Hermite interpolation. Hermite_interp.pdf, InterpolationRunge.m**4/18**:*sections 7.1, 7.2, 7.3.*Newton-Cotes quadrature. Newton-Cotes-quadrature.pdf

**Assignment 1**, due Feb. 21, updated. assignment1.pdf.

**Assignment 2**, due March 7. assignment2.pdf.

**Assignment 3**, due March 26. assignment3.pdf.

**Assignment 4**, due April 18. assignment4.pdf.

**Assignment 5**, due May 3. assignment5.pdf.

The figure on the left is from this Wikipedia page for a Newton fractal. It is a fractal created by applying Newton’s method to a complex valued function.

Here is a link to NYU’s accessibility page: Accessibility.