Course Content

Lecture slides and supplemental materials are posted below.

0. The Fundamentals

• L-1 Mon 22 Aug 2022: welcome to MCS 471
          Julia programs: polyval.jl and binarynum.jl
          Jupyter notebook: polyval.ipynb
• L-2 Wed 24 Aug 2022: floating-point arithmetic
          Julia program: machineprecision.jl
          Jupyter notebook: floatingpoint.ipynb

1. Root Finding

• L-3 Fri 26 Aug 2022: bisection and fixed-point iterations
          Julia programs: bisection.jl and fixedpoint.jl
          Jupyter notebook: bisectcobweb.ipynb
• L-4 Mon 29 Aug 2022: numerical conditioning
          Jupyter notebook: conditioning.ipynb
• L-5 Wed 31 Aug 2022: root finding with Newton's method
          Julia programs: takederivative.jl, newtonupdate.jl, and newtonoperator.jl
          Jupyter notebook: newtonsmethod.ipynb
• L-6 Fri 2 Sep 2022: root finding without derivatives
          Julia programs: secantmethod.jl and falseposition.jl
          Jupyter notebook: rootfindsecant.ipynb
• L-7 Wed 7 Sep 2022: the golden section search method
          a Julia program: goldensection.jl
          a Jupyter notebook: goldensection.ipynb

2. Numerical Linear Algebra

• L-8 Fri 9 Sep 2022: introduction to linear algebra
          a Julia program: lufac.jl
          a Jupyter notebook: linearalgebra.ipynb
• L-9 Mon 12 Sep 2022: condition of linear systems
          a Jupyter notebook: condlinsys.ipynb
• L-10 Wed 14 Sep 2022: row pivoting for numerical stability
          a Julia program: plufac.jl
          a Jupyter notebook: rowpivoting.ipynb
• L-11 Fri 16 Sep 2022: iterative methods for linear systems
          Julia functions and programs: jacobi.jl runjacobi.jl gauss_seidel.jl rungauss_seidel.jl sor.jl, and runsor.jl
          a Jupyter notebook: iterlinsys.ipynb
• L-12 Mon 19 Sep 2022: the Cholesky factorization
          Julia functions and programs: ourcholesky.jl and runcholesky.jl
          a Jupyter notebook: posdefifun.ipynb
• L-13 Wed 21 Sep 2022: conjugate gradient and multivariate Newton
          a Jupyter notebook: multinewton.ipynb

3. Interpolation

• L-14 Fri 23 Sep 2022: polynomial interpolation
          two Julia programs: lagrange.jl and neville.jl
          a Jupyter notebook: interpolation.ipynb
• L-15 Mon 26 Sep 2022: Newton interpolation
          one Julia program: newdivdif.jl
          a Jupyter notebook: newdivdif.ipynb
• L-16 Wed 28 Sep 2022: Chebyshev interpolation and rational approximations
          a Jupyter notebook: chebyshev.ipynb.
• L-17 Fri 30 Sep 2022: cubic splines and Bezier curves
          a Jupyter notebook: bezier.ipynb

4. Fitting Data

• L-18 Mon 3 Oct 2022: least squares
          a Jupyter notebook: leastsquares.ipynb
• L-19 Wed 5 Oct 2022: orthogonalization
          two Julia programs: gsqr.jl and houseqr.jl
          a Jupyter notebook: orthogonalization.ipynb
• L-20 Fri 7 Oct 2022: Krylov and Preconditioned GMRES
          two Julia programs: eigvalpower.jl and gmres.jl
          a Jupyter notebook: krylov.ipynb
• L-21 Mon 10 Oct 2022: nonlinear least squares
          a Julia program: gaussnewton.jl
          a Jupyter notebook: gaussnewton.ipynb