AM205

Course material for APMTH 205 (numerical methods) lectured in Fall 2022 at Harvard SEAS.

Acknowledgements

The material is based on that of previous years lectured by Prof. Chris Rycroft (2014-2021), Dr. David Knezevic (2013), and Prof. Efthimios Kaxiras (until 2012).

Lectures

ZIP archive with interactive HTML slides: am205_2022_slides.zip

• Unit 0. Introduction (PDF | HTML | Examples)
• Unit 1. Data fitting (PDF | HTML | Examples)
• Unit 2. Numerical linear algebra (PDF | HTML | Examples)
• Unit 3. Numerical calculus (PDF | HTML | Examples)
• Unit 4. Optimization (PDF | HTML | Examples)
• Unit 5. Eigenvalue problems and iterative methods (PDF | HTML | Examples)

Homework

• HW0. Introduction (PDF | Solution | Source)
• HW1. Data fitting (PDF | Data | Solution | Source)
• HW2. Numerical linear algebra (PDF | Data | Solution | Source)
• HW3. Numerical calculus (PDF | Solution | Source)
• HW4. PDEs, nonlinear equations, optimization (PDF | Solution | Source)
• HW5. PDEs, optimization, iterative methods (PDF | Data | Solution | Source)

Quizzes

• Quiz 1. Data fitting (PDF | Solution | Source)
• Quiz 2. Numerical linear algebra (PDF | Solution | Source)
• Quiz 3. Numerical calculus (PDF | Solution | Source)
• Quiz 4. Optimization (PDF | Solution | Source)

Gallery

These images have been used to illustrate the material. The code to generate them is available in media. Click on the image to see the relevant slide.

Unit 0. Introduction

• unit0/fd.py

  

Unit 1. Data fitting

• unit1/data.py

  

• unit1/fit_2d.py

  

• unit1/monomials.py

  

• unit1/lagrange_two.py

  

• unit1/runge.py

  
  

• unit1/cheb.py

  

• unit1/cheb_conv.py

  

• unit1/lebesgue.py

  

• unit1/data_anim.py

  

• unit1/nonpoly_fit.py

  

• unit1/invar_anim.py

  

• unit1/underlstsq.py

  

• unit1/nonpoly_fit_abs.py

  

• unit1/nonlin_lstsq.py

  

Unit 2. Numerical linear algebra

• unit2/electric_circuit.py

  

• unit2/spring.py

  

• unit2/norm_inf.py

  

• unit2/unit_circle_norm.py

  

• unit2/householder.py

  

• unit2/svd_drawing.py

  

• unit2/pca_dataset.py

  

• unit2/pcavideo/pcavideo.py

  
  
  

Unit 3. Numerical calculus

• unit3/quad_rect.py

  

• unit3/heat_1d.py

  

• unit3/heat_1d_time.py

  

• unit3/lagrange_blowup.py

  

• unit3/legendre.py

  

• unit3/legendre_roots.py

  

• unit3/sparsity.py

  

• unit3/lotka_volterra.py

  

• unit3/lambdastab.py

  

• unit3/stabregion_euler.py

  

• unit3/stabregion.py

  

• unit3/stabregion_fehlberg.py

  

• unit3/shooting.py

  

• unit3/conic.py

  

• unit3/advection_exp.py

  

• unit3/char_bc.py

  

• unit3/char_div.py

  

• unit3/grid.py

  

• unit3/wave.py

  

• unit3/sawtooth_mode.py

  

• unit3/theta_stab.py

  

• unit3/grid_xy.py

  

• unit3/grid_xy_flat.py

  

• unit3/poisson.py

  

Unit 4. Optimization

• unit4/bisection.py

  

• unit4/linear_prog.py

  

• unit4/global.py

  

• unit4/fixed.py

  

• unit4/coercive.py

  

• unit4/convex.py

  

Unit 5. Eigenvalue problems and iterative methods

• unit5/harmonics.py

  

• unit5/multigrid.py