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

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# AM205

Course material for APMTH 205 (numerical methods)
lectured in Fall 2022 at [Harvard SEAS](https://seas.harvard.edu/applied-mathematics/courses).

## Acknowledgements

The material is based on that of previous years lectured by
[Prof. Chris Rycroft](https://people.math.wisc.edu/~chr/am205) (2014-2021),
[Dr. David Knezevic](https://courses.seas.harvard.edu/courses/am205/fall13) (2013),
and Prof. Efthimios Kaxiras (until 2012).

## Lectures

ZIP archive with interactive HTML slides: [am205_2022_slides.zip](https://pkarnakov.github.io/am205/slides/am205_2022_slides.zip)

* Unit 0. Introduction
  ([PDF](https://pkarnakov.github.io/am205/slides/am205_unit0.pdf)
  | [HTML](https://pkarnakov.github.io/am205/slides/unit0)
  | [Examples](examples/unit0))
* Unit 1. Data fitting
  ([PDF](https://pkarnakov.github.io/am205/slides/am205_unit1.pdf)
  | [HTML](https://pkarnakov.github.io/am205/slides/unit1)
  | [Examples](examples/unit1))
* Unit 2. Numerical linear algebra
  ([PDF](https://pkarnakov.github.io/am205/slides/am205_unit2.pdf)
  | [HTML](https://pkarnakov.github.io/am205/slides/unit2)
  | [Examples](examples/unit2))
* Unit 3. Numerical calculus
  ([PDF](https://pkarnakov.github.io/am205/slides/am205_unit3.pdf)
  | [HTML](https://pkarnakov.github.io/am205/slides/unit3)
  | [Examples](examples/unit3))
* Unit 4. Optimization
  ([PDF](https://pkarnakov.github.io/am205/slides/am205_unit4.pdf)
  | [HTML](https://pkarnakov.github.io/am205/slides/unit4)
  | [Examples](examples/unit4))
* Unit 5. Eigenvalue problems and iterative methods
  ([PDF](https://pkarnakov.github.io/am205/slides/am205_unit5.pdf)
  | [HTML](https://pkarnakov.github.io/am205/slides/unit5)
  | [Examples](examples/unit5))

## Homework

* HW0. Introduction
  ([PDF](https://pkarnakov.github.io/am205/homework/am205_hw0.pdf)
  | [Solution](https://pkarnakov.github.io/am205/homework/am205_hw0_sol.pdf)
  | [Source](homework/hw0_intro))
* HW1. Data fitting
  ([PDF](https://pkarnakov.github.io/am205/homework/am205_hw1.pdf)
  | [Data](https://pkarnakov.github.io/am205/homework/am205_hw1_data.zip)
  | [Solution](https://pkarnakov.github.io/am205/homework/am205_hw1_sol.pdf)
  | [Source](homework/hw1_data_fitting))
* HW2. Numerical linear algebra
  ([PDF](https://pkarnakov.github.io/am205/homework/am205_hw2.pdf)
  | [Data](https://pkarnakov.github.io/am205/homework/am205_hw2_data.zip)
  | [Solution](https://pkarnakov.github.io/am205/homework/am205_hw2_sol.pdf)
  | [Source](homework/hw2_linear))
* HW3. Numerical calculus
  ([PDF](https://pkarnakov.github.io/am205/homework/am205_hw3.pdf)
  | [Solution](https://pkarnakov.github.io/am205/homework/am205_hw3_sol.pdf)
  | [Source](homework/hw3_calculus))
* HW4. PDEs, nonlinear equations, optimization
  ([PDF](https://pkarnakov.github.io/am205/homework/am205_hw4.pdf)
  | [Solution](https://pkarnakov.github.io/am205/homework/am205_hw4_sol.pdf)
  | [Source](homework/hw4_optimization))
* HW5. PDEs, optimization, iterative methods
  ([PDF](https://pkarnakov.github.io/am205/homework/am205_hw5.pdf)
  | [Data](https://pkarnakov.github.io/am205/homework/am205_hw5_data.zip)
  | [Solution](https://pkarnakov.github.io/am205/homework/am205_hw5_sol.pdf)
  | [Source](homework/hw5_iter))

## Quizzes

* Quiz 1. Data fitting
  ([PDF](https://pkarnakov.github.io/am205/quizzes/am205_quiz1.pdf)
  | [Solution](https://pkarnakov.github.io/am205/quizzes/am205_quiz1_sol.pdf)
  | [Source](quizzes/am205_quiz1_sol.md))
* Quiz 2. Numerical linear algebra
  ([PDF](https://pkarnakov.github.io/am205/quizzes/am205_quiz2.pdf)
  | [Solution](https://pkarnakov.github.io/am205/quizzes/am205_quiz2_sol.pdf)
  | [Source](quizzes/am205_quiz2_sol.md))
* Quiz 3. Numerical calculus
  ([PDF](https://pkarnakov.github.io/am205/quizzes/am205_quiz3.pdf)
  | [Solution](https://pkarnakov.github.io/am205/quizzes/am205_quiz3_sol.pdf)
  | [Source](quizzes/am205_quiz3_sol.md))
* Quiz 4. Optimization
  ([PDF](https://pkarnakov.github.io/am205/quizzes/am205_quiz4.pdf)
  | [Solution](https://pkarnakov.github.io/am205/quizzes/am205_quiz4_sol.pdf)
  | [Source](quizzes/am205_quiz4_sol.md))

## Gallery

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

### Unit 0. Introduction

* [`unit0/fd.py`](media/unit0/media/fd.py)

### Unit 1. Data fitting

* [`unit1/data.py`](media/unit1/media/data.py)

* [`unit1/fit_2d.py`](media/unit1/media/fit_2d.py)

* [`unit1/monomials.py`](media/unit1/media/monomials.py)

* [`unit1/lagrange_two.py`](media/unit1/media/lagrange_two.py)

* [`unit1/runge.py`](media/unit1/media/runge.py)

* [`unit1/cheb.py`](media/unit1/media/cheb.py)

* [`unit1/cheb_conv.py`](media/unit1/media/cheb_conv.py)

* [`unit1/lebesgue.py`](media/unit1/media/lebesgue.py)

* [`unit1/data_anim.py`](media/unit1/media/data_anim.py)

* [`unit1/nonpoly_fit.py`](media/unit1/media/nonpoly_fit.py)

* [`unit1/invar_anim.py`](media/unit1/media/invar_anim.py)

* [`unit1/underlstsq.py`](media/unit1/media/underlstsq.py)

* [`unit1/nonpoly_fit_abs.py`](media/unit1/media/nonpoly_fit_abs.py)

* [`unit1/nonlin_lstsq.py`](media/unit1/media/nonlin_lstsq.py)

### Unit 2. Numerical linear algebra

* [`unit2/electric_circuit.py`](media/unit2/media/electric_circuit.py)

* [`unit2/spring.py`](media/unit2/media/spring.py)

* [`unit2/norm_inf.py`](media/unit2/media/norm_inf.py)

* [`unit2/unit_circle_norm.py`](media/unit2/media/unit_circle_norm.py)

* [`unit2/householder.py`](media/unit2/media/householder.py)

* [`unit2/svd_drawing.py`](media/unit2/media/svd_drawing.py)

* [`unit2/pca_dataset.py`](media/unit2/media/pca_dataset.py)

* [`unit2/pcavideo/pcavideo.py`](media/unit2/media/pcavideo/pcavideo.py)

### Unit 3. Numerical calculus

* [`unit3/quad_rect.py`](media/unit3/media/quad_rect.py)

* [`unit3/heat_1d.py`](media/unit3/media/heat_1d.py)

* [`unit3/heat_1d_time.py`](media/unit3/media/heat_1d_time.py)

* [`unit3/lagrange_blowup.py`](media/unit3/media/lagrange_blowup.py)

* [`unit3/legendre.py`](media/unit3/media/legendre.py)

* [`unit3/legendre_roots.py`](media/unit3/media/legendre_roots.py)

* [`unit3/sparsity.py`](media/unit3/media/sparsity.py)

* [`unit3/lotka_volterra.py`](media/unit3/media/lotka_volterra.py)

* [`unit3/lambdastab.py`](media/unit3/media/lambdastab.py)

* [`unit3/stabregion_euler.py`](media/unit3/media/stabregion_euler.py)

* [`unit3/stabregion.py`](media/unit3/media/stabregion.py)

* [`unit3/stabregion_fehlberg.py`](media/unit3/media/stabregion_fehlberg.py)

* [`unit3/shooting.py`](media/unit3/media/shooting.py)

* [`unit3/conic.py`](media/unit3/media/conic.py)

* [`unit3/advection_exp.py`](media/unit3/media/advection_exp.py)

* [`unit3/char_bc.py`](media/unit3/media/char_bc.py)

* [`unit3/char_div.py`](media/unit3/media/char_div.py)

* [`unit3/grid.py`](media/unit3/media/grid.py)

* [`unit3/wave.py`](media/unit3/media/wave.py)

* [`unit3/sawtooth_mode.py`](media/unit3/media/sawtooth_mode.py)

* [`unit3/theta_stab.py`](media/unit3/media/theta_stab.py)

* [`unit3/grid_xy.py`](media/unit3/media/grid_xy.py)

* [`unit3/grid_xy_flat.py`](media/unit3/media/grid_xy_flat.py)

* [`unit3/poisson.py`](media/unit3/media/poisson.py)

### Unit 4. Optimization

* [`unit4/bisection.py`](media/unit4/media/bisection.py)

* [`unit4/linear_prog.py`](media/unit4/media/linear_prog.py)

* [`unit4/global.py`](media/unit4/media/global.py)

* [`unit4/fixed.py`](media/unit4/media/fixed.py)

* [`unit4/coercive.py`](media/unit4/media/coercive.py)

* [`unit4/convex.py`](media/unit4/media/convex.py)

### Unit 5. Eigenvalue problems and iterative methods

* [`unit5/harmonics.py`](media/unit5/media/harmonics.py)

* [`unit5/multigrid.py`](media/unit5/media/multigrid.py)

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