Skip to content

UW AMATH 301. Scientific computing and numerical methods for physical, biological, and engineering problems. Topics include root-finding, optimization, curve fitting, solving linear systems, singular value decomposition (SVD, PCA), numerical differentiation and integration, solving first-order and higher order ODEs, stability and stiffness of OD…

License

Notifications You must be signed in to change notification settings

tengjuilin/intro-sci-computing

Repository files navigation

Introduction to Scientific Computing

License Website DOI

AMATH 301 covers numerical methods and programming skills needed to solve physical, biological, and engineering problems. Content is transcribed from MATLAB (originally taught in the course) to Python for open source reference. Taken in Sp20 with Dr. Craig Gin.

Note: Starred topics (*) are not covered in Sp20 but covered in previous years.

Root-Finding and Optimization

Topic Applications Numerical Methods
Python Skills
Jupyter
Notebook
Online
Root finding algorithms Solving function values Bisection method
Newton's method
scipy.optimize.root_scalar()
ipynb html
Unconstrained optimization Finding max and min of convex functions Golden section search
Gradient descent
scipy.optimize.fminbound()
scipy.optimize.fmin()
ipynb html
Constrained optimization* Finding max and min of functions with constraints Linear programming
Genetic algorithm
scipy.optimize.linprog()
scipy.optimize.differential_evolution()
ipynb html
Curve fitting and interpolation Fitting data
Interpolating between data
Sum of squared error
Sum of absolute error
Maximum absolute error
scipy.optimize.fmin()
scipy.optimize.curve_fit()
numpy.polyfit()
numpy.polyval()
scipy.interpolate.interp1d()
ipynb html

Linear Algebra

Topic Applications Numerical Methods
Python Skills
Jupyter
Notebook
Online
Matrix operations in python Dot product
Norm
Matrix multiplication
@
numpy.linalg.norm()
ipynb html
Solving linear systems
with direct methods
Solving linear systems repeatedly Matrix inversion
LU decomposition
np.linalg.lu()
scipy.linalg.solve()
ipynb html
Solving linear systems
with iterative methods
Solving sparse linear systems Jacobi method
Gauss-Seidel method
numpy.linalg.eig()
numpy.linalg.eigvals()
ipynb html
Singular value decomposition (SVD)
(Principle component analysis, PCA)
Dimensionality reduction
Image compression
SVD, PCA algorithm
scipy.linalg.svd()
ipynb html

Numerical Calculus

Topic Applications Numerical Methods
Python Skills
Jupyter
Notebook
Online
Numerical differentiation Differentiate functions
Differentiate data
Forward difference
Backward difference
Central difference
Other second order methods
numpy.gradient()
ipynb html
Numerical integration Single integrals
Double integrals
Triple integrals
(functions and data)
Left end point rule
Right endpoint rule
Midpoint rule
Trapezoidal rule
Simpson's rule
scipy.integrate.quad()
scipy.integrate.dblquad()
scipy.integrate.tplquad()
ipynb html

Ordinary Differential Equations (ODEs)

Topic Applications Numerical Methods
Python Skills
Jupyter
Notebook
Online
Solving first-order ODEs Solving first-order ODEs Forward Euler
Backward Euler
Midpoint method
Fourth-order Runge-Kutta (RK4)
scipy.integrate.solve_ivp()
ipynb html
Solving higher-order ODEs Solving higher-order ODEs
Systems of first-order ODEs
Forward Euler
Backward Euler
scipy.integrate.solve_ivp()
ipynb html
Stability and stiffness of ODEs Choosing integration methods
Choosing time steps
Forward Euler
Backward Euler
scipy.integrate.solve_ivp()
ipynb html
Chaotic systems part 1* Lorenz system scipy.integrate.solve_ivp() ipynb html
Chaotic systems part 2* Lorenz system scipy.integrate.solve_ivp() ipynb html

Phase Portrait Applications

Topic Applications Numerical Methods
Python Skills
Jupyter
Notebook
Online
Spring-mass-damper system Physics scipy.integrate.solve_ivp() ipynb html
Linear, nonlinear pendulum Physics scipy.integrate.solve_ivp() ipynb html
Two-eyed monster Applied math scipy.integrate.solve_ivp() ipynb html
Population dynamics
Predator-pray model
Competition model
Ecology scipy.integrate.solve_ivp() ipynb html
FitzHugh-Nagumo neuron excitation model part 1* Neuroscience scipy.integrate.solve_ivp() ipynb html
FitzHugh-Nagumo neuron excitation model part 2* Neuroscience scipy.integrate.solve_ivp() ipynb html
FitzHugh-Nagumo neuron excitation model part 3* Neuroscience scipy.integrate.solve_ivp() ipynb html
Coupled harmonic oscillator* Physics scipy.integrate.solve_ivp() ipynb html

Fourier Transform

Topic Applications Numerical Methods
Python Skills
Jupyter
Notebook
Online
Fourier transform* Power spectrum density
Noise filtering
Image compression
Discrete Fourier transform
Fast Fourier transform
numpy.fft.fft()
numpy.fft.ifft()
numpy.fft.fftfreq()
numpy.fft.fft2()
ipynb html

Gallery

lourenz_3d_small_cube.mp4
lourenz_3d_large_cube.mp4
lourenz_3d_rot.mp4
lourenz_spin.mp4
lourzenz_time_step.mp4
neuron_base_case.mp4
neuron_one_eyed.mp4
neuron_two_eyed.mp4
neuron_loop.mp4
neuron_decreaing_current.mp4
neuron_increasing_current.mp4
neuron_oscillating_current_fast.mp4
neuron_oscillating_current_slow.mp4

About

UW AMATH 301. Scientific computing and numerical methods for physical, biological, and engineering problems. Topics include root-finding, optimization, curve fitting, solving linear systems, singular value decomposition (SVD, PCA), numerical differentiation and integration, solving first-order and higher order ODEs, stability and stiffness of OD…

Topics

Resources

License

Stars

Watchers

Forks