Numerical Analysis with Applications in Python#
This is Jupyterbook for the course notes Numerical Analysis for Ordinary and Partial Differential Equations.
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Part 1 Numerical Solutions to Ordinary Differential Equations#
Chapter 1 Numerical Solutions to Initial Value Problems#
Chapter 2 Higher Order Methods#
Chapter 3 Runge–Kutta methods#
Chapter 4 Multi-step methods#
Chapter 5 Analsyis of Methods for Initial Value Problems#
Part 2 Numerical Solutions to Boundary Value Problems#
Chapter 6 Boundary Value Problems#
Part 3 Numerical Solutions to Partial Differential Equations#
Chapter 8 Parabolic equations (Heat Equation)#
Chapter 9 Elliptic PDE’s (Poisson Equation)#
Chapter 10 Hyperbolic Equations#
References#
[1] Strogatz, S. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (studies in nonlinearity), Westview Press; 2 edition (29 July 2014)
[2] Brian Bradie, A Friendly Introduction to Numerical Analysis
[3] Atkinson, Han Elementary Numerical Analysis
[4] Richard L. Burden, J. Douglas Faires, Numerical Analysis, Brooks/Cole 1997
[5] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag 1980
[6] G D Smith Numerical Solution of Partial Differential Equations: Finite Difference Method Oxford 1992
Supplementary Video Lectures#
Steven Strogatz. (2021, March 1). Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University [Video]. YouTube. https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V
Popular Videos#
The Relationship Equation - Numberphile. (2015, April 3). [Video]. YouTube. https://www.youtube.com/watch?v=BkOIw7vAZCQ
How Wolves Change Rivers. (2014, February 13). [Video]. YouTube. https://www.youtube.com/watch?v=ysa5OBhXz-Q
Popular Press Reading#
Tree, I. (2018). Wilding: The return of nature to a British farm. Pan Macmillan.
Strogatz, S. (2004). Sync: The emerging science of spontaneous order. Penguin UK.
Podcasts#
Strogatz, S. (2019-2021). Joy of X. Quanta Magazine. https://www.quantamagazine.org/tag/the-joy-of-x