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Introduction to Numerical Methods for Engineers

This is a summary of the lecture notes and exercises for the course Ingenieurwissenschaftliche Grundlagen 3 (Numerische Methoden) at the University of Augsburg.

Content

Further Reading Materials

Numerische Methoden für Ingenieure, Johannes Gottschling and Dieter Schramm

Fundamentals of Numerical Computation Website for the book on numerics with Julia examples. Compact explanations of mathematics and implementations/algorithms are nicely explained here.

MIT - 18.330: Introduction to Numerical Analysis Part of our lectures are based on this.

Differential Equations

University of Washington - Mechanical Engineering Analysis Lecture Videos Lectures with numerical methods for solving differential equations in the second part of the course.

Singular Value Decomposition (SVD) and Principal Component Analysis (PCA)

About the Book | DATA DRIVEN SCIENCE & ENGINEERING Data Driven Engineering (SVD and PCA in the first chapter)

Videos: Singular Value Decomposition (SVD)

Tutorial on PCA (Pendulum with Cameras)

Machine Learning and Foundations:

Matrix Cookbook Formula collection for matrix calculation

Mathematics for Machine Learning

Chapter 5 is interesting for us:

  • Section 5.1 Differentiation of Univariate Functions
  • Section 5.2 Partial Differentiation and Gradients
  • Section 5.3 Gradients of Vector-Valued Functions
  • Section 5.4 Gradients of Matrices
  • Section 5.5 Useful Identities for Computing Gradients
  • Section 5.6 Backpropagation and Automatic Differentiation
  • Section 5.7 Higher-Order Derivatives
  • Section 5.8 Linearization and Multivariate Taylor Series

Probabilistic Machine Learning: An Introduction Beautifully written book on Machine Learning with a good overview of mathematical foundations.

Probabilistic Machine Learning: Advanced Topics Advanced topics in Probabilistic Machine Learning. These are indeed advanced topics and much is very close to the current state of research (Challenging but exciting).

Julia Material (only necessary if you want to continue to engage with it after the course):

Get started with Julia

Think Julia: How to Think Like a Computer Scientist

Julia Tutorial - Getting started

Software Engineering - Julia Data Science

Algortihms for optimization with Julia