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).