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Introduction to Numerical Methods for Engineers
1. Taylor Approximation
Taylor Series
2. Root Finding
2.1 Bisection Method
2.2 Newton’s Method
3. Derivatives
3.1 Introduction to Derivatives of a function with multiple variables
3.2 Computing Derivatives of Functions
4. Linear Equations
4.1 Linear Algebra in Julia
4.2 Conditioning of linear equations
4.3 Gaussian Elimination
4.4 LU Factorization
5. Root Finding with Multiple Variables
5.1 Defining the Root Finding Prblem with Multiple Variables
5.2 Newton Method with multiple variables
6. Least Squares
6.1 Linear Least Squares Tasks
7. Introduction to Neural Networks
7.1 Predicting currents in the Openmanipulator joints with a neural network
8. Ordinary Differential Equations (ODEs)
8.1. Introduction to ODEs
8.2. Understanding Ordinary Differential Equations - Direction Fields
8.3. Introduction to Numerically solving Ordinary Differential Equations - Euler Method
8.4. Stability and Stiffness of Numerical Methods
8.5. Higher Order Methods to solve ODEs
9. Singular Value Decomposition (SVD)
9.1 Quick Overview of the Definition of SVD
9.2 Introduction to Principal Component Analysis (PCA)
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