Applied Mathematics
7.4
Interpolation Methods
Scientific Programming
Preface
1
Installing Python and Setup
2
Acknowledgements
Programming fundamentals
3.1
Best practices
3.2
Basics
3.3
Functions
3.4
Data structures
3.5
Objects
3.6
File I/O
3.7
Debugging
3.8
Version control
3.9
PDF Reports with LaTeX
3.10
Interactive HTML Reports
NumPy/SciPy
4.1
NumPy Arrays
4.2
Linear Algebra
4.3
Optimization
4.4
Interpolation
4.5
Pandas
SymPy
5.1
Introduction
Matplotlib
6.1
Simple Plotting Examples
6.2
Animations
6.3
Interpolated Polygon Plots
Applied Mathematics
7.1
Introduction to Applied Mathematics
7.2
Root Finding Methods
7.3
Linear Ordinary Differential Equations
7.4
Interpolation Methods
7.5
Numerical Differentiation
7.6
Numerical Integration
7.7
Numerical Methods for Solving Ordinary Differential Equations (ODEs)
7.8
2D Interpolation - Bi-linear Shape Functions
7.9
Optimization Methods
Applications
8.1
Introduction to Applications
8.2
Computational Thinking
8.3
Kinematics - Constraint Solving
8.4
Implementing FEM in python
8.5
Systematic Truss Analysis
8.6
Visualizing Truss Mesh
8.7
Parsing a mesh
8.8
Fusion360 API
8.9
Real-time simulation of a pendulum
MechanicsKit API
9.1
MechanicsKit API Reference
9.2
LaTeX Display Functions
9.3
Mesh Class
9.4
OneArray Class
9.5
Plotting Functions
9.6
Colormap Utilities
9.7
Gaussian Quadrature
9.8
fplot()
Examples
9.9
patch()
Examples
Table of contents
Introduction
Linear Interpolation
Piecewise Linear Interpolation
Higher order polynomial Interpolation
Deriving Basis Functions
Spline Interpolation
Hermite Interpolation
Bèzier curves
The Least Squares Method
LSM using Matrices
Continuous Least Squares Method
Applied Mathematics
7.4
Interpolation Methods
7.4
Interpolation Methods
Introduction
Linear Interpolation
Piecewise Linear Interpolation
Higher order polynomial Interpolation
Deriving Basis Functions
Spline Interpolation
Hermite Interpolation
Bèzier curves
The Least Squares Method
LSM using Matrices
Continuous Least Squares Method
7.3
Linear Ordinary Differential Equations
7.5
Numerical Differentiation