1
State Space
2
Operating with Vectors
3
Trajectories and Time Series
4
Models and Change Vectors
- 4.1 Introduction to Models and Change Equations: The Bathtub4.2 Models and Change Equations in 2 Dimensions: Shark Meets Tuna4.3 From Change Equations to Change Vectors4.4 State spaces and change vectors in 2D4.5 Trajectories in 2D4.6 Logistic Growth4.7 Models and Vectorfields: a nonlinear example in 1D4.8 Modeling Chemical Reactions4.9 Epidemiology4.10 Immune Dynamics
5
Euler's Method
7
Linear Stability Analysis
8
Higher Dimensions
9
The Lac operon: a biological switch
10
Bifurcation
12
The Central Dogma
13
Stable Oscillations in Science (and Music)
14
Oscillations in Physiology
16
Chaos 1
17
Chaos 2
19
Chaos 4
20
Chaos and Cardiology
21
Applications of Linear Algebra
Vectors and Trajectories - a little history
Summary
- set of “real numbers” = 1D line (geometric picture)
- pairs of real numbers \( \mathbb{R}^2 = \mathbb{R} \times \mathbb{R} \) or \( \mathbb{R}2 \)
- Descartes’ idea: pairs of numbers = points in the 2D plane.
- Same for \( \mathbb{R}^n\).
- Riemann
- concept of “generalized space” (for example, Shark-Tuna space)
