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# UCLA - LIFESCI 30 - Life Science 30A Notes Week 3 - Class Notes

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UCLA - LIFESCI 30 - Life Science 30A Notes Week 3 - Class Notes

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1.5 -- Seeing Change Geometrically    - change instruction ​: X’  - tangent space ​: set of all possible values of X’  - change vector ​: the change instruction that we get from X’  - vector field ​: the change equation is a function from the state space to the tangent space  (vector field: state space → tangent space)

1.6 -- Trajectories    - initial condition ​: the starting point of a trajectory

1.7 -- Change and Behavior    - calculus ​: based on the concept of infinitesimal limits  - shadowing lemma ​: as Δt gets smaller and smaller, the resulting curve gets closer and  closer to the true curve  - Euler’s Method ​:  1. Start from the point X’.
2. Evaluate X’ at X
0 . We will call this X’ 0 3. Multiply the change vector X’ by the small number Δt.  4. Add (Δt * X’ 0 ) to X 0 , and call the result X 1 5. Repeat steps 1 through 4.  - numerical integration ​: generating a time series or trajectory from a model and an initial  condition.

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##### Description: These notes cover what was discussed in class during Week 3. The material can be found in sections 1.5, 1.6, and 1.7 in the textbook.
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