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UCLA - LIFESCI 30 - Life Sci 30A Midterm Study Guide - Study Guide

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UCLA - LIFESCI 30 - Life Sci 30A Midterm Study Guide - Study Guide

School: University of California - Los Angeles
Department: Life Science
Course: Life Sciences 30A - Mathematics for Life Scientists
Professor: W.j. Conley
Term: Winter 2019
Tags: Math
Name: Life Sci 30A Midterm Study Guide
Description: This study guide covers all the material that might be tested on the midterm. It contains information from sections 1.1 through 1.7 in the textbook, as well as everything discussed in class.
Uploaded: 01/23/2019
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background image 1.1 -- Feedback    - time series ​: a graph that shows how quantities change over time  - feedback loop ​: the current state of a system affects the future state of that system by  changing the inflows and outflows of the system’s components  - positive feedback ​: positive value of a variable leads to an increase in that  variable, and a negative value of a variable leads to a decrease  - negative feedback ​: positive value of a variable leads to a decrease in that  variable, and a negative value of that variable leads to an increase in that variable  - This can be represented by B = D - B 0 , where B is the discrepancy, D is  the current value, and B 0  is the set point  - dynamical system ​: refers to any system in the real world in which some quantity is  changing over time  - state variables ​: functions of time  - Lotka-Volterra model ​: a pair of nonlinear differential equations used to describe  dynamics of biological systems (e.g., predator-prey interactions)   
 
1.2 -- Functions    - function ​: a relationship between a set of inputs and a set of outputs in which each input is  assigned exactly one output  - linear interpolation ​: straight lines are drawn between data points  - domain ​: set of input values that a function can accept  - real numbers (R) ​: whole numbers, fractions, irrational numbers, and the negative values  of these   - R + ​ ​ : non-negative real numbers (0 and greater)  - codomain ​: set of values in which a function’s output lies  - composition of functions ​: one function is made up of two previous functions linked end  to end  - f: X → Y and g: Y → Z   - g   f : X → Z, also written as g(f(x))  - set ​: contains a series of mathematical values  - expressed using curly brackets {}  - Z ​: integers (whole numbers)  - Z +  : integers greater than 0  - image (AKA range) ​: set of all values that f(x) actually takes, subset of the codomain  - one-to-one function ​: two inputs lead to the same output 
background image 1.3 -- States and State Space    - state ​: the condition of a system at a given time  - e.g.,  [50 tune, 17 sharks] or [50,17]  - state variables ​: variables we use to describe the state of a system, functions of time,  must be quantitative  - state space ​: the set of all conceivable state values of a system  - assumption of continuity: we assume that state variables are continuously changing  - tuple ​: an ordered pair, or vector, of numbers  - state point ​: point in space that represents a system’s state  - one-variable system ​: uses a number line as its state space  - SIR model ​: a common epidemiology model   - S ​: susceptible individuals  - I ​: infected individuals  - R ​: recovered individuals  - scalar ​: has value rather than direction  - vector space ​: two-dimensional space  - dimension ​: the number of axes needed to represent a system’s state  - change ​: movement through state space   
 
1.4 -- Modeling Change    - model ​: a set of hypotheses about the causes of change in a given system  - x’ ​: in a change equation, the change in x (a state variable)  - stocks ​: state variables in change equations  - parameter ​: a constant for a given model  - logistic equation ​: x’ = bx - cx​ 2  or x’ = bx(1-(x/k))  - b ​ = births  - c ​ = constant of proportionality (how much food each organism needs)  - ​= current population size  - k ​ = carrying capacity  - Lotka-Volterra predator-prey equations ​: used to model predator-prey interactions  - S’ ​ = mƁST - dS  - T’ ​ = bT - ƁST  - ​= sharks  - T ​ = tuna  - m ​ = constant of proportionality 

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Join more than 18,000+ college students at University of California - Los Angeles who use StudySoup to get ahead
School: University of California - Los Angeles
Department: Life Science
Course: Life Sciences 30A - Mathematics for Life Scientists
Professor: W.j. Conley
Term: Winter 2019
Tags: Math
Name: Life Sci 30A Midterm Study Guide
Description: This study guide covers all the material that might be tested on the midterm. It contains information from sections 1.1 through 1.7 in the textbook, as well as everything discussed in class.
Uploaded: 01/23/2019
3 Pages 66 Views 52 Unlocks
  • Better Grades Guarantee
  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
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