UCLA  LIFESCI 30  Life Sci 30A Midterm Study Guide  Study Guide
View Full MaterialSchool: 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
This preview shows pages 1  2 of a 3 page document.
Sign up
to view the rest of the content
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

LotkaVolterra model
: a pair of nonlinear differential equations used to describe
dynamics of biological systems (e.g., predatorprey 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 + : nonnegative 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  onetoone function : two inputs lead to the same output
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 + : nonnegative 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  onetoone function : two inputs lead to the same output
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

onevariable 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
: twodimensional 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)  x = current population size  k = carrying capacity  LotkaVolterra predatorprey equations : used to model predatorprey interactions  S’ = mƁST  dS  T’ = bT  ƁST  S = sharks  T = tuna  m = constant of proportionality
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)  x = current population size  k = carrying capacity  LotkaVolterra predatorprey equations : used to model predatorprey interactions  S’ = mƁST  dS  T’ = bT  ƁST  S = sharks  T = tuna  m = constant of proportionality
This is the end of the preview. Please
Sign up
to view the rest of the content
Join more than 18,000+ college students at University of California  Los Angeles who use StudySoup to get ahead
3
Pages
66
Views
52
Unlocks
 Better Grades Guarantee
 24/7 Homework help
 Notes, Study Guides, Flashcards + More!
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!
Join StudySoup for FREE
Get Full Access to
UCLA  Study Guide
Already have an account?
Login here
Reset your password
I don't want to reset my password
Need help? Contact support
We're here to help
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Password Reset Request Sent
An email has been sent to the email address associated to your account.
Follow the link in the email to reset your password.
If you're having trouble finding our email please check your spam folder
Incorrect Password
The password used to log in with this account is incorrect
Forgot password? Reset it here