LS 30A: MATHEMATICS FOR LIFE SCIENTISTS FALL 2019 – LECTURES 2 and 3 STUDY GUIDE FOR THE FINAL EXAM

LS 30A: MATHEMATICS FOR LIFE SCIENTISTS FALL 2019 – LECTURES 2 and 3 STUDY GUIDE FOR THE FINAL EXAM IN SHORT You need to know all the material that was covered in the lectures and also all the material from the textbook that corresponds to what was covered in the lectures, with a small number of exceptions that will be indicated below. The Further Exercises from your homework are the best indication of what to expect. You will need a basic, non-programmable calculator on this exam. The following is an enumeration of the central topics we have covered. You must know these topics in order to do well on the Final Exam. All page references are to the WITH CLICKERS PAGE BY PAGE (i.e. the final) version of the lecture. TOPICS TO REVIEW FOR THE FINAL EXAM LECTURE 1 1. Examples of dynamical systems 2. The distinction between the system and a model of that system 3. Be able to interpret a time series graph 4. The definitions of positive and negative feedback loops 5. Examples of both kinds of feedback loops 6. Positive feedback tends to cause instability, negative feedback tends to cause stability. LECTURE 2 1. The definition of a function 2. The domain of a function 3. The distinction between the codomain and the range of a function 4. The composition of functions is only defined when the range of the first function is contained in the domain of the second function. 5. In this way, the second function can ‘understand’ as input anything the first function can produce as output. LECTURE 3 1. The definition of a state of a system 2. The definition of the state space of a system 3. State variables (as functions of time) of a model of a system 4. Examples of different kinds of state spaces 5. The addition of vectors, the scalar multiplication of a vector by a number 6. The geometric meaning of the two operations 7. The definition of a vector space 8. Change as movement through state space This study source was downloaded by from CourseH on :13:25 GMT -06:00 LECTURE 4 1. Inflows and outflows; stocks 2. Parameters and how they differ