1. Topic Overview and Study Checklist

2. From Chapter 7 in the white textbook: Modeling with Differential Equations basic models exponential logistic modified logistic selection disease model

3. From Chapter 7 in the white textbook: Analysis of Models (Differential Equations) equilibria stability phase-line diagrams

4. From Chapter 7 in the white textbook: Solutions of Differential Equations sketch solutions based on qualitative information use Euler’s Method to generate approximate numerical values of the solution find algebraic solutions of separable DEs

5. From Chapter 7 in the white textbook: Systems of Differential Equations Example: Predator-prey models

6. From Chapter 7 in the white textbook: Previous Multiple Choice Question:

7. From Chapter 7 in the white textbook: Previous Multiple Choice Question:

8. From the Red Module: Calculus on Functions of Two Variables: Basics: domain range graphs contour maps

9. From the Red Module: Calculus on Functions of Two Variables: Limits and Continuity define the limit of a function in R 3 show that a limit does not exist compute a limit when it does exist use limits and the definition of continuity to determine if a function f(x,y) is continuous or not at a point (a,b)

10. From the Red Module: Calculus on Functions of Two Variables: Partial Derivatives definitions computations interpretations (in applications or geometrically) Chain Rule computations applications interpretations

11. From the Red Module: Calculus on Functions of Two Variables: Directional Derivatives definition theorem computations interpretations (in applications or geometrically)

12. From the Red Module: Calculus on Functions of Two Variables: Gradient Vectors definition computations properties interpretations (in applications or geometrically)

13. From the Red Module: Calculus on Functions of Two Variables: Tangent Planes formula how it is constructed geometrically Linearizations formula when a linearization is a good approximation Differentiability (heavy theory!) in words, what does it mean for a function f(x,y) to be differentiable at a point (a,b)? theorem

14. From the Red Module: Calculus on Functions of Two Variables: Second-Order Partial Derivatives compute interpret Local Extreme Values find critical points by solving a system of equations use the Second Derivatives Test to classify points know how to use alternative arguments to classify points if Second Derivatives Test does not apply

15. From the Red Module: Previous Matching Question:

16. From the Red Module: Previous True or False Question:

17. From the Red Module: Previous Multiple Choice Question:

18. From the Grey Module: Stochastic Models definition basic examples: flipping a coin, rolling a die population model with immigration other definitions: statistic, random experiment

19. From the Grey Module: Basics of Probability Theory definitions sample space event + simple event intersection union compliment mutually exclusive/disjoint sets

20. From the Grey Module: Basics of Probability Theory probability definition assigning probabilities to equally likely simple events

21. From the Grey Module: Conditional Probability definition law of total probability (tree!) Baye’s theorem Applications:

22. From the Grey Module: Independence Definition Applications:

23. From the Grey Module: Discrete Random Variables definition examples probability mass function (definition, properties, histograms) cumulative distribution function (definition, properties, graphs) calculating probabilities mean, variance, standard deviation (definitions, properties, calculations)

24. From the Grey Module: Special Discrete Distributions Binomial Poisson know probability mass function, mean and standard deviation for each be able to identify when a random variable can be described by one of these distributions

25. From the Grey Module: Continuous Random Variables definition examples probability density function (definition, properties, graph) cumulative distribution function (definition, properties, graph) calculating probabilities mean, variance, standard deviation (definitions, calculations)

26. From the Grey Module: Special Continuous Distributions Normal (and Standard Normal) know probability density function (formula, properties, graph) + corresponding cumulative distribution function (definition, area interpretation) how to compute z-scores and use table of values for F(z) standard calculations applications

27. From the Grey Module: Central Limit Theorem statement of theorem (you should be able to explain in words what this theorem says and when it applies) computations + applications

28. From the Grey Module: Previous Multiple Choice Question:

29. From the Grey Module: Previous True or False Question: