1. Final Exam Information These slides and more detailed information will be posted on the webpage later…

2. General Information Date: Friday, April 24th* Time: Location: varies – refer to final exam timetable * as of March 31 st, 2015

3. General Information exam is out of 80 marks (roughly the length of two tests) exam questions include multiple choice, true or false, and "complete solution" questions style and level of difficulty will be similar to tests you may write in pencil (your exam is not returned to you)

4. Math 1LT3 Exam Review Session Date: Wednesday, April 22 nd Location: HH 302 Time: 2:30pm – 4:30pm

5. How to Study  Study class notes. All theory, and the most relevant examples are done in lectures. Make sure you can do all exercises that that were discussed in class.  Suggestion: Study in reverse order. Start with probability and statistics, then functions of several variables, and then differential equations.

6. How to Study  Re-do a selection of questions from the lecture notes (examples), assignments, and practice problems. Do not read solutions; instead, do questions yourself, and only when you get stuck, look at solutions.  Review your tests from this term. Make sure you can do all test questions without referring to notes or solutions (blank tests will be posted on the course website for you to practice). Also, look at your tests critically, understand things that you did not correctly, so that you do not repeat the same mistakes.

7. How to Study  Attend the review session. Bring your questions to the review session after you have completed most of your studying to fill in any gaps.  Use the math help centre (check online for exam hours) for additional help and/or use the 1LT3 Facebook group to ask/answer questions or organize study groups.

8. Topic Overview and Study Checklist

9. From Chapter 8 in the hardcover textbook: Modeling with Differential Equations basic models exponential logistic modified logistic selection disease model

10. From Chapter 8 in the hardcover textbook: Analysis of Models (Differential Equations) equilibria stability phase-line diagrams

11. From Chapter 8 in the hardcover 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

12. From Chapter 8 in the hardcover textbook: Systems of Differential Equations Example: Predator-prey models

13. From Chapter 8 in the hardcover textbook: Previous Multiple Choice Question:

14. From Chapter 8 in the hardcover textbook: Previous Multiple Choice Question:

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

16. From the Functions of Several Variables 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)

17. From the Functions of Several Variables Module: Calculus on Functions of Two Variables: Partial Derivatives definitions computations interpretations (in applications or geometrically)

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

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

20. From the Functions of Several Variables 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 in words, what does it mean for a function f(x,y) to be differentiable at a point (a,b)? theorem

21. From the Functions of Several Variables 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

22. From the Functions of Several Variables Module: Previous Matching Question:

23. From the Functions of Several Variables Module: Previous True or False Question:

24. From the Functions of Several Variables Module: Previous Multiple Choice Question:

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

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

27. From the Probability and Statistics Module: Basics of Probability Theory probability definition assigning probabilities to equally likely simple events

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

29. From the Probability and Statistics Module: Independence Definition Applications:

30. From the Probability and Statistics 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)

31. From the Probability and Statistics 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

32. From the Probability and Statistics 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)

33. From the Probability and Statistics 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

34. From the Probability and Statistics 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

35. From the Probability and Statistics Module: Previous Multiple Choice Question:

36. From the Probability and Statistics Module: Previous True or False Question:

37. Final Grade Calculation Option 1: Best 2 out of 3 tests (60%) final exam (40%) Option 2: Best 2 out of 3 tests (10%) final exam (90%) Your final grade will be the maximum of these two grading options.

38. My Exam Office Hours Starting next week: Mondays and Wednesdays 4:30 pm – 5:30 pm Hamilton Hall, 425

39. Thank you!