Review for Math Xb Exam 1

Important Information

The exam will be given on Thursday 7 March.
The exam will be given from 7:00-9:00pm.
The exam will be given in Sci Ctr Lecture Hall D.
You may use your calculator and one standard-sized page of notes during the exam.
There will be a course-wide review on Wednesday March 6 from 7:30-9:30pm in Science Center Lecture Hall E.

Major Topics for the First Exam

Quantities defined by their rates of change
Slope fields and equilibrium solutions
Symbolic solutions of differential equations
Euler's method for approximation functions using their rates of change
Finite geometric series
Applications of finite geometric series, especially mortgage calculations
Infinite geomstric series
The concepts of convergence and divergence of an infinite series
General (i.e. not necessarily geometric) infinite series
Using convergence tests (especially the n term test and the ratio test) to determine the convergence or divergence of an infinite series
Approximating the area under a curve

Suggestions for Review

Probably the first place to begin is with your homework assignments. If there were any homework assignments (or particular problems) that gave you a lot of trouble, make sure that you download the solutions for that assignment and read the solutions thoroughly. (You can go straight to the homework page by clicking here.)
A useful next move is to read the notes that you have taken in class. The major topics for this exam are listed above. For each of these major topics, condense your class notes into a one-page (no longer, otherwise you might start to simply transcribe your notes without thinking carefully about the content of the notes) summary of that topic.
When you have completed all of your one-page summaries, make the page of notes that you are allowed to take into the exam with you. This exercise will consist of distilling the truly essential points from your summaries so that everything will fit onto a single page (both sides) of notes.
When you have thoroughly reviewed everything that you have encountered in the course so far, then you will be ready to get the most out of the practice problems.
Try to use the practice problems as a diagnostic for the efficacy of your other forms of review.
- If you find that you can take almost all of the practice problems in your stride without having to constantly refer back to your class notes, or to flip to the answers in the back, then you are probably in good shape for the exam.
- If you attempt the practice problems and find that you have to refer back to your class notes a lot, or can only "get" the problems by flipping to the answers in the back, then you might consider trying to identify the specific areas of the math that are still giving you problems and review them a second time.

Practice Problems

Click on the links shown below to download sets of practice problems. The current set of practice problems concentrates on series and their applications. Within the next few days another set of problems will be posted that concentrate on differential equations, solutions of differential equations, slope fields, equilibrium solutions and Euler's method.

Download Problems	Problem Set Concentrates On...
Problem Set 1a	Series. Geometric series. Applications of geometric series (e.g. mortgage calculations). Infinite series. Convergence tests. Setting up series to model situations.
Problem Set 1b	Setting up differential equations to model situations. Using Euler's Method to approximate functions defined by rates of change. Deciding when the estimates provided by Euler's Method are under- or over-estimates of the "true" values of a function. Verifying that given functions solve differential equations and initial conditions. Drawing and interpreting slope fields. Matching slope fields and differential equations. Locating the equilibrium solutions of a differential equation. Classifying equilibrium solutions as stable, unstable or semi-stable.

Download Problems

Problem Set Concentrates On...

Problem Set 1a

Series. Geometric series. Applications of geometric series (e.g. mortgage calculations). Infinite series. Convergence tests. Setting up series to model situations.

Problem Set 1b

Setting up differential equations to model situations. Using Euler's Method to approximate functions defined by rates of change. Deciding when the estimates provided by Euler's Method are under- or over-estimates of the "true" values of a function. Verifying that given functions solve differential equations and initial conditions. Drawing and interpreting slope fields. Matching slope fields and differential equations. Locating the equilibrium solutions of a differential equation. Classifying equilibrium solutions as stable, unstable or semi-stable.