Courses   <-  Sean Forman   <-  You Are Here Applied Calculus I

April 27, 2005

Final Exam Review. The final exam is Thursday, May 5th from 2pm-4pm in Bellarmine 217 (not our normal room). If you miss the final exam, and have a valid excuse (death in family, grave illness, ...), I will give you makeup exam on Tuesday, May 10th. I will grade the finals as soon as possible and then enter grades online, so there is no need to e-mail me. I'll get it to you as soon as I can.

The final is cumulative and will be taken roughly equally from each of the two exams with a very small part from the material on Newton's Method. All material that we have covered is fair game, including material that was not covered on a previous exam. Understanding the previous exams would likely guarantee you a C (or maybe a B) on the final, but would not be sufficient for an A.

If you did poorly on the second exam, you have the option of counting the material from test two on the final as one third of our second exam score. However, this means that if you do worse, you will hurt your second exam grade. E-mail me if you wish to use this option.

You will not need a special calculator, one able to do basic arithmetric, some trig, logs and exponentials will be sufficient. Any calculator capable of doing symbolic differentiation will not be allowed (for example the TI-89 and above).

You are expected to memorize all major formulas for derivatives. Formulas that you will be given:

• The unit circle that was given on the second exam.

• The equation for elasticity of demand, but not what the result means.

• The equations for compound interest $A = P (1 + r)^n$ and $A = Pe^{rn}$.

• Any area or volume formulas relating to circles or cylinders.

Finals week office hours

• Monday, May 2, 1-5pm
• Tuesday, May 3, 1-3pm
• Wednesday, May 4, 10am-Noon
• Wednesday, May 4, 1-3pm (in the LRC), LRC has dedicated math tutoring from 11-6 on Wednesday.
• Thursday, May 5, possibly by e-mail, but I have other meetings.

I will also attempt to answer any e-mail promptly. I do not get voicemail over the weekend.

Here is a summary of all of the topics covered in the course. You've learned a lot! There may be other topics not listed here. You are responsible for all material covered in class and on homework. The solutions to all assigned homework problems, exams and quizzes is available on reserve in the library. Go to the front desk and ask for the homework solutions to Dr. Forman's Math 1251 class. Don't wait until the last minute as others may want it then as well. And don't steal any homework solutions as that would make you a jerk.

• Section 1.1 Interval and set notation, lines (slope, point-slope, etc.),

• Section 1.2 Exponent rules

• Section 1.3 Functions, domains, ranges, factoring, quadratic equation, vertices, breakeven points.

• Section 1.4 Types of functions and their domains, composition of functions, more factoring.

• Section 2.1 Limits, various types of answers to limits, infinite limits, continuity

• Section 2.2 Rates of change, slopes of tangent lines. Computing the derivative using the definition of the derivative (no shortcuts allowed).

• Section 2.3 Basic Differentiation formulas: power rule, constant rules, sum and difference rule.

• Section 2.4 Product and quotient rules.

• Section 2.5 Higher order differentiation, acceleration and velocity. Be sure to understand what the units are for these problems.

• Section 2.6 Chain Rule alone and chain rule used with other rules.

• Section 2.7 Non-differentiable functions. The three situations where a funcition is not differentiable.

• Section 3.1 Graphing using the first derivative. Finding critical values. Intervals where the function is increasing or decreasing. First derivative test. Sketching given the sign diagrams. I could ask a question such as: if $f'(x) = x-2$, which of the following could represent the graph of $f(x)$.

• Section 3.2 Graphing using the second derivative. Concavity. Second derivative test. Inflection points, sketching given the sign diagrams. I could ask a question such as: If $f''(x) = x-2$, which of the following could represent the graph of $f(x)$.

• Section 3.3, 3.4 & 3.5 Absolute max's and min's on a closed or open interval. A variety of optimization problems. You should be able to do the homework story problems that were assigned. Major types include Area/Perimeter problems, Profit, Revenue with $x$= number of $10 reductions, optimal lot size, tax revenue, and others. In some cases, I may ask you just to set up the problem.

• Section 3.6 Implicit differentiation and using it to find dy/dx. Basic related rates problems.

• Section 4.1 Exponential functions, $e^x$, interest rate problems with compounding. Present value problems, depreciation, domain and range.

• Section 4.2 Logarithmic functions, domain and range, log rules, time to double, triple, etc. C-14 dating.

• Section 4.3 Derivatives of natural logarithms and exponentials. Related story problems.

• Section 4.4 Relative rates of change and elasticity of demand problems. You will need to remember these formulas on your own.

• Section 8.1 Radians to degrees, degrees to radians, co-terminal angles, arc length.

• Section 8.2 Definition of sin and cos with triangles and the unit circle. Finding these values in other quadrants. Finding these values using your calculator (degrees or radians). A couple story problems. The most basic identities (p. 621). Basic Graphing or identifying graphs.

• Section 8.3 Derivatives of sine and cosine and related story problems.

• Section 8.5 Other trig functions and their derivatives.

Some ideas (not exhaustive) on how to do well on the final.

• Review all problems that were given on previous exams and quizzes. Re-work them all without looking at the solutions, then double check your answers. Any that you get wrong, look for similar odd problems to work in the book. It may help to explicitly write the reasons that the steps necessary to do the problem. For instance, ``Problem is a quotient, so use the quotient rule.'' This can help if you get nervous during exams.

• Review each homework set and check for any sets that were difficult and you might need to review.

• Create flash cards for all of the derivative rules and memorize them.

• Select practice derivative problems and be able to do them well.

• Start before Wednesday.

• No partying or cramming on Wednesday, get some sleep the night before.