Solutions for our first midterm:

• Solutions for Oct 27th, 1999 midterm

The first midterm will be held on Wednesday, Oct. 27, from 7:30 to 9:30 pm.  Students in MWF sections should take the exam in Science Center Hall C, students in T/Th sections should take the exam in Science Center Hall D.

There will be a coursewide review held on Saturday, Oct. 23rd from 3:30 to 5pm in Science Center Hall D - everyone is welcome to come.  Remember also to take advantage of the Math Question Center which meets from Sunday to Thursday from 8 to 10 pm in Loker.

On this first midterm you should be prepared to answer questions from any of the following topics: (note the first test just covers material from the series part of the semester, you will not be tested on any new material from sections 7.5 and 7.6 which you might have covered before the exam)

• Basic infinite series information: definition of convergence/divergence (i.e. know what partial sums are), sigma notation
• Geometric series:  know how to recognize them,  and how to find the sum of a convergent geometric series
• P-series: know what values of p do they converge
• Harmonic series: basic example of a diverging series whose individual terms diminish to zero
• Convergence Tests:
• Comparison Tests (including limit comparison test),
• Ratio Tests,
• Divergence Test,
• Alternating Series Test
• Alternating series: for converging alternating series know how to bound the difference between a partial sum and the actual sum
• Power series: know what they are, know how to find intervals/radii of convergence (check your endpoints for convergence!)
• Taylor/Maclaurin series (note a Maclaurin series is simply a Taylor series around the point x=0):
• know how to calculate Taylor series by taking ,
• know how they "evolve" from the best linear, quadratic, cubic, etc. approximations of functions,
• know how to find new series from old ones by substitutions and simple algebraic manipulations,
• know how to differentiate/integrate series to find series for new functions (note the radius of convergence stays the same, but you need to recheck the endpoints for convergence!)
• know your basic Taylor series for sin x, cos x, e^x, and 1/(1-x)
• Note there are several topics which will not be covered on the exam:
• No root test or integral test
• No conditional versus absolute convergence questions
• Nothing from section 11.9 (i.e. no error estimations based on material from section 11.9)

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Old Exams for practise:

• Note that although the class is quite similar from last year to this year, we did not cover section 11.9 this semester.  This means you shouldn't panic if you can't do the questions involving remainder estimates.  However, you should be able to solve all of the other questions.
• We will post solutions to these two exams shortly... first try to do them on your own!
• Exam 1, Fall 98  (Solutions)
• (please note correction on 2(a), the answer should read "...series converges only for x=3")
• Exam 1, Spring 99  (Solutions)