![]() Spring 2005 |
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| Solutions |
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Integration Synopsis
For the first exam in the spring of 2005 we will be omitting probabilityquestions. Because arclength and average value are being covered so close to the exam, they will not be examined on this first exam, but are fair game in the future. When you look at old exams, be aware that we have not covered the topics of surface area and fluid pressure.
Below you can find the exam and the solutions to the spring 03's and the fall 04's first midterm:
Spring 03's First Midterm Solutions
Fall 04's First Midterm Solutions
Here are some previous exams and solutions that should provide a good review of the material you have covered to date.
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Here is a review sheet prepared for the second midterm.
   Review Sheet
Below you can find the exam and the solutions to spring 03's second midterm:   Spring 03's Second Midterm   Spring 03's Second Midterm Solutions Here are some previous exams and solutions that should provide a good review of the material you have covered to date. Because of changes in the syllabus, you are not responsible for problems that involve the Taylor remainder theorem.These problems are noted below:
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Past final exams can be found below. You are not responsible for problems requiring the Taylor Remainder, Surface Area, and solving differential equations with series.
Here is a differential equation review sheet.    Differential Review
And a more qualitative one.    Take Two    Take Two Solutions (Note: Part of #8 is mysteriously absent. The equation is x'' +x' + 4x =0 and the initial conditions are x(0) = -1 and x'(0) = -1.)
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| Math 1b, Spring, 2005, math1b@fas.harvard.edu, Department of Mathematics, Faculty of Art and Sciences, Harvard University |