Harvard University,FAS
Summer 2005

Mathematics Math1b
Summer 2005

Introduction to Functions and Calculus II
and Differential equations

Course Head: Robin Gottlieb

Office: SciCtr 430
Email: gottlieb@math.harvard.edu
Mainpage Syllabus Calendar Homework Exams Supplements Links

Exams

Technique Test Solutions
The first midterm
Integration Synopsis 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 fall 04's first midterm:

  Fall 04's First Midterm

  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.

Fall 2001 (Questions 2,3,5,7, and 8 only) Solutions
Spring 2000 (Questions 2,5,6, and 7c only) Solutions
Spring 1999 (Questions 1,2,3, and 4 only) Solutions
Fall 1998 (Questions 5,6 and 7 only) Solutions
Review Problem Sheet
Solutions

The second midterm

Here is a review sheet prepared for the second midterm.

Review Sheet
(Neglect page 7)

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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:

Spring 1999 Solutions
Fall 1999 Solutions
Fall 1998 Solutions
Review Problem Sheet
(Neglect 25c) 		Solutions
Fall 2003Hard! Solutions

Final

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.

Fall 1995 Solutions
Fall 1998 (Omit 3a) Solutions
Fall 1999 Solutions
In #8: the differ'l eqn
is BOTH first order
linear AND separable.
The answer is y = Ce^(x^2/2) - 1.
(The exponent got cut off.)
Spring 1999 (Omit 2b)
Also, note that in 3, you could
have simply been asked for the solution. 		Soltutions

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.)



Maths 1b, Summer, 2005, maths1b@fas.harvard.edu, Department of Mathematics, Faculty of Art and Sciences, Summer School, Harvard University