Mathematics 103.02 - Intermediate Calculus

Fall Semester 2010


Calculus with Analytic Geometry, Sixth Edition, by Edwards and Penney and published by Prentice-Hall


William K. Allard, Professor of Mathematics
  • Office: 029A Physics Building
  • Phone: (919) 660-2861
  • Fax: (919) 660-2821
  • E-mail:
  • Office Hours: Monday, Wednesday and Friday, 11:15am-12:15pm, 2:00pm-3:00pm, and by appointment.
  • Time and Place for Mathematics 103.02, Fall Semester 2010

  • Monday, Wednesday and Friday, 10:20-11:10 AM, Physics 047
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    Syllabus and Homework

    Click here to see the "Official" Web page; it includes the syllabus and the list of homework problems.

    Most students succeed in this course only if they do the homework on time. I encourage you to work on the homework in groups; of course you cannot submit work you copied from someone else; also, make sure you really understand any problem you do with someone else. You may want to use Maple or Mathematica or some other computer program to assist you in doing the homework and I encourage you to do so. I will use one or both of these programs in class to the extent that time permits.

    You will note that the syllabus is broken into 35 lessons. We have 42 class periods, 3 of which will be tests. That leaves 4 class days to catch up and review.

    Believe me when I tell you this course moves very fast! For that reason it is essential that you discipline yourself to keep up.


    There will be three in class tests each of which will count 20% of your grade;he first test will be Wednesday, October 6; the second test will be Friday, November 5 and the third will be Friday, December 3. There will be a quiz on Friday of each week; the quizzes will count 10% of your grade. There will be a "block" final exam which is to say that all sections will take the same exam at the same time; this will count 30% of your grade. Grades on homework will be assigned and recorded and will be used to decide borderline cases although I won't use it to raise a "B" to an "A".

    I encourage you to look at web sites other instructors may post to see tests and other materials. We will attempt to ensure that grading is consistent across the sections; this means, say, that work worth a B in one section will be worth a B in any other section.

    Help Room and Tutoring

    Click here for information about help for students taking courses like Mathematics 103.


    In previous calculus courses you learned to differentiate and integrate functions of one real variable and to apply these techniques to solve problems of various sorts. There are many interesting and important problems whose solution requires the differentiation and integration of functions of more than one variable, and that is what we intend to teach you how to do in this course. As should not be surprising, one encounters new difficulties in dealing with functions of more than one variable. The best way to overcome these difficulties, at least in the opinion of the Supervisor of this course, is to make sure that you can draw a good picture, at least in your head if not on paper, of every new concept and situation you will encounter. You can get into trouble if you rely solely on your ability to manipulate symbols according to formal rules.

    Many intructors prefer to teach several variable calculus than one variable calculus because of the its geometrical emphasis. It's more fun for them. We hope you will feel the same way.

    Tests Already Given This Semester

  • Answer key to my Test One from this semester PDF Version
  • Answer key to my Test Two from this semester PDF Version
  • Answer key to my Test Three from this semester PDF Version
  • Answer key to my Test One from Fall 2006 PDF Version
  • Answer key to my Test Two from Fall 2006 PDF Version
  • Final Exam Schedule

    The final exam will take place Saturday, December 18 from 9am to noon in Physics 047 which is the room in which we meet.

    Solutions to some quizzes.

  • Solution to Quiz Three PDF Version
  • Solution to Quiz Four PDF Version
  • Solution to Quiz Seven PDF Version
  • Solution to Quiz Nine PDF Version
  • Solution to Quiz Ten PDF Version
  • Supplementary Material

  • Vectors PDF Version Last changed on 9/2/2010.
  • Lines and planes in Euclidean space PDF Version Last changed on 9/2/2010.
  • Lines in space PDF Version Last changed on 9/15/2010.
  • Curves in Euclidean space PDF Version Last changed on 9/15/2010.
  • Arclength reparameterization, curvature and torsion; the Serret-Frenet frame PDF Version Last changed on 9/2/2010.
  • Functions and relations PDF Version
  • Minima and maxima PDF Version
  • Differentiation with respect to a coordinate PDF Version
  • Curves PDF Version
  • The differential and affine approximation PDF Version
  • Solution of Problem 29 in 13.6 (differentials) using Maple PDF Version
  • The second derivative test PDF Version
  • Integration in the plane PDF Version
  • Integration in polar coordinates PDF Version
  • n-coordinates PDF Version
  • The Chain Rule PDF Version Last modified October 3, 2010
  • A problem on implicit differentiation PDF Version
  • The general transformation formula for integrals PDF Version
  • Equality of mixed partial derivatives PDF Version
  • Green's Theorem PDF Version
  • The flow of a vector field PDF Version
  • A summary of the basic integral theorems of vector calculus PDF Version
  • Quiz Ten (Due Monday, November 29) PDF Version
  • Return to: Duke University * Mathematics Department
    Last modified: December 10, 2010 Click here to see tests already given this semester in any of the sections. Looking at these tests is a very good way to study for the final exam!