Math 251 (Fall 2013)

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Course Information

Description: Multivariable Calculus.

Instructor: Casian Pantea. email me

Class schedule: Mondays, Wednesdays 4-5:50PM in Armstrong Hall room 112, starting August 19.

Office hours: Mondays 2-3PM, Wednesdays 6-7PM in Armstrong Hall 305B.

Additional help: Monday-Thursday 8AM-3PM, Friday 8AM-2PM.

Info sheet containing more or less the stuff on this webpage.

Textbooks and resources

Textbook: The main book is Essential Calculus Early Transcendentals, Stewart (first edition)

Useful free resources:

Linear algebra notes

Linear Algebra Done Wrong, Treil
Linear Algebra -- wiki textbook
Professor Moseley's notes

Web goodies

Khan Academy


Grading scheme

  • 45% Final exam on Monday December 16 2013, 3-5PM in Armstrong Hall room 112
  • 25% Best of two midterm exams
  • 15% Homework assignments
  • 15% Quizzes


  • There will be seven quizzes (one every two weeks), out of which the best six will count towards your grade.
  • Quizzes will test the material covered during the previous two weeks.
  • No make-up quizzes will be given.


  • Homework will be assigned once every two weeks, and due two weeks later (please see the course schedule below for exact dates).
  • Three or four random problems will be chosen and graded for each homework.
  • Your best six homework papers will count towards the final grade.
  • Late turn-ins will not be accepted.


  • There will be two 75-minutes in-class midterm exams, on October 2 and November 6.
  • Your best midterm exam will count towards the final grade.
  • Calculators will not be allowed.
  • No make-up midterm will be given.

Final Exam

  • December 16 2013, 3-5PM in Armstrong Hall room 112
  • Final is cumulative.

Course Schedule

Date Topic Resources HW/Quiz
Aug 19 Matrices and systems of linear equations Class notes
Gauss elimination
Reduced row echelon (Gauss-Jordan) form
Reduced row echelon form (Khan Academy)
Solving linear equations (Moseley)
Evaluation Test
Aug 21 Systems of linear equations (continued)
Matrix operations
Class notes
Matrix multiplication
Matrix Multiplication (Khan Academy)
Computing inverses
HW1 posted
Aug 26 Rn as a vector space.
Linear transformations in Rn
Class notes Quiz 1 solutions
Aug 28 Image of a linear transformation, span, linear independence Class notes
Sep 4 Vectors in 3D. Dot product 10.1 - 10.3 HW1 due
HW2 posted
Sep 9 Cross product 10.4 Quiz 2 solutions
Sep 11 Lines, planes 10.5
Sep 16 Cylinders and quadrics; vector functions, curves. 10.6-10.7 HW2 due
HW3 posted
Sep 18 Arc length, curvature; velocity and acceleration 10.8 - 10.9
Sep 23 Functions of several variables 11.1 Quiz 3 solutions
Sep 25 Limits, continuity 11.2
Sep 30 Review
Partial derivatives
11.3 HW3 due
HW4 posted
Oct 2 Midterm 1
Chain rule
11.5 Midterm 1
Oct 7 Directional derivative, gradient vector 11.6 Quiz 4 solutions
Oct 9 Tangent planes and linear approximation 11.4
Oct 16 Maximum and minimum values 11.7 HW4 due
HW5 posted
Oct 21 Lagrange multipliers; Double integrals 11.8-12.1 Quiz 5 solutions
Oct 23 Double integrals, polar coordinates 12.2 - 12.3
Oct 28 Applications of double integrals; triple integrals 12.4-12.5 HW5 due
HW6 posted
Oct 30 Cylindrical and spherical coordinates 12.6 - 12.7
Nov 4 Change of variables 12.8 Quiz 6 solutions
Nov 6 Midterm 2
Midterm 2
Nov 11 Vector fields. Line integrals 13.1-13.2 HW6 due
HW7 posted
Nov 13 Fundamental theorem for line integrals 13.3
Nov 18 Green's theorem 13.4 Quiz 7
Nov 21 Curl and divergence 13.5
Dec 2 Linear algebra review
Dec 4 Review
Dec 9 Review HW7 due
Dec 16 Final exam 3-5PM in Armstrong Hall room 112

Where does your score stand?

Doing well in this class

The material in this class is dense and not trivial. As is often the case in math courses, we will constantly build upon previous stuff; therefore, not leaving gaps in your understanding of the material is crucial for succeeding. This will require a sustained effort on your part, and in addition to attending lectures, you are encouraged to take advantage of instructor's office hours and the drop-in Math Learning Center. Of course, this is not a substitute for also working on your own; it is essential to think about the material, read the suggested texts, and solve homework problems by yourself. This last bit is a prerequisite to being able to solve problems under the pressure of a quiz or an exam.

Accessibility Needs

If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Disability Services (304-293-6700).