These notes are, for the most part, provided in the form of .pdf files
which the student can access with Acrobat Reader, which is freely
available from the Adobe website.)
A notation (Information) following the hyperlink indicates that the
material
is for the student's information only and will not be explicitly tested
on exams, etc.
The posting date shown indicates the most recent date of posting; thus a lecture
might be posted originally on one date and then corrected, and posted again, at a later date.
The lecture date indicates the first day a particular set of notes was used in class.
Vector spaces
Posted January 14, 2008.
Lecture of Wednesday, January 16, 2008.
The Dot Product
Posted January 14, 2008.
Suggested Exercises. Text, pp. 21, ff.: 5,7,9,15,19,21; pp. 36 ff.: 3,5,7,9,13,15,17,19.
Lecture of Friday, January 18, 2008.
The Cross Product
Posted January 16, 2008.
Lecture of Wednesday, January 23, 2008.
Vector Functions
Posted January 22, 2008.
Lecture of Friday, January 25, 2008.
Properties of Curves
Posted January 16, 2008.
The Wednesday and Friday lectures above relate to sections 4.1 and
4.2 of Chapter 4 in the text.
Suggested exercises: pp. 273 ff.: 1 - 11 odd, 19; pp. 281 ff.: 1 - 9 odd.
Additional Suggested Problems
Posted January 28, 2008.
Key to Additional Suggested Problems
Posted January 29, 2008.
Lecture of Monday, January 28, 2008.
Integration with Respect to Arclength
Posted January 28, 2008.
Lectures of Friday, February 1 and Monday, February 4, 2008.
Scalar Valued Functions and the Gradient Vector
Posted February 6, 2008.
Lecture of Wednesday, February 6, 2008.
Stationary Points, Minima and Maxima
Posted February 6, 2008.
Suggested Exercises. Text, pp. 159 ff.: 12, 12, 16, 17;
pp. 171 ff.: 1, 3, 5, 6, 7, 9, 13, 15, 25;
pp. 222 ff.: 1, 3, 5, 7, 9, 11, 17, 21, 23, 27.
Lecture of Monday, February 11, 2008.
Streamlines and Contour Surfaces
Posted February 14, 2008.
Lectures of Wednesday, February 13, and Friday, February 15, 2008.
Second Order Partial Derivatives; the Hessian
Posted February 14, 2008.
Suggested Exercises: Text, p. 191: 1, 3, 5, 7; p. 202: 1, 3, 5;
p. 222 ff.: 1, 3, 5, 7, 11, 13, 17, 21, 23.
Lecture of Wednesday, February 20, 2008.
Lagrange Multipliers, Page 1
Lagrange Multipliers, Page 2
Lagrange Multipliers, Page 3
Posted February 20, 2008.
Suggested Exercises: Text, pp. 243, 244: 1 - 11 (odd).
Lectures of Monday, February 25 and Wednesday, February 27, 2008.
The Line Integral
Posted February 24, 2008.
Lecture of Friday, February 29, 2008.
Exact Vector Fields, Page 1
Exact Vector Fields, Page 2
Exact Vector Fields, Page 3
Exact Vector Fields, Page 4
Posted February 29, 2008. Suggested exercises on last page.
Lectures of Monday, March 10, and Wednesday, March 12, 2008.
Green's Theorem in the Plane
Posted March 10, 2008.
Lectures of Monday, March 17, and Wednesday, March 19, 2008.
Linear Approximations; the Jacobian Matrix
Posted March 21, 2008.
Lectures of Friday, March 21, and Monday, March 24, 2008.
Changing Variables in Multiple Integrals
Posted March 21, 2008.
Lectures of Wednesday, March 26 and Friday, March 28, 2008.
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 1
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 2
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 3
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 4
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 5
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 6
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 6a
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 7
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 8
Sequences, Contraction Fixed Point, Implicit Function Thm., Page 9
(Page 6a inserted and pages 8, 9 added on Monday, March 31.
Posted March 31, 2008.
Lectures of Monday, April 7, and Wednesday, April 9, 2008.
Surface Integrals
Posted April 14, 2008.
Lecture of Friday, April 11, 2008.
Divergence and Curl
Posted April 14, 2008.
Suggested Exercises: Text, pp. 471 ff.: 3, 5 (treat u,v as parameters here), 6, 9, 11, 13, 15.
pp. 480 ff.: 1, 3, 7, 9. pp. 573 ff.: 1, 3, 5, 7, 9.
Lecture of Monday, April 14, and Friday, April 18, 2008.
Gauss Divergence Theorem
Posted April 14, 2008.
Lectures of Monday, April 21, and Wednesday, April 23, 2008.
Stokes Theorem and Applications
Posted April 23, 2008. Example 3 on page 6 corrected April 25, 2008.
Lecture of Friday, April 25, 2008. See pp. 532 - 537 in text.
