Quick Links:
Instructor:
Ralf Wittenberg
K-10536, 291-4792
ralf@sfu.ca |
Lectures:
M, W, F 8:30-9:20am
in K 9500 |
Text:
Davis & Snider,
Introduction to Vector Analysis
Wm.C. Brown |
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Announcements:
- Welcome to MATH 252!
- Lecture notes (including those for the second lecture, for many students shortened by snow-induced transportation delays) are available on the Library Reserves
- Homework Set 1 due 14 January
Vector Analysis
The mathematical description of much of physics and engineering, including mechanics, continuum and fluid mechanics, and electromagnetism, depends heavily on the language of vectors, particularly in three dimensions. In this course we will develop the theory of vector analysis, the differential and integral calculus of scalar and vector functions in one and several dimensions, leading us to the great theorems of Green, Gauss and Stokes. We will aim for an appreciation both of the underlying mathematics as well as of some of the applications that have historically motivated this theory. As time permits, we will explore how one can extend the linear structure of vector algebra to more general vector spaces of polynomials and functions, including an introduction to Fourier series.
- Lecture 1: 5 January
Introduction:
Course outline: vector analysis and its applications; historical introduction, vectors and quaternions (for interest only); introduction to vectors
Reading: D&S Appendix A; Ch.1 (1.1, 1.2)
- Lecture 2: 7 January (snow-delayed...)
Vector Geometry: Operations on vectors: addition and scalar multiplication; vector spaces; Cartesian coordinates; types of vectors; geometrical and analytical descriptions
Reading: D&S Ch.1 (1.2, 1.3, 1.4, 1.5, 1.6, 1.7)
- Homework Set 1
- Suggested additional exercises for this lecture (optional):
1.2 - 7; 1.3 - 4, 13, 14; 1.4 - 4, 10, 13; 1.5 - 1, 8, 8, 15, 19, 21; 1.6 - 1, 4
- Lecture 3: 9 January
Scalar Product: Geometry using vectors; the inner (dot) product, orthogonality, projections
Reading: D&S Ch.1 (1.7, 1.9)
- Homework Set 1
- Problems (HW Set 2): 1.7 - 3; 1.9 - 20, 21, 24, 25, 28
- Suggested additional exercises for this lecture (optional):
1.7 - 9, 11, 12, 15, 19, 22, 25; 1.9 - 2, 5, 9, 11, 13, 18, 19, 27
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