## Math 311 - Vector Analysis - Fall 2012

Instructor: Greg von Winckel (Office phone: 272-7945)

Class times: Tuesday and Thursday 14:00-15:15 in Sarah Raynolds Hall room 101

Office hours: Thursday 15:30-17:00 on the ground floor of SMLC

Prerequisite: Math 264 - multivariable calculus

## Free supplementary text online: A Quick Introduction to Tensor Analysis

## Course outline

This course develops the geometrical ideas of two and three dimensional vector calculus. It is good preparation for advanced engineering and physics courses, Classical Mechanics, Statics, Kinematics, Dynamics and Vibrations, Electromagnetics and Wave Propagation, Fluid Flow and Elasticity.

Vector Algebra; Scalar and Vector Products; vector identities; lines, planes and vector geometry. Vector functions; diferentiation; space curves, velocity, acceleration; curvature and torsion. Scalar and Vector Fields; gradients and level lines; flow lines; divergence and flux; curl and circulation; Laplacian and tension. Orthogonal curvilinear coordinates. Line, surface and volume integrals. The theorems of Gauss, Stokes and Helmholtz. Orthogonal matrices and rotations in 3 dimensions. Quaternions. Vector equations of Classical Mechanics.

**Topics to be covered include:**Vector Algebra; Scalar and Vector Products; vector identities; lines, planes and vector geometry. Vector functions; diferentiation; space curves, velocity, acceleration; curvature and torsion. Scalar and Vector Fields; gradients and level lines; flow lines; divergence and flux; curl and circulation; Laplacian and tension. Orthogonal curvilinear coordinates. Line, surface and volume integrals. The theorems of Gauss, Stokes and Helmholtz. Orthogonal matrices and rotations in 3 dimensions. Quaternions. Vector equations of Classical Mechanics.