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45788-UlabyISMCh03

# 45788-UlabyISMCh03 - 107 Chapter 3 Vector Analysis...

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107 Chapter 3: Vector Analysis Lesson #14 Chapter — Section: 3-1 Topics: Basic laws of vector algebra Highlights: Vector magnitude, direction, unit vector Position and distance vectors Vector addition and multiplication - Dot product - Vector product - Triple product Special Illustrations: CD-ROM Module 3.2

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108 Lessons #15 and 16 Chapter — Section: 3-2 Topics: Coordinate systems Highlights: Commonly used coordinate systems: Cartesian, cylindrical, spherical Choice is based on which one best suits problem geometry Differential surface vectors and differential volumes Special Illustrations: Examples 3-3 to 3-5 Technology Brief on “GPS” (CD-ROM) Global Positioning System The Global Positioning System (GPS), initially developed in the 1980s by the U.S. Department of Defense as a navigation tool for military use, has evolved into a system with numerous civilian applications including vehicle tracking, aircraft navigation, map displays in automobiles, and topographic mapping. The overall GPS is composed of 3 segments. The space segment consists of 24 satellites (A), each circling Earth every 12 hours at an orbital altitude of about 12,000 miles and transmitting continuous coded time signals. The user segment consists of hand-held or vehicle-mounted receivers that determine their own locations by receiving and processing multiple satellite signals. The third segment is a network of five ground stations , distributed around the world, that monitor the satellites and provide them with updates on their precise orbital information. GPS provides a location inaccuracy of about 30 m, both horizontally and vertically, but it can be improved to within 1 m by differential GPS (see illustration).
109 Lesson #17 Chapter — Section: 3-3 Topics: Coordinate transformations Highlights: Basic logic for decomposing a vector in one coordinate system into the coordinate variables of another system Transformation relations (Table 3-2) Special Illustrations: Example 3-8

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110 Lesson #18 Chapter — Section: 3-4 Topics: Gradient operator Highlights: Derivation of T in Cartesian coordinates Directional derivative T in cylindrical and spherical coordinates Special Illustrations: Example 3-10(b) CD-ROM Modules 3.5 or 3.6 CD-ROM Demos 3.1-3.9 (any 2)
111 Lesson #19 Chapter — Section: 3-5 Topics: Divergence operator Highlights: Concept of “flux” Derivation of . E Divergence theorem Special Illustrations: CD-ROM Modules 3.7-3.11 (any 2) CD-ROM Demos 3.10-3.15 (any 1 or 2)

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112 Lesson #20 Chapter — Section: 3-6 Topics: Curl operator Highlights: Concept of “circulation” Derivation of x B Stokes’s theorem Special Illustrations: Example 3-12
113 Lesson #21 Chapter — Section: 3-7 Topics: Laplacian operator Highlights: Definition of 2 V Definition of 2 E Special Illustrations: Technology Brief on “X-Ray Computed Tomography” X-Ray Computed Tomography Tomography is derived from the Greek words tome , meaning section or slice, and graphia , meaning writing.

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45788-UlabyISMCh03 - 107 Chapter 3 Vector Analysis...

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