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Páginas: 49 (12185 palabras)
Publicado: 11 de junio de 2012
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
108
Lessons #15 and 16
Chapter — Section: 3-2 Topics: Coordinatesystems 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 milesand 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 providesa 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
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: Divergenceoperator 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)
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 #21Chapter — 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. Computed tomography, also known as CT scan or CAT scan (for computed axial tomography),refers to a technique capable of generating 3-D images of the x-ray attenuation (absorption) properties of an object. This is in contrast with the traditional x-ray technique which produces only a 2-D profile of the object. CT was invented in 1972 by British electrical engineer Godfrey Hounsfield, and independently by Allan Cormack, a South African-born American physicist. The two inventors sharedthe 1979 Nobel Prize for Physiology or Medicine. Among diagnostic imaging techniques, CT has the decided advantage in having the sensitivity to image body parts on a wide range of densities, from soft tissue to blood vessels and bones.
114
CHAPTER 3
Chapter 3
Section 3-1: Vector Algebra
Problem 3.1 Vector A starts at point 1 a unit vector in the direction of A. Solution: 1 3 and ends...
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
108
Lessons #15 and 16
Chapter — Section: 3-2 Topics: Coordinatesystems 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 milesand 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 providesa 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
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: Divergenceoperator 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)
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 #21Chapter — 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. Computed tomography, also known as CT scan or CAT scan (for computed axial tomography),refers to a technique capable of generating 3-D images of the x-ray attenuation (absorption) properties of an object. This is in contrast with the traditional x-ray technique which produces only a 2-D profile of the object. CT was invented in 1972 by British electrical engineer Godfrey Hounsfield, and independently by Allan Cormack, a South African-born American physicist. The two inventors sharedthe 1979 Nobel Prize for Physiology or Medicine. Among diagnostic imaging techniques, CT has the decided advantage in having the sensitivity to image body parts on a wide range of densities, from soft tissue to blood vessels and bones.
114
CHAPTER 3
Chapter 3
Section 3-1: Vector Algebra
Problem 3.1 Vector A starts at point 1 a unit vector in the direction of A. Solution: 1 3 and ends...
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