Solid geometry with MATLAB programming [E-Book] / Nita H. Shah, Falguni S. Acharya
Saved in:
Full text |
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Personal Name(s): | Shah, Nita H., author |
Acharya, Falguni S., author | |
Edition: |
1st edition |
Imprint: |
Aalborg :
River Publishers,
2023
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Physical Description: |
1 online resource (242 pages) |
Note: |
englisch |
ISBN: |
9788770227612 9788770227605 |
Series Title: |
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Mathematical, statistical and computational modelling for engineering series
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- Front Cover
- Solid Geometry with MATLAB Programming
- Contents
- Preface
- 1 Plane
- 1.1 Definition
- 1.2 General Equation of the First Degree in x, y, z Represents a Plane
- 1.3 Transformation of General form to Normal Form
- 1.4 Direction Cosines of the Normal to a Plane
- 1.5 Equation of a Plane Passing through a Given Point
- 1.6 Equation of the Plane in Intercept Form
- 1.7 Reduction of the General Equation of the Plane to the Intercept Form
- 1.8 Equation of a Plane Passing through three Points
- 1.9 Equation of any Plane Parallel to a Given Plane
- 1.10 Equation of Plane Passing through the Intersection of Two Given Planes
- 1.11 Equation of the Plane Passing through the Intersection
- 1.12 Angle between Two Planes
- 1.13 Position of the Origin w.r.t. the Angle between Two Planes
- 1.14 Two Sides of a Plane
- 1.15 Length of the Perpendicular from a Point to a Plane
- 1.16 Bisectors of Angles between Two Planes
- 1.17 Pair of Planes
- 1.18 Orthogonal Projection on a Plane
- 1.19 Volume of a Tetrahedron
- Exercise
- 2 Straight Line
- 2.1 Representation of Line (Introduction)
- 2.2 Equation of a Straight Line in the Symmetrical Form
- 2.3 Equation of a Straight Line Passing through Two Points
- 2.4 Transformation from the Unsymmetrical to the Symmetrical Form
- 2.5 Angle between a Line and a Plane
- 2.6 Point of Intersection of a Line and a Plane
- 2.7 Conditions for a Line to Lie in a Plane
- 2.8 Condition of Coplanarity of Two Straight Lines
- 2.9 Skew Lines and the Shortest Distance between Two Lines
- 2.10 Equation of Two Skew Lines in Symmetric Form
- 2.11 Intersection of Three Planes
- Exercise
- 3 Sphere
- 3.1 Definition
- 3.2 Equation of Sphere in Vector Form
- 3.3 General Equation of the Sphere
- 3.4 Equation of Sphere Whose End-Points of a Diameter are Given.
- 3.5 Equation of a Sphere Passing through the Four Points
- 3.6 Section of the Sphere by a Plane
- 3.7 Intersection of Two Spheres
- 3.8 Intersection of Sphere S and Line L
- 3.9 Tangent Plane
- 3.10 Equation of the Normal to the Sphere
- 3.11 Orthogonal Sphere
- Exercise
- 4 Cone
- 4.1 Definition
- 4.2 Equation of a Cone with a Conic as Guiding Curve
- 4.3 Enveloping Cone to a Surface
- 4.4 Equation of the Cone whose Vertex is the Origin is Homogeneous
- 4.5 Intersection of a Line with a Cone
- 4.6 Equation of a Tangent Plane at (a, b, r) to the Cone with Vertex Origin
- 4.7 Conditions for Tangency
- 4.8 Right Circular Cone
- Exercise
- 5 Cylinder
- 5.1 Definition
- 5.2 Equation of the Cylinder whose Generators Intersect the Given Conic
- 5.3 Enveloping Cylinder
- 5.4 Right Circular Cylinder
- Exercise
- 6 Central Conicoid
- 6.1 Definition
- 6.2 Intersection of a Line with the Central Conicoid
- 6.3 Tangent Lines and Tangent Plane at a Point
- 6.4 Condition of Tangency
- 6.5 Normal to Central Conicoid
- 6.6 Plane of Contact
- 6.7 Polar Plane of a Point
- Exercise
- 7 Miscellaneous Examples using MATLAB
- Index
- About the Authors
- Back Cover.