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E-raamat: Solid Geometry with MATLAB Programming

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Solid Geometry with MATLAB ProgrammingSuurem pilt
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Solid geometry is defined as the study of the geometry of three-dimensional solid figures in Euclidean space. There are numerous techniques in solid geometry, mainly analytic geometry and methods using vectors, since they use linear equations and matrix algebra. Solid geometry is quite useful in everyday life, for example, to design different signs and symbols such as octagon shape stop signs, to indicate traffic rules, to design different 3D objects like cubicles in gaming zones, innovative lifts, creative 3D interiors, and to design 3D computer graphics. Studying solid geometry helps students to improve visualization and increase logical thinking and creativity since it is applicable everywhere in day-to-day life. It builds up a foundation for advanced levels of mathematical studies. Numerous competitive exams include solid geometry since its foundation is required to study other branches like civil engineering, mechanical engineering, computer science engineering, architecture, etc.

This book is designed especially for students of all levels, and can serve as a fundamental resource for advanced level studies not only in mathematics but also in various fields like engineering, interior design, architecture, etc. It includes theoretical aspects as well as numerous solved examples. The book includes numerical problems and problems of construction as well as practical problems as an application of the respective topic. A special feature of this book is that it includes solved examples using the mathematical tool MATLAB.
Preface ix
1 Plane
1(44)
1.1 Definition
1(1)
1.2 General Equation of the First Degree in x, y, z Represents a Plane
1(2)
1.3 Transformation of General form to Normal Form
3(1)
1.4 Direction Cosines of the Normal to a Plane
4(1)
1.5 Equation of a Plane Passing through a Given Point
5(1)
1.6 Equation of the Plane in Intercept Form
6(1)
1.7 Reduction of the General Equation of the Plane to the Intercept Form
7(3)
1.8 Equation of a Plane Passing through three Points
10(5)
1.9 Equation of any Plane Parallel to a Given Plane
15(1)
1.10 Equation of Plane Passing through the Intersection of Two Given Planes
16(1)
1.11 Equation of the Plane Passing through the Intersection
17(4)
1.12 Angle between Two Planes
21(2)
1.13 Position of the Origin w.r.t. the Angle between Two Planes
23(1)
1.14 Two Sides of a Plane
24(2)
1.15 Length of the Perpendicular from a Point to a Plane
26(2)
1.16 Bisectors of Angles between Two Planes
28(3)
1.17 Pair of Planes
31(4)
1.18 Orthogonal Projection on a Plane
35(1)
1.19 Volume of a Tetrahedron
36(9)
Exercise
42(3)
2 Straight Line
45(44)
2.1 Representation of Line (Introduction)
45(1)
2.2 Equation of a Straight Line in the Symmetrical Form
45(1)
2.3 Equation of a Straight Line Passing through Two Points
46(3)
2.4 Transformation from the Unsymmetrical to the Symmetrical Form
49(4)
2.5 Angle between a Line and a Plane
53(1)
2.6 Point of Intersection of a Line and a Plane
54(1)
2.7 Conditions for a Line to Lie in a Plane
55(1)
2.8 Condition of Coplanarity of Two Straight Lines
56(13)
2.9 Skew Lines and the Shortest Distance between Two Lines
69(3)
2.10 Equation of Two Skew Lines in Symmetric Form
72(8)
2.11 Intersection of Three Planes
80(9)
Exercise
87(2)
3 Sphere
89(44)
3.1 Definition
89(1)
3.2 Equation of Sphere in Vector Form
89(2)
3.3 General Equation of the Sphere
91(1)
3.4 Equation of Sphere Whose End-Points of a Diameter are Given
91(2)
3.5 Equation of a Sphere Passing through the Four Points
93(12)
3.6 Section of the Sphere by a Plane
105(1)
3.7 Intersection of Two Spheres
106(9)
3.8 Intersection of Sphere S and Line L
115(1)
3.9 Tangent Plane
116(1)
3.10 Equation of the Normal to the Sphere
117(10)
3.11 Orthogonal Sphere
127(6)
Exercise
129(4)
4 Cone
133(34)
4.1 Definition
133(1)
4.2 Equation of a Cone with a Conic as Guiding Curve
133(5)
4.3 Enveloping Cone to a Surface
138(4)
4.4 Equation of the Cone whose Vertex is the Origin is Homogeneous
142(7)
4.5 Intersection of a Line with a Cone
149(1)
4.6 Equation of a Tangent Plane at (a, 0,7) to the Cone with Vertex Origin
150(2)
4.7 Conditions for Tangency
152(4)
4.8 Right Circular Cone
156(11)
Exercise
164(3)
5 Cylinder
167(18)
5.1 Definition
167(1)
5.2 Equation of the Cylinder whose Generators Intersect the Given Conic
168(2)
5.3 Enveloping Cylinder
170(5)
5.4 Right Circular Cylinder
175(10)
Exercise
182(3)
6 Central Conicoid
185(18)
6.1 Definition
185(1)
6.2 Intersection of a Line with the Central Conicoid
185(1)
6.3 Tangent Lines and Tangent Plane at a Point
186(2)
6.4 Condition of Tangency
188(3)
6.5 Normal to Central Conicoid
191(6)
6.6 Plane of Contact
197(1)
6.7 Polar Plane of a Point
197(6)
Exercise
201(2)
7 Miscellaneous Examples using MATLAB
203(24)
Index 227(2)
About the Authors 229
Nita H. Shah received her PhD in Statistics from Gujarat University in 1994. From February 1990 until now Professor Shah has been Head of the Department of Mathematics in Gujarat University, India. She is a post-doctoral visiting research fellow of University of New Brunswick, Canada. Professor Shahs research interests include inventory modeling in supply chains, robotic modeling, mathematical modeling of infectious diseases, image processing, dynamical systems and their applications, etc. She has published 13 monographs, 5 textbooks, and 475+ peer-reviewed research papers. Four edited books have been prepared for IGI-global and Springer with coeditor Dr. Mandeep Mittal. Her papers are published in high-impact journals such as those published by Elsevier, Interscience, and Taylor and Francis. According to Google scholar, the total number of citations is over 3334 and the maximum number of citations for a single paper is over 177. She has guided 28 PhD Students and 15 MPhil students. She has given talks in USA, Singapore, Canada, South Africa, Malaysia, and Indonesia. She was Vice-President of the Operational Research Society of India. She is Vice-President of the Association of Inventory Academia and Practitioner and a council member of the Indian Mathematical Society.

Falguni S. Acharya is a Professor and Head of the Department of Applied Sciences and Humanities, Parul University, Gujarat, India. Dr Acharya has 23 years of teaching experience and 13 years of research experience. Research interests are in the fields of mathematical control theory in differential and fractional differential systems/inclusions with impulse and mathematical modeling of dynamical systems. She has published 16 articles, one international book and one book chapter.
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