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The topics of this textbook are curves in differential geometry and they are studied by means of parametrization. Particularly; curvilinear coordinates, plane curves and skew curves like; helices, involutes, evolutes, spherical indicatrix, circles and spheres of curvatures. It also introduces some quadratic surfaces, theory of contacts, curves-surfaces contacts relationships, envelops, and the geometry of curves in differential geometry in general. The main properties of these objects, which will be studied, are notions related to the shape; specifically; tangents, principle normals,...

This textbook is written to develop thorough understanding the mastery behind the foundations of geometry that needed to solve geometric problems using vectors in three dimensional Euclidean space at a useful proficiency level, it introduces a comprehensive study on three dimensional Euclidean spaces' objects, namely; points, line segments, vectors, straight lines, planes, spheres, cylinders, quadratic surfaces in general analytically, and includes different comparisons between such studied objects among themselves, it focuses on the orthogonal projections of a point and directed line segment...

This book is developed and written for undergraduate and postgraduate students who are studying functional analysis. It gives answers for many important questions, supplies students with adequate studies required for their future academic needs? On the other side, it introduces some recent results for researchers. It is readable, available and flexible in use because it introduces the basics of linear algebra, linear spaces, basis and dimension supported with many examples, basic concepts of functional analysis especially; the normed, the metric, and inner product spaces' concepts and the...

This text book introduces a comprehensive study on two dimensional conic sections, pair of straight lines, circles, ellipses, parabolas, and hyperbolas (standard and general forms). It focuses mainly on the study of tangent lines, normal lines, tangential chords, pole and polar, reflection properties, relations between such studied objects, translations, and rotation of axes. The text book ends with displaying some of their important applications.