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Differential geometry. Global analysis --- Differentiable mappings --- SINGULARITIES (Mathematics) --- Singularities (Mathematics) --- Geometry, Algebraic --- Differentiable maps --- Mappings, Differentiable --- Differential topology --- Mappings (Mathematics) --- Differentiable mappings. --- Singularities (Mathematics). --- Variétés (mathématiques) --- Applications différentiables. --- Manifolds (Mathematics) --- Singularités (mathématiques) --- Applications différentiables

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This book, first published in 2004, is a genuine introduction to the geometry of lines and conics in the Euclidean plane. Lines and circles provide the starting point, with the classical invariants of general conics introduced at an early stage, yielding a broad subdivision into types, a prelude to the congruence classification. A recurring theme is the way in which lines intersect conics. From single lines one proceeds to parallel pencils, leading to midpoint loci, axes and asymptotic directions. Likewise, intersections with general pencils of lines lead to the central concepts of tangent, normal, pole and polar. The treatment is example based and self contained, assuming only a basic grounding in linear algebra. With numerous illustrations and several hundred worked examples and exercises, this book is ideal for use with undergraduate courses in mathematics, or for postgraduates in the engineering and physical sciences.

Geometry. --- Mathematics. --- Math --- Science --- Mathematics --- Euclid's Elements --- Geometry

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This is a genuine introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book contains several hundred worked examples and exercises, making it suitable for adoption as a course text. From the lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, whilst the ideas of linear systems are used to discuss the classical group structure on the cubic.

Curves, Algebraic.

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Algebraic topology --- 515.1 --- Topology --- Differentiable mappings. --- Stability. --- 515.1 Topology --- Differentiable mappings --- Applications différentiables --- Singularities (Mathematics) --- Singularités (mathématiques) --- Differential topology --- Topologie différentielle --- Applications différentiables --- Singularités (mathématiques) --- Topologie différentielle --- Analyse sur une variété