Here is a genuine introduction to the differential geometry of plane curves for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. This well-illustrated text contains several hundred worked examples and exercises, making it suitable for adoption as a course text. Key concepts are illustrated by named curves, of historical and scientific significance, leading to the central idea of curvature. The author introduces the core material of classical kinematics, developing the geometry of trajectories via the ideas of roulettes and centrodes, and culminating in the inflexion circle and cubic of stationary curvature.
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"This book is pleasant for a student...It contains many interesting properties and features of curves which usually are not shown in a regular undergraduate course." Mathematical Reviews
Book Description
This genuine introduction to the differential geometry of plane curves is designed as a first text for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. The book assumes only foundational year mathematics: it is well illustrated, and contains several hundred worked examples and exercises, making it suitable for adoption as a course text.
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First Sentence:
We need to lay firm foundations for later work. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
inflexion circle, irregular parameter, limiting tangent line, standard hyperbola, parametric equivalence, orthogonal bisector, moving centrode, fixed centrode, ordinary cusp, unit speed curve, cuspidal tangent, congruent curves, double slider, taking moduli, standard conics, two inflexions, planar kinematics, standard ellipse, ordinary vertices, self crossing, limiting gradient, complex number notation, generic motion, circle envelope, instantaneous centre Key Phrases - Capitalized Phrases (CAPs): (learn more)
Factor Theorem, Uniqueness Theorem, Envelope Theorem, Serret-Frenet Formulas, Proof Write, Proof Let, Proof By Lemma, Variability Condition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We need to lay firm foundations for later work. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
inflexion circle, irregular parameter, limiting tangent line, standard hyperbola, parametric equivalence, orthogonal bisector, moving centrode, fixed centrode, ordinary cusp, unit speed curve, cuspidal tangent, congruent curves, double slider, taking moduli, standard conics, two inflexions, planar kinematics, standard ellipse, ordinary vertices, self crossing, limiting gradient, complex number notation, generic motion, circle envelope, instantaneous centre Key Phrases - Capitalized Phrases (CAPs): (learn more)
Factor Theorem, Uniqueness Theorem, Envelope Theorem, Serret-Frenet Formulas, Proof Write, Proof Let, Proof By Lemma, Variability Condition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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