A01=J.W. Rutter
advanced curve problem solving
algebraic
Algebraic Curve
Algebraic Curves
analytic curve analysis
angle
argand
Argand Diagram
Author_J.W. Rutter
Category=PBM
curvature applications
cusp
diagram
differential geometry
envelope construction
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
graph
Homogeneous Polynomial
Isolated Singular Points
non-regular
Non-regular Points
Non-singular Point
Non-vanishing Derivative
Nonsingular Point
ordinary
Ordinary Cusp
Osculating Circle
Parabola Y2
Parametric Curve
Parametric Equation
Plane Algebraic Curve
points
polar
Polar Equation
Polar Graph Paper
Real Linear Factors
Regular Point
Semi-cubical Parabola
Semicubical Parabola
Simple Inflexion
Simple Undulation
Singular Points
singularity classification
Tangent Vector
transcendental functions
Product details
- ISBN 9781138430372
- Weight: 860g
- Dimensions: 156 x 234mm
- Publication Date: 02 Aug 2017
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving.
Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness.
The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations.
The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.
