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© 2010

Modeling of Curves and Surfaces with MATLAB®

  • Covers basic MATLAB® and complex geometrical modeling problems related to analysis and differential equations

  • Provides more than 150 stimulating exercises and problems and over 300 figures reproducible using MATLAB®

  • Includes applications including numerous examples and exercises from a variety of real-world fields such as physics, engineering, biology, computer science, and IT

Textbook

Table of contents

  1. Front Matter
    Pages i-xv
  2. Functions and Transformations

    1. Front Matter
      Pages 1-1
    2. Vladimir Rovenski
      Pages 3-82
    3. Vladimir Rovenski
      Pages 83-134
    4. Vladimir Rovenski
      Pages 135-158
    5. Vladimir Rovenski
      Pages 159-197
  3. Curves and Surfaces

    1. Front Matter
      Pages 200-200
    2. Vladimir Rovenski
      Pages 201-244
    3. Vladimir Rovenski
      Pages 245-284
    4. Vladimir Rovenski
      Pages 285-321
    5. Vladimir Rovenski
      Pages 323-356
    6. Vladimir Rovenski
      Pages 357-411
  4. Back Matter
    Pages 413-452

About this book

Introduction

This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions.

The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors, transformations using matrices, and then studies more complex geometrical modeling problems related to analysis of curves and surfaces. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format.

This text greatly extends the author’s previous title, Geometry of Curves and Surfaces with Maple (Birkhäuser, © 2000), and has a different focus. In addition to being applications driven and motivated by numerous examples and exercises from real-world fields, the book also contains over 60 percent new material, including new sections with complex numbers, quaternions, matrices and transformations, hyperbolic geometry, fractals, and surface-splines and over 300 figures reproducible using MATLAB® programs.

This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines, engineers, computer scientists, and instructors of applied mathematics.

Keywords

Graph MATLAB computer computer science modeling visualization

Authors and affiliations

  1. 1., Department of Mathematics and Computer SUniversity of HaifaHaifaIsrael

Bibliographic information

Reviews

From the reviews:

“The book is devoted to various geometrical topics as graphs of functions, transformations, curves and surfaces as well as their applications in many other disciplines. … The book is written for a large audience of advanced undergraduate and postgraduate students, engineers and computer scientists, instructors of applied mathematics and it is an excellent textbook to be used in lectures as well as for self-study reference.” (Marian Ioan Munteanu, Zentralblatt MATH, Vol. 1206, 2011)