Geometric Algebra Computing in Engineering and Computer Science 2010th Edition by Eduardo Bayro Corrochano, Gerik Scheuermann ISBN 1849961077 9781849961073

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Product details:

ISBN 10: 1849961077
ISBN 13: 9781849961073
Author: Eduardo Bayro Corrochano, Gerik Scheuermann

This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Its accessible style is enhanced by examples, figures and experimental analysis.

Geometric Algebra Computing in Engineering and Computer Science 2010th Table of contents:

Part I: Introduction to Geometric Algebra

1. Foundations of Geometric Algebra

   • Overview of geometric algebra.
   • Geometric algebra vs. traditional linear algebra and vector spaces.
   • Algebraic operations: addition, multiplication, and geometric product.

2. Geometric Objects and Multivectors

   • Basic geometric objects: points, lines, planes, and volumes.
   • Representing multivectors and their geometric interpretations.

3. Clifford Algebra and Its Computation

   • Introduction to Clifford algebra (generalized geometric algebra).
   • Relationship with geometric algebra and its computational uses.
   • Norms, inner products, and outer products in geometric algebra.

Part II: Geometric Algebra in Engineering

4. Applications to Robotics

   • Kinematics and dynamics of rigid body motion.
   • Geometric algebra for robot motion planning and control.
   • Pose and transformations in robotics.

5. Computer Graphics and Visualization

   • Geometric transformations in computer graphics.
   • Using geometric algebra for rendering, rotation, and scaling.
   • Efficient computation in graphical transformations.

6. Signal Processing and Control Systems

   • Signal processing techniques using geometric algebra.
   • Geometric methods in control theory and analysis of dynamic systems.

7. Mechanical and Civil Engineering Applications

   • Modeling stress, strain, and other physical quantities in mechanics.
   • Geometric algebra in finite element analysis and structural engineering.
   • Applications in civil engineering design and construction.

Part III: Advanced Topics in Geometric Algebra

8. Geometric Algebra in Physics

   • Applications in classical mechanics, electromagnetism, and relativity.
   • The use of geometric algebra in quantum mechanics.
   • Field theory and differential forms in geometric algebra.

9. Computational Methods in Geometric Algebra

   • Numerical techniques for implementing geometric algebra algorithms.
   • Geometric algebra for parallel computing and high-performance applications.
   • Use of geometric algebra in simulation and modeling software.

10. Geometric Algebra for Machine Learning and AI

    • Geometric algebra in pattern recognition and classification tasks.
    • Applications in deep learning, computer vision, and robotics.
    • Leveraging geometric algebra in neural network architectures.

Part IV: Case Studies and Real-World Applications

11. Geometric Algebra in 3D Graphics and Animation

    • Practical case studies in graphics and animation using geometric algebra.
    • Implementing 3D transformations and rendering techniques.

12. Geometric Algebra in Engineering Simulations

    • Real-world applications in engineering simulations.
    • Integrating geometric algebra in commercial software tools for engineering design.

13. Applications in Aerospace and Automotive Engineering

    • Aerospace applications of geometric algebra: flight dynamics, navigation, and control.
    • Automotive applications: path planning, vehicle dynamics, and control systems.

Part V: Future Directions

14. Emerging Trends in Geometric Algebra
    • Future research directions and the growing role of geometric algebra in computing.
    • The evolution of geometric algebra software tools.
    • Interdisciplinary applications of geometric algebra in engineering and computer science.

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