Outline (Table Of Contents)

Home: Galileo's Wisdom

Prolog: On Optimizing the Design of Introductory Mathematics 

Standard Algebraic Tools for Linear Geometry

          Rules for Vector Addition

          Rules for Multiplication by Scalars

          Parametric Equations

Introduction to Geometric Algebra and Basic 2D Applications

          Defining and Interpreting the Geometric Product 

          Rotors and Rotations in the Euclidean Plane 

          Vector Identities and Plane Trigonometry with GA 

          Modeling Real Objects and Motions with Vectors

          High School Geometry with Geometric Algebra 

          Basic Kinematic Models of Particle Motion

                    Free Particle Model

                    Constant Acceleration Model

                    Circular Motion Model

                    General Kinematic Theorem

                    General Keplerian Motion

          Planar Rigid Body Motion and Reference Frames

          The Zeroth Law of Physics

Special Relativity with Geometric Algebra

          Defining Spacetime

          Spacetime Maps

                    Particle History and Proper Velocity

          Spacetime Trigonometry

                    Time Dilation and Desynchronization

                    Lorentz Contraction

                    Doppler Shift

          Lorentz transformations

                    Velocity Composition

                    Active Lorentz Transformations            

          Energy and Momentum

                    The Proper Momentum

                    The Photon

                    Energy-Momentum Conservation

          Universal Laws for Spacetime Physics

© David Hestenes 2005, 2014