Description: Introduction A Brief History of the World A Summary of the Topics Examples and Exercises Basic Concepts from Physics Rigid Body Classification Rigid Body Kinematics Newton's Laws Forces Momenta Energy Rigid Body Motion Newtonian Dynamics Lagrangian Dynamics Euler's Equations of Motion Deformable Bodies Elasticity, Stress, and Strain Mass-Spring Systems Control Point Deformation Free-Form Deformation Implicit Surface Deformation Fluids and Gases Vector Calculus Strain and Stress Conservation Laws A Simplified Model for Fluid Flow Implementing the Simplified 2D Model Implementing the Simplified 3D Model Variations of the Simplified Model Physics Engines The Physics Tick Collision Culling Test-Intersection Queries Collision Detection with Convex Polyhedra Unconstrained Motion Acceleration-Based Constrained Motion Velocity-Based Constrained Motion Variations Linear Algebra A Review of Number Systems Systems of Linear Equations Matrices Vector Spaces Advanced Topics Affine Algebra Introduction Coordinate Systems Subspaces Transformations Barycentric Coordinates Calculus Univariate Calculus Multivariate Calculus Applications Quaternions Rotation Matrices The Classical Approach A Linear Algebraic Approach Interpolation of Quaternions Derivatives of Time-Varying Quaternions Differential Equations First-Order Equations Existence, Uniqueness, and Continuous Dependence Second-Order Equations General-Order Differential Equations Systems of Linear Differential Equations Equilibria and Stability Ordinary Difference Equations Definitions Linear Equations Constant Coefficient Equations Systems of Equations Numerical Methods Euler's Method Higher-Order Taylor Methods Methods via an Integral Formulation Runge-Kutta Methods Multistep Methods Predictor-Corrector Methods Extrapolation Methods Verlet Integration Numerical Stability and Its Relationship to Physical Stability Stiff Equations Linear Complementarity and Mathematical Programming Linear Programming The Linear Complementarity Problem Mathematical Programming Applications Contact Forces

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