Technical Books

These notes provide an introduction to the mechanics of elastic solids for beginning graduate students. They may be downloaded without charge. Topics covered includes Kinematics Deformation, Kinematics Motion, Mechanical Balance Laws and Field Equations, Thermodynamic Balance Laws and Field Equations, Singular Surfaces and Jump Conditions, Constitutive Principles, Elastic Materials, Linearized Elasticity, Compressible Fluids, Liquid Crystals.

This note explains the following topics: Tensor calculus, Tensor algebra, Tensor analysis, Kinematics, Rates of kinematic quantities, Gradients of kinematic quantities, Balance equations, Concept of mass flux, Concept of stress, Balance of mass, Balance of linear momentum, Balance of angular momentum, Balance of energy, Constitutive equations, Linear constitutive equations.

This note will create a much more stable basis for continued work or study in the field of mechanics of continua, be they solid or fluid. Topics covered includes: Vectors and second order tensors, Change of coordinates, Higher order tensors, Derivatives, Analysis of small deformations, Kinematics, The dynamic equations of continuum mechanics, Elastic materials, Isotropic linearly elastic solids, Compatibility and Plane elasticity, Variational principles, Newtonian fluids and Elastic fluids.

Topic of continuum mechanics deals with the basics equations of motion that governs the mechanics of both solid and fluid objects in nature. Topics covered includes: Set, notation, Functions, Vectors, Matrices, Tensors, Kinematics, Stress measures and stress rates, Balance law, Balance laws.

This note explains the following topics: Vectors, Tensors, Tensor properties, Vector and tensor fields, Configurations, Motion, The Lagrangian description of motion, Stretch and strain tensors, The polar decomposition, Velocity gradients, and rates of deformation, Balance of mass, Reynolds transport theorem, Linear and angular momentum, Models of viscous fluids, Material symmetry, Classical continuum mechanics, The heat transport equation, The free energy functional, Phase separation-non convex free energy, The Cahn-Hilliard formulation.

This note covers the following topics: Mathematical preliminaries, Stress, Motion and deformation, Balance of mass, Momentum and energy and ideal constitutive relations.

This note explains the following topics: Notations and tensor algebra, Kinematics of finite deformation, Balance laws, Euclidean objectivity, Principle of material frame indifference, Material symmetry, Elastic solids, Viscoelastic materials, Second law of thermodynamics, Some problems in finite elasticity, Wave propagation in elastic bodies and mixture theory of porous media.

This note contains below topics, Geometric formulation of nonlinear elasticity, PortHamiltonian model of nonlinear elasticity, PortHamiltonian model of fluid flow, Constitutive relations.

This note contains below topics, A short review of convenient calculus in infinite dimensions, Manifolds with corners, Whitney manifold germs, Manifolds of mappings, Regular Lie groups, Spaces of embeddings or immersions and shape spaces, Weak Riemannian manifolds, Robust weak Riemannian manifolds and Riemannian submersions.

This note covers the following topics: Conserved Quantities, Energy and Momentum, Charge, Angular Momentum, Particle categories, Leptons and Lepton Number, Baryons and Baryon Number.

This note covers the following topics: introduction, calculus of variations basics, the action, Lagrangian and lagrangian density, particles, fields, canonical variables, the euler-lagrange equations and dynamics in particles, fields, Noether's theorem and conservation laws.

We are working on the detailed description of this book, we will update this section soon.

These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension. The various chapters cover the following topics: Meaning of a conservation equation and definition of weak solutions, Hyperbolic systems, Shock waves: Rankine-Hugoniot equations and admissibility,Genuinely nonlinear and linearly degenerate characteristic fields, Centered rarefaction waves,The general solution of the Riemann problem, Wave interaction estimates,Weak solutions to the Cauchy problem, with initial data having small total variation, Approximations generated by the front-tracking method and by the Glimm scheme, Vanishing viscosity approximations.

This note covers the following topics: introduction, conservation laws, the wheatstone bridge electric circuit, the golden ratio, embryonic development.

These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension.