Technical Books

This note contains below topics, Mathematical Reasoning Proof Principles and Logic, Relations Functions Partial Functions, Some Counting Problems Binomial Coefficients, Partial Orders and Equivalence Relations, Graphs Basic Notions.

This book contains below topics, Functions between finite sets, Binomial coefficients, Recursive matrices and generating functions, Multisets and multiset coefficients, Equations with natural integer solutions, Three statistics of Quantum Physics, Compositions of finite sets and multinomial coefficients, Equivalence relations and partitions, Permutations, Some polynomial identities, An introduction to the MoebiusRota inversion theory.

This book contains below topics, Sue gets an A in the class, We haveP Q and P, soQ follows Sue gets an A, am asleep if dream, dream only if am asleep, In order to dream, must be asleep, To dream, it is necessary that am asleep, To be asleep, it is sucient to dream, dream if am asleep, am asleep only if dream, It is necessary that dream in order to be asleep, It is sucient that be asleep in order to dream.

These notes are an attempt to summarize some of the key mathematical aspects of differential geometry,as they apply in particular to the geometry of surfaces in R3. Covered topics are, Some fundamentals of the theory of surfaces, Some important parameterizations of surfaces, Variation of a surface, Vesicles, Geodesics, parallel transport and covariant differentiation.

This note covers the following topics, Matrix Exponential, Some Matrix Lie Groups, Manifolds and Lie Groups, The Lorentz Groups, Vector Fields, Integral Curves, Flows, Partitions of Unity, Orientability, Covering Maps, The LogEuclidean Framework, Spherical Harmonics, Statistics on Riemannian Manifolds, Distributions and the Frobenius Theorem, The LaplaceBeltrami Operator and Harmonic Forms, Bundles, Metrics on Bundles, Homogeneous Spaces, Cli ord Algebras, Cli ord Groups, Pin and Spin and Tensor Algebras.

This note contains below topics, Symplectic Manifolds, Symplectomorphisms, Local Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps Revisited and Symplectic Toric Manifolds.

This book describes the fundamentals of metric differential geometry of curves and surfaces.

The purpose of this course note is the study of curves and surfaces, and those are in general, curved. The book mainly focus on geometric aspects of methods borrowed from linear algebra, proofs will only be included for those properties that are important for the future development.

This note covers the following topics, Manifolds as subsets of Euclidean space, Abstract Manifolds, Tangent Space and the Differential, Embeddings and Whitneys Theorem, The de Rham Theorem, Lie Theory, Differential Forms, Fiber Bundles.

This book explains the following topics, General Curve Theory, Planar Curves, Space Curves, Basic Surface Theory, Curvature of Surfaces, Surface Theory, Geodesics and Metric Geometry, Riemannian Geometry, Special Coordinate Representations.

This note contains below topics, Preliminaries Sets Maps and Diagrams, Groups, Manifolds, Lie Groups, Some Classical Examples of Lie Groups, Medical Applications Prediction of Injuries.

The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. This book contains below topics, Preliminaries, Curves in Space, Surfaces in Space, Curvature, Special Types of Curve, Special Types of Surface, Tensor Differentiation.

This book contains below topics, CHAPTER CUR VES IN THREEDIMENSIONAL SPACE, The length integral and the natural parametrization of a c urve, Curves as trajectories of material points in mechanics, CHAPTER ELEMENTS OF VECTORIAL AND TENSORIAL ANALYSIS, Vectorial and tensorial elds in the space, Tensor product and contraction, The algebra of tensor elds, Symmetrization and alternation, Dierentiation of tensor elds, The metric tensor and the volume pseudotensor, The properties of pseudotensors.

This book contains below topics, Sites and Sheaves, Simplicial Presheaves, Strict Hypercompleteness, The Plus Construction, Applications, Augmented and Truncated Simplicial Presheaves, Verdier Sites, Matching Verdier Sites, Lurie s Lemma, Homotopical Categories, Some History.

This book covers the following topics, Laplaces equation, Sobolev spaces, Elliptic PDEs, The Heat and Schrodinger Equations, Parabolic Equations, Hyperbolic Equations and Friedrich symmetric systems.