Mathematics

Yuliya Mishura, Georgiy Shevchenko, “Theory and Statistical Applications of Stochastic Processes”

An R Companion to Applied Regression, 2nd Edition by John Fox, Harvey Sanford Weisberg

Elementary Differential Equations

Easy Algebra Step-by-Step, 2nd Edition

Finite Element Concepts: A Closed-Form Algebraic Development By Gautam Dasgupta

Yuliya Mishura, Georgiy Shevchenko, “Theory and Statistical Applications of Stochastic Processes”

2017 | ISBN-10: 1786300508 | 400 pages | PDF | 4 MB

This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.

An R Companion to Applied Regression, 2nd Edition by John Fox, Harvey Sanford Weisberg

English | November 29th, 2010 (2011 Edition) | ASIN: B008P5BJIO, ISBN: 141297514X | 344 Pages | EPUB | 12.49 MB

This is a broad introduction to the R statistical computing environment in the context of applied regression analysis. It is a thoroughly updated edition of John Fox’s bestselling text An R and S-Plus Companion to Applied Regression (SAGE, 2002). The Second Edition is intended as a companion to any course on modern applied regression analysis.

The authors provide a step-by-step guide to using the high-quality free statistical software R, an emphasis on integrating statistical computing in R with the practice of data analysis, coverage of generalized linear models, enhanced coverage of R graphics and programming, and substantial web-based support materials.

Elementary Differential Equations

English | 2013 | ISBN: 0534368417 | 664 Pages | PDF | 7.83 MB

This text has been written in clear and accurate language that students can read and comprehend. The author has minimized the number of explicitly state theorems and definitions, in favor of dealing with concepts in a more conversational manner. This is illustrated by over 250 worked out examples. The problems are extremely high quality and are regarded as one of the text’s many strengths. This book also allows the instructor to select the level of technology desired. Trench has simplified this by using the symbols C and L. C exercises call for computation and/or graphics, and L exercises are laboratory exercises that require extensive use of technology. Several sections include informal advice on the use of technology. The instructor who prefers not to emphasize technology can ignore these exercises.

Finite Element Concepts: A Closed-Form Algebraic Development By Gautam Dasgupta

English | EPUB | 2017 (2018 Edition) | 333 Pages | ISBN : 1493974211 | 4.13 MB

This text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids. The book is divided into two distinct parts of nine chapters and seven appendices. The first chapter reviews the energy concepts in structural mechanics with bar problems, which is continued in the next chapter for truss analysis using Mathematica programs.

The Courant and Clough triangular elements for scalar potentials and linear elasticity are covered in chapters three and four, followed by four-node elements. Chapters five and six describe Taig’s isoparametric interpolants and Iron’s patch test. Rayleigh vector modes, which satisfy point-wise equilibrium, are elaborated on in chapter seven along with successful patch tests in the physical (x,y) Cartesian frame. Chapter eight explains point-wise incompressibility and employs (Moore-Penrose) inversion of rectangular matrices. The final chapter analyzes patch-tests in all directions and introduces five-node elements for linear stresses. Curved boundaries and higher order stresses are addressed in closed algebraic form. Appendices give a short introduction to Mathematica, followed by truss analysis using symbolic codes that could be used in all FEM problems to assemble element matrices and solve for all unknowns. All Mathematica codes for theoretical formulations and graphics are included with extensive numerical examples.