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Ten Equations to Explain the Mysteries of Modern Astrophysics

From Information and Chaos Theory to Ghost Particles and Gravitational Waves

by Santhosh Mathew

2019

This book introduces ten equations that transcend the boundaries of time and space. It takes readers through a journey of self-discovery where they will learn the history, science, and significance of these equations in the context of their lives. Moreover, the mathematical beauty of these equations is presented in a profoundly modest fashion to highlight the idea that equations are eternal but humans are transient. Each chapter offers readers a sublime experience and provides insights into the laws of nature that address the ever-expanding intricacy of our universe. The history of humankind, according to Franz Kafka, is the instant between two strides taken by a traveler. Therefore, what remains eternal when we finish our journey on this tiny rocky planet is our deep desire to connect wi...

The Foundations of Real Analysis

A Fundamental Course with 347 Exercises and Detailed Solutions

by Richard Mikula

2015

This textbook covers the subject of real analysis from the fundamentals up through beginning graduate level. It is appropriate as an introductory course text or a review text for graduate qualifying examinations. Some special features of the text include a thorough discussion of transcendental functions such as trigonometric, logarithmic, and exponential from power series expansions, deducing all important functional properties from the series definitions. The text is written in a user-friendly manner, and includes full solutions to all assigned exercises throughout the text.

The Math Handbook for Students with Math Difficulties, Dyscalculia, Dyslexia or ADHD

(Grades 1-7)

by Helmy Faber

2017

The Math Handbook has been developed for students with Dyscalculia and others who are struggling with mathematics. The book is based upon the Singapore Primary Mathematics curriculum, as well as the International Math curriculum. More than twenty topics are covered and explained step by step through visual representation to convey mathematical concepts. It has been specially developed for: • Students who have been diagnosed with Dyscalculia; other terms may include Mathematics Learning Disability, or Mathematics Disorder • Students who have been diagnosed with Dyslexia; as according to research more than fifty percent of those experience difficulties with mathematics. Some students may have Dyslexia and Dyscalculia as co-existing disorders • Students diagnosed with ADHD; as they may ...

A Brief Course in Linear Algebra

Matrices and Matrix Equations for Undergraduate Students in Applied Mathematics, Science and Engineering

by Whye-Teong Ang

2019

This book contains a brief course in elementary linear algebra with emphasis on solving systems of linear algebraic and ordinary differential equations. It is written for undergraduate students in the disciplines of applied mathematics, science and engineering. Topics covered include basics of matrices and vectors, systems of linear algebraic equations, matrix inverse, matrix determinant, eigenvalues and eigenvectors, matrix diagonalization, and systems of first order linear ordinary differential equations. The connections between the topics are carefully elucidated. Derivations or proofs are given in detail for all the main results in the book. Basic knowledge of the arithmetic of complex numbers and exposure to elementary functions and calculus are assumed. Problems are set at the end of...

Differential Inclusions in Modeling and Simulation

Interdisciplinary Applications, Reachable Sets, Uncertainty Treatment for Educators and Researchers of Computer Modeling and Simulation

by Stanislaw Raczynski

2019

The purpose of this book is to reach a circle of readers in the field of modeling and simulation, and similar. The examples and applications are multidisciplinary because of the multidisciplinary nature of modeling and simulation (MS). The book is not aimed for mathematicians, though some theoretical issues are also included. One of the aims of the book is to call into question a common paradigm that prevails among MS specialists telling that everything in the real world what is continuous in time, can be described by the ordinary or partial differential equations (ODEs, PDEs). My point is that this is not exactly true. So, we should look for a wider set of modeling tools. Differential inclusions (DIs) are used as an generalization of the ODE models.An important topic of the book that appe...

How to Solve Large Linear Systems

Using a Stable Cybernetic Approach for Non-Cumulative Computation, Avoiding Underflow and Overflow, with Unconditional and Uniform Convergence

by Aleksa Srdanov and Aleksandra Jankovic

2019

Solving the linear equation system n x n can also be a problem for a computer, even when the number of equations and unknowns is relatively small (a few hundred). All existing methods are burdened by at least one of the following problems: 1) Complexity of computation expressed through the number of operations required to be done to obtaining solution; 2) Unrestricted growth of the size of the intermediate result, which causes overflow and underflow problems; 3) Changing the value of some coefficients in the input system, which causes the instability of the solution; 4) Require certain conditions for convergence, etc.In this paper an approximate and exact methods for solving a system of linear equations with an arbitrary number of equations and the same number of unknowns is presented. Al...

Double Helix of Phyllotaxis

Analysis of the Geometric Model of Plant Morphogenesis

by Boris Rozin

2020

This book is devoted to anyone who is in search of beauty in mathematics, and mathematics in the beauty around us. Attempting to combine mathematical rigor and magnificence of the visual perception, the author is presenting the mathematical study of phyllotaxis, the most beautiful phenomenon of the living nature. The distinctive feature of this book is an animation feature that explains the work of mathematical models and the transformation of 3D space.The analysis of the phyllotactic pattern as a system of discrete objects together with the mathematical tools of generalized sequences made it possible to find a universal algorithm for calculating the divergence angle. In addition, it is serving as a new proof of the fundamental theorem of phyllotaxis and analytically confirming well-known ...

Reading Physics

A Guide to Understanding Basic Classical Mechanics without Mathematical Expressions

by Jae Jun Kim, Ph.D.

2023

This book was written to help college students understand physics without complicated math. Each year thousands of college students pursuing business and humanities degrees find themselves taking a course in introductory physics. But many will have serious trouble solving physics problems because they do not have enough experience using mathematical equations. Understanding physics is challenging without a strong math background, but not impossible. Unlike other introductions to physics, this book explains the basic concepts in classical mechanics with a minimal amount mathematical expressions so new students can spend their time learning physics, not math. The result is not only a better understanding of physics, but possibly a better grade. This study guide covers the three aspects of ...