Tensor Calculus With Applications

This second edition textbook offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Calculus is a prerequisite for u

The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering stud

Master Your Coursework with Collins College Outlines The Collins College Outline for Introduion to Calculus tackles such topics as funions, limits, continuity, derivatives and their applications

Updated and expanded to include the optional use of graphing calculators, this combination textbook and workbook is a good teach-yourself refresher course for men and women who took a calculus course

Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal formath and physics students.

Suitable for an introductory undergraduate course (the first half of the book is calculus-free). Coverage includes divisibility and primes; modular arithmetic; fundamental theorems of modular arithmet

This introductory text explores the essentials of partial differential equations applied to common problems in engineering and the physical sciences. It reviews calculus and ordinary differential equ

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal spe

This classic, calculus-based introduction to the theory and application of statistics provides an unusually comprehensive depth and breadth of coverage and reflects the latest in statistical thinking

This concise text was created as a workbook for learning to use vector calculus in practical calculations and derivations. Its only prerequisite is a familiarity with one-dimensional differential and integral calculus. Though it often makes use of physical examples, knowledge of physics itself is not required to study the mathematics of vector calculus. The approach is suitable for advanced undergraduates and graduate students in mathematics, physics, and other areas of science.The two-part treatment opens with a brief text that develops vector calculus from the very beginning and then addresses some more detailed applications. Topics include vector differential operators, vector identities, integral theorems, Dirac delta function, Green's functions, general coordinate systems, and dyadics. The second part consists of answered problems, all closely related to the development of vector calculus in the text. Those who study this book and work out the problems will find that rather than m

John E. Freund's Mathematical Statistics with Applications , Eighth Edition, provides a calculus-based introduction to the theory and application of statistics, based on comprehensive coverage tha

For freshman/sophomore, 2-semester or 2–3 quarter courses in Finite Math & Applied Calculus or Mathematics for Business. A strong foundation and logical progression through finit

This updated and revised first-course textbook in applied probability provides a contemporary and lively post-calculus introduction to the subject of probability. The exposition reflects a desirable b

Soo Tan's APPLIED CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Ninth Edition balances applications, pedagogy, and technology to provide you with the context you need to stay motivated in th

This book is the result of the authors' work in fractional calculus, and more particularly, in functions for the solutions of fractional differential equations, which is fostered in the behavior of ge

Finite Mathematics and Calculus with Applications, Tenth Edition by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, li

Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in die

This is a textbook for a second course on differential equations or mathematical modeling after a student has obtained a background in multivariable calculus and possibly a first course on differentia

This text balances accessibility and rigor in teaching stochastic calculus to advanced undergraduate and graduate students in mathematics, economics, and finance. Avoiding the measure-theoretic formal

This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity.

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity.

Soo Tan's APPLIED CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Ninth Edition balances applications, pedagogy, and technology to provide readers with the context they need to stay motivated

With its comprehensive coverage of hydraulics and hydrology in a non-calculus format, the Fourth Edition of INTRODUCTION TO HYDRAULICS & HYDROLOGY continues the same straightforward, practical app

Principles of Physics: A Calculus Approach is designed for a one-year introductory calculus-based physics course for engineering and science students as well as premed students. This book has two main objectives: to provide students with a clear and logical presentation of the basic concepts and principles of physics; and to strengthen their understanding of these concepts and principles through a board of interesting real-world applications.● Style The book is written in a clear, logical, and engaging style.● Pitfall Prevention Over 140 Pitfall Preventions are provided to help students avoid common mistakes and misunderstandings.● Problem-Solving Strategies This helps students identify necessary steps for solving problems.● Worked Examples These examples are set off in boxes, and the answers are highlighted with a tan screen.● Problems Over 2,100 end-of-chapter problems are provided with varied levels of difficulty.● Review Problems These problems can be used by students in preparing

Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping.

This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics. Focusing upon problems with one independent variable, the text connects the abst

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy

Based on the best-selling Calculus and Its Applications by Marv Bittinger, this new text is appropriate for a two-semester calculus course for life science majors. With four new chapters and two new c

This accessible introduction to Calculus is designed to demonstrate how calculus applies to various fields of study. The text is packed with real data and real-life applications to business, economics

Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text be

De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters include Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, and the book ends with the general Gauss-Bonnet theorem. The text includes well over 150 exercises, and gives the background to the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone studying cohomology, curvature, and their applications.

In many problems of applied mathematics, science, engineering or economics, an energy expenditure or its analogue can be approximated by upper and lower bounds. This book provides a unified account of the theory required to establish such bounds, by expressing the governing conditions of the problem, and the bounds, in terms of a saddle functional and its gradients. There are several features, including a chapter on the Legendre dual transformation and some of its singularities. Many substantial examples and exercises are included, especially from the mechanics of fluids, elastic and plastic solids and from optimisation theory. The saddle functional viewpoint gives the book a wide scope. The treatment is straightforward, the only prerequisite being a basic knowledge of the calculus of variations. Part of the book is based on final-year undergraduate courses. This is developed into an account which will interest a wide range of students and professionals in applied mathematics, engineer