Mathematics

No detailed description available for "Multivariable and Vector Calculus".

No detailed description available for "Finite Element Analysis".

Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists with the tools and techniques of tensor analysis for applications in practical problem solving and analysis activities. It includes expanded content on the application of mechanical stress transformation. The geometry is limited to the Euclidean space/geometry, where the Pythagorean Theorem applies, with well-defined Cartesian coordinate systems as the reference. Quantities defined in curvilinear coordinate systems, like cylindrical, spherical, parabolic, etc. are discussed and several examples and coordinates sketches with related calculations are presented. In addition, the book has several worked-out examples for helping the readers with mastering the topics provided in the prior sections.

Designed for students, faculty, and professionals, this book describes the role of mathematics in the world of economics and business. Beginning with the fundamental nature of numbers and progressing into more complex realms like hyperreal numbers and the intricacies of set theory, this book constructs a strong foundational understanding of mathematical concepts. The book uses PYTHON code throughout the text to illustrate problems numerically. As readers advance, the text seamlessly integrates essential topics such as linear simultaneous equations, which are pivotal in analyzing market equilibrium, and covers the mechanics of matrices for solving larger equation systems. Furthermore, chapters dedicated to calculus, especially its applications in economics and the innovative use of infinitesimal methods, equip learners with tools to tackle profit maximization challenges, factor optimization, and beyond. Later chapters unfold the world of differential and difference equations, revealing their significance in analyzing dynamic systems. All these concepts are illuminated through practical examples and numerous images from economics and business, ensuring relevance and clarity.

This monograph contains a collection of integrals, some more challenging than others, with their worked-out solutions as indefinite integrals. The integrals were randomly selected, modified, or designed with the condition of having closed forms solutions with common functions. This list is meant for helping readers in practicing and getting hints for working out solutions to similar integrals that they might encounter. Readers might want to add their own favorite integrals to this list. We also present the application of some integrals in engineering related topics. For example, nonuniform loading, hydrostatic force, moment of inertia, polar moment of inertia, etc. We introduce an up-to-date online software tool, WolframAlpha, that can be used for comparing our answers for the integrals listed. However, readers may want to update to WolframAlpha Pro for recovering some of the integrals’ step-by-step solutions. In addition, similar CAS (computer algebra system) tools like Maple, Mathematica, or Mathcad may also be employed.

No detailed description available for "Commutative Algebra".

Finite Element Analysis, 2/E is a comprehensive guide that explores the versatility and affordability of the finite element method (FEM) as a powerful tool for solving engineering problems across various industries. This book provides a practical introduction to FEM analysis, covering applications in mechanical engineering, civil engineering, electrical engineering, and physics. It presents a balanced blend of theory and applications, catering to both beginners and those seeking to enhance their FEM skills. The book emphasizes a comparative approach by presenting solutions to problems through three different methods: analytical, FEM hand calculations, and software-based methods. This enables readers to grasp the strengths and limitations of each approach, enhancing their understanding of FEM techniques..

This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook.

Features:

• Includes numerous computer illustrations and tutorials using MATLAB®and Maple®
• Covers the major topics of vector geometry, differentiation, and integration in several variables
• Instructors’ ancillaries available upon adoption

No detailed description available for "Linear Algebra".

No detailed description available for "Essentials of Modern Algebra".