Thinking About Equations
A Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering
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Beschreibung
An accessible guide to developing intuition and skills forsolving mathematical problems in the physical sciences andengineering
Equations play a central role in problem solving across variousfields of study. Understanding what an equation means is anessential step toward forming an effective strategy to solve it,and it also lays the foundation for a more successful andfulfilling work experience. Thinking About Equationsprovides an accessible guide to developing an intuitiveunderstanding of mathematical methods and, at the same time,presents a number of practical mathematical tools for successfullysolving problems that arise in engineering and the physicalsciences.
Equations form the basis for nearly all numerical solutions, andthe authors illustrate how a firm understanding of problem solvingcan lead to improved strategies for computational approaches. Eightsuccinct chapters provide thorough topical coverage, including:
* Approximation and estimation
* Isolating important variables
* Generalization and special cases
* Dimensional analysis and scaling
* Pictorial methods and graphical solutions
* Symmetry to simplify equations
Each chapter contains a general discussion that is integratedwith worked-out problems from various fields of study, includingphysics, engineering, applied mathematics, and physical chemistry.These examples illustrate the mathematical concepts and techniquesthat are frequently encountered when solving problems. Toaccelerate learning, the worked example problems are grouped by theequation-related concepts that they illustrate as opposed tosubfields within science and mathematics, as in conventionaltreatments. In addition, each problem is accompanied by acomprehensive solution, explanation, and commentary, and numerousexercises at the end of each chapter provide an opportunity to testcomprehension.
Requiring only a working knowledge of basic calculus andintroductory physics, Thinking About Equations is anexcellent supplement for courses in engineering and the physicalsciences at the upper-undergraduate and graduate levels. It is alsoa valuable reference for researchers, practitioners, and educatorsin all branches of engineering, physics, chemistry, biophysics, andother related fields who encounter mathematical problems in theirday-to-day work.
Autor*in
Matt A. Bernstein
Themen in »Thinking About Equations«
Applied Mathematics in Science Applied Mathmatics in Engineering Mathematical Modeling Mathematics Mathematik Mathematik in den Ingenieurwissenschaften Mathematik in den Naturwissenschaften Mathematische Modellierung