{"product_id":"thinking-about-equations-a-practical-guide-for-developing-mathematical-intuition-in-the-physical-sciences-and-engineering-paperback-softback-9780470186206","title":"Thinking About Equations; A Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering (Paperback \/ softback) 9780470186206","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThinking About Equations\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMatt A. Bernstein (Author), William A. Friedman (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470186206, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 30 July 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e272 pages, Charts: 1 B\u0026amp;W, 0 Color; Drawings: 15 B\u0026amp;W, 0 Color; Graphs: 43 B\u0026amp;W, 0 Color\u003cbr\u003e23.5 x 15.5 x 1.6 cm, 0.467 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cb\u003eAn accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering\u003c\/b\u003e  \u003cp\u003eEquations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. \u003ci\u003eThinking About Equations\u003c\/i\u003e provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences.\u003c\/p\u003e \u003cp\u003eEquations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eApproximation and estimation\u003c\/li\u003e \u003cli\u003eIsolating important variables\u003c\/li\u003e \u003cli\u003eGeneralization and special cases\u003c\/li\u003e \u003cli\u003eDimensional analysis and scaling\u003c\/li\u003e \u003cli\u003ePictorial methods and graphical solutions\u003c\/li\u003e \u003cli\u003eSymmetry to simplify equations\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eEach chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension.\u003c\/p\u003e \u003cp\u003eRequiring only a working knowledge of basic calculus and introductory physics, \u003ci\u003eThinking About Equations\u003c\/i\u003e is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cb\u003ePreface.\u003c\/b\u003e  \u003cp\u003e\u003cb\u003eAcknowledgments.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eList of Worked-Out Example Problems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Equations Representing Physical Quantities.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Systems of Units.\u003c\/p\u003e \u003cp\u003e1.2 Conversion of Units.\u003c\/p\u003e \u003cp\u003e1.3 Dimensional Checks and the Use of Symbolic Parameters.\u003c\/p\u003e \u003cp\u003e1.4 Arguments of Transcendental Functions.\u003c\/p\u003e \u003cp\u003e1.5 Dimensional Checks to Generalize Equations.\u003c\/p\u003e \u003cp\u003e1.6 Other Types of Units.\u003c\/p\u003e \u003cp\u003e1.7 Simplifying Intermediate Calculations.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 A Few Pitfalls and a Few Useful Tricks.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 A Few Instructive Pitfalls.\u003c\/p\u003e \u003cp\u003e2.2 A Few Useful Tricks.\u003c\/p\u003e \u003cp\u003e2.3 A Few “Advanced” Tricks.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Limiting and Special Cases.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Special Cases to Simplify and Check Algebra.\u003c\/p\u003e \u003cp\u003e3.2 Special Cases and Heuristic Arguments.\u003c\/p\u003e \u003cp\u003e3.3 Limiting Cases of a Differential Equation.\u003c\/p\u003e \u003cp\u003e3.4 Transition Points.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Diagrams, Graphs, and Symmetry.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction.\u003c\/p\u003e \u003cp\u003e4.2 Diagrams for Equations.\u003c\/p\u003e \u003cp\u003e4.3 Graphical Solutions.\u003c\/p\u003e \u003cp\u003e4.4 Symmetry to Simplify Equations.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Estimation and Approximation.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Powers of Two for Estimation.\u003c\/p\u003e \u003cp\u003e5.2 Fermi Questions.\u003c\/p\u003e \u003cp\u003e5.3 Estimates Based on Simple Physics.\u003c\/p\u003e \u003cp\u003e5.4 Approximating Definite Integrals.\u003c\/p\u003e \u003cp\u003e5.5 Perturbation Analysis.\u003c\/p\u003e \u003cp\u003e5.6 Isolating Important Variables.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Introduction to Dimensional Analysis and Scaling.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Dimensional Analysis: An Introduction.\u003c\/p\u003e \u003cp\u003e6.2 Dimensional Analysis: A Systematic Approach.\u003c\/p\u003e \u003cp\u003e6.3 Introduction to Scaling.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generalizing Equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Binomial Expressions.\u003c\/p\u003e \u003cp\u003e7.2 Motivating a General Expression.\u003c\/p\u003e \u003cp\u003e7.3 Recurring Themes.\u003c\/p\u003e \u003cp\u003e7.4 General yet Simple: Euler’s Identity.\u003c\/p\u003e \u003cp\u003e7.5 When to Try to Generalize.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Several Instructive Examples.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Choice of Coordinate System.\u003c\/p\u003e \u003cp\u003e8.2 Solution Has Unexpected Properties.\u003c\/p\u003e \u003cp\u003e8.3 Solutions in Search of Problems.\u003c\/p\u003e \u003cp\u003e8.4 Learning from Remarkable Results.\u003c\/p\u003e \u003cp\u003eExercises.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex.\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52257177633048,"sku":"9780470186206","price":54.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470186206.jpg?v=1781277986","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/thinking-about-equations-a-practical-guide-for-developing-mathematical-intuition-in-the-physical-sciences-and-engineering-paperback-softback-9780470186206","provider":"Freshly Printed Books","version":"1.0","type":"link"}