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This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have indicated a need for, in addition to more emphasis on how analysis

Proof theory. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Logic, Symbolic and mathematical --- 517.1 --- Proof theory --- 517 --- 517 Analysis --- Analysis

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Ordinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology. This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of ordinary differential equations in a short time.

Differential equations. --- 517.91 Differential equations --- Differential equations

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This introductory text presents ordinary differential equations with a modern approach to mathematical modelling in a one semester module of 20-25 lectures.Presents ordinary differential equations with a modern approach to mathematical modellingDiscusses linear differential equations of second order, miscellaneous solution techniques, oscillatory motion and laplace transform, among other topicsIncludes self-study projects and extended tutorial solutions

Differential equations. --- 517.91 Differential equations --- Differential equations --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis

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Semigroups --- Cauchy problem --- Functional differential equations --- 517.5 --- Theory of functions --- 517.5 Theory of functions --- Group theory --- Differential equations, Functional --- Differential equations --- Functional equations --- Differential equations, Partial

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How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun. John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.

Engineering mathematics. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Engineering --- Engineering analysis --- Mathematics