Stimulating, thought-provoking study shows how abstract methods of pure mathematics can be used to systematize problem-solving techniques in applied mathematics. Topics include methods for solving integral equations, finding Green’s function for ordinary or partial differential equations, and for finding the spectral representation of ordinary differential operators.
Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and content of the book covers C.S.E. and 'O' level G.C.E. examinations in Applied Mathematics and Mechanics as well as the relevant parts of the syllabuses for Physics and General Science courses related to Engineering, Building, and Agriculture. The book is also written for the home study reader who is interested in widening his mathematical appreciation or simply reviving forgotten ideas. The author hopes that the style of presentation will be found sufficiently attractive to recapture those who may at one time have lost interest.
"A longtime classic text in applied mathematics, this volume also serves as a reference for undergraduate and graduate students of engineering. Topics include real variable theory, complex variables, linear analysis, partial and ordinary differential equations, and other subjects. Answers to selected exercises are provided, along with Fourier and Laplace transformation tables and useful formulas. 1978 edition"--
An accessible, practical introduction to the principles of differential equations The field of differential equations is a keystone of scientific knowledge today, with broad applications in mathematics, engineering, physics, and other scientific fields. Encompassing both basic concepts and advanced results, Principles of Differential Equations is the definitive, hands-on introduction professionals and students need in order to gain a strong knowledge base applicable to the many different subfields of differential equations and dynamical systems. Nelson Markley includes essential background from analysis and linear algebra, in a unified approach to ordinary differential equations that underscores how key theoretical ingredients interconnect. Opening with basic existence and uniqueness results, Principles of Differential Equations systematically illuminates the theory, progressing through linear systems to stable manifolds and bifurcation theory. Other vital topics covered include: Basic dynamical systems concepts Constant coefficients Stability The Poincaré return map Smooth vector fields As a comprehensive resource with complete proofs and more than 200 exercises, Principles of Differential Equations is the ideal self-study reference for professionals, and an effective introduction and tutorial for students.
This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.
Suitable for advanced courses in applied mathematics, this text covers analysis of lumped parameter systems, distributed parameter systems, and important areas of applied mathematics. Answers to selected problems. 1970 edition.
Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I realized that my own research students did not learn much in this course at my university. Then I learned that the available textbooks were too introduc tory. While teaching this course without an assigned text, I wrote up my lecture notes and gave them to the students. This textbook is a result of that endeavor. When I took this course many, many, years ago, the primary references were the two volumes of P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953). The present text returns the contents to a similar level, although the syllabus is quite different than given in this venerable pair of books.
