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2019 | Buch

Engineering Analysis

verfasst von: Prof. Dr. Merle C. Potter

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The purpose of this book is to introduce undergraduate students of engineering and the physical sciences to applied mathematics often essential to the successful solutions of practical problems. The topics selected are a review of Differential Equations, Laplace Transforms, Matrices and Determinants, Vector Analysis, Partial Differential Equations, Complex Variables, and Numerical Methods. The style of presentation is such that the step-by-step derivations may be followed by the reader with minimum assistance. Liberal use of approximately 160 examples and 1000 homework problems serves to aid students in their study. This book presents mathematical topics using derivations (similar to the technique used in engineering textbooks) rather than theorems and proofs typically found in textbooks written by mathematicians. Engineering Analysis is uniquely qualified to help apply mathematics to physical applications (spring-mass systems, electrical circuits, conduction, diffusion, etc.), in a manner as efficient and understandable as possible.
This book was written to provide for an additional mathematics course after differential equations, to permit several topics to be introduced in one semester, and to make the material comprehensible to undergraduates.The book comes with an Instructor Solutions Manual, available on request, that provides solutions to all problems and also a Student Solutions Manual that provides solutions to select problems (the answers to which are given at the back of the book).

Inhaltsverzeichnis

Frontmatter

Chapter 1. Ordinary Differential Equations

Abstract

Differential equations* play a vital role in the solutions to many problems encountered when modeling physical phenomena. All the disciplines in the physical sciences, with their own unique interests representing a variety of physical situations, require that the student be able to derive the necessary mathematical equation (often a differential equation) and then solve the equation to obtain the desired solution. We shall consider a variety of physical situations that lead to differential equations, using representative problems from several disciplines, and standard methods used to solve the equations will be developed.

Merle C. Potter

Chapter 2. Power-Series Methods

Abstract

We have studied linear differential equations with constant coefficients and have solved such equations using exponential functions. In general, a linear differential equation with variable coefficients cannot be solved by the use of exponential functions. We did, however, solve a special equation with variable coefficients, the Cauchy equation, by assuming a simple power solution.

Merle C. Potter

Chapter 3. Laplace Transforms

Abstract

The solution of a linear, ordinary differential equation with constant coefficients may be obtained by using the Laplace transformation. It is particularly useful in solving nonhomogeneous equations that result when modeling systems involving discontinuous, periodic input functions, such as was done with the Fourier series in Chapter 1. It is not necessary, however, when using Laplace transforms that a homogeneous solution and a particular solution be added together to form the general solution.

Merle C. Potter

Chapter 4. Matrices and Determinants

Abstract

Problems in the real world can often be expressed with sufficient accuracy in terms of linear equations. Such equations may be algebraic equations, ordinary or partial differential equations, or integral equations.

Merle C. Potter

Chapter 5. Vector Analysis

Abstract

One of the major changes in undergraduate science curricula, and in engineering curricula in particular, brought about by the modern space age has been the introduction of vector analysis into several courses. The use of vector analysis comes rather naturally, since many of the quantities encountered in the modeling of physical phenomena are vector quantities; examples of such quantities are velocity, acceleration, force, electric and magnetic fields, and heat flux.

Merle C. Potter

Chapter 6. Partial Differential Equations

Abstract

The physical systems studied thus far have been described primarily by ordinary differential equations. We are now interested in studying phenomena that require partial derivatives in the describing equations as they are formed in modeling the particular phenomena. Partial differential equations arise where the dependent variable depends on two or more independent variables.

Merle C. Potter

Chapter 7. Complex Variables

Abstract

The use of complex numbers has been illustrated when the solution of a particular equation involves the quantity \( \sqrt { - 1} \). The solution of the differential equation describing the motion of a spring–mass system is an example. Various relationships have been used involving complex numbers; in this chapter these relationships will be discussed in detail.

Merle C. Potter

Chapter 8. Numerical Methods

Abstract

In previous chapters analytical solution techniques to both ordinary and partial differential equations were presented. More often than not, problems are encountered for which the describing differential equations are extremely difficult, if not impossible, to solve analytically. Fortunately, since the latter part of the 1950s, the digital computer has become an increasingly useful tool for solving differential equations, whether they be ordinary or partial, linear or nonlinear, homogeneous or nonhomogeneous, or first order or tenth order.

Merle C. Potter

Backmatter

Titel: Engineering Analysis
verfasst von: Prof. Dr. Merle C. Potter
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-91683-5
Print ISBN: 978-3-319-91682-8
DOI: https://doi.org/10.1007/978-3-319-91683-5

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