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Linearity plays a critical role in the study of elementary
differential equations; linear differential equations, especially
systems thereof, demonstrate a fundamental application of linear
algebra. In Differential Equations with Linear Algebra, we explore
this interplay between linear algebra and differential equations
and examine introductory and important ideas in each, usually
through the lens of important problems that involve differential
equations. Written at a sophomore level, the text is accessible to
students who have completed multivariable calculus. With a
systems-first approach, the book is appropriate for courses for
majors in mathematics, science, and engineering that study systems
of differential equations.
Because of its emphasis on linearity, the text opens with a full
chapter devoted to essential ideas in linear algebra. Motivated by
future problems in systems of differential equations, the chapter
on linear algebra introduces such key ideas as systems of algebraic
equations, linear combinations, the eigenvalue problem, and bases
and dimension of vector spaces. This chapter enables students to
quickly learn enough linear algebra to appreciate the structure of
solutions to linear differential equations and systems thereof in
subsequent study and to apply these ideas regularly.
The book offers an example-driven approach, beginning each chapter
with one or two motivating problems that are applied in nature. The
following chapter develops the mathematics necessary to solve these
problems and explores related topics further. Even in more
theoretical developments, we use an example-first style to build
intuition and understanding before stating or proving general
results. Over 100 figures provide visual demonstration of key
ideas; the use of the computer algebra system Maple and Microsoft
Excel are presented in detail throughout to provide further
perspective and support students' use of technology in solving
problems. Each chapter closes with several substantial projects for
further study, many of which are based in applications.
Errata sheet available at:
www.oup.com/us/companion.websites/9780195385861/pdf/errata.pdf
This book is designed to serve as a core text for courses in
advanced engineering mathematics required by many engineering
departments. The style of presentation is such that the student,
with a minimum of assistance, can follow the step-by-step
derivations. Liberal use of examples and homework prob lems aid the
student in the study of the topics presented. Ordinary differential
equations, including a number of physical applica tions, are
reviewed in Chapter One. The use of series methods are presented in
Chapter Two, Subsequent chapters present Laplace transforms, matrix
theory and applications, vector analysis, Fourier series and
transforms, partial differential equations, numerical methods using
finite differences, complex vari ables, and wavelets. The material
is presented so that four or five subjects can be covered in a
single course, depending on the topics chosen and the completeness
of coverage. Incorporated in this textbook is the use of certain
computer software packages. Short tutorials on Maple, demonstrating
how problems in engineering mathematics can be solved with a
computer algebra system, are included in most sections of the text.
Problems have been identified at the end of sections to be solved
specifically with Maple, and there are computer laboratory
activities, which are more difficult problems designed for Maple.
In addition, MATLAB and Excel have been included in the solution of
problems in several of the chapters. There is a solutions manual
available for those who select the text for their course. This text
can be used in two semesters of engineering mathematics. The many
helpful features make the text relatively easy to use in the
classroom.
< div="">This book introduces undergraduate students of
engineering and science to applied mathematics essential to the
study of many problems. Topics are differential equations, power
series, Laplace transforms, matrices and determinants, vector
analysis, partial differential equations, complex variables, and
numerical methods. Approximately, 160 examples and 1000 homework
problems aid students in their study. This book presents
mathematical topics using derivations rather than theorems and
proofs. This textbook is uniquely qualified to apply mathematics to
physical applications (spring-mass systems, electrical circuits,
conduction, diffusion, etc.), in a manner that is efficient and
understandable. This book is written to support a mathematics
course after differential equations, to permit several topics to be
covered in one semester, and to make the material comprehensible to
undergraduates. An Instructor Solutions Manual, and also a Student
Solutions Manual that provides solutions to select problems, is
available. ^
This book is designed to serve as a core text for courses in
advanced engineering mathematics required by many engineering
departments. The style of presentation is such that the student,
with a minimum of assistance, can follow the step-by-step
derivations. Liberal use of examples and homework prob lems aid the
student in the study of the topics presented. Ordinary differential
equations, including a number of physical applica tions, are
reviewed in Chapter One. The use of series methods are presented in
Chapter Two, Subsequent chapters present Laplace transforms, matrix
theory and applications, vector analysis, Fourier series and
transforms, partial differential equations, numerical methods using
finite differences, complex vari ables, and wavelets. The material
is presented so that four or five subjects can be covered in a
single course, depending on the topics chosen and the completeness
of coverage. Incorporated in this textbook is the use of certain
computer software packages. Short tutorials on Maple, demonstrating
how problems in engineering mathematics can be solved with a
computer algebra system, are included in most sections of the text.
Problems have been identified at the end of sections to be solved
specifically with Maple, and there are computer laboratory
activities, which are more difficult problems designed for Maple.
In addition, MATLAB and Excel have been included in the solution of
problems in several of the chapters. There is a solutions manual
available for those who select the text for their course. This text
can be used in two semesters of engineering mathematics. The many
helpful features make the text relatively easy to use in the
classroom.
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