Modern Advanced Mathematics for Engineers

A convenient single source for vital mathematical concepts, writtenby engineers and for engineers.

Builds a strong foundation in modern applied mathematics forengineering students, and offers them a concise and comprehensivetreatment that summarizes and unifies their mathematical knowledgeusing a system focused on basic concepts rather than exhaustivetheorems and proofs.

The authors provide several levels of explanation and exercisesinvolving increasing degrees of mathematical difficulty to recalland develop basic topics such as calculus, determinants, Gaussianelimination, differential equations, and functions of a complexvariable. They include an assortment of examples ranging fromsimple illustrations to highly involved problems as well as anumber of applications that demonstrate the concepts and methodsdiscussed throughout the book. This broad treatment also offers:*Key mathematical tools needed by engineers working incommunications, semiconductor device simulation, and control theory* Concise coverage of fundamental concepts such as sets, mappings,and linearity * Thorough discussion of topics such as distance,inner product, and orthogonality * Essentials of operatorequations, theory of approximations, transform methods, and partialdifferential equationsIt makes an excellent companion to lessgeneral engineering texts and a useful reference for practitioners. Dedication.

Preface.

The Basic of Set Theory.

Relations and Mappings.

Mathematical Logic.

Algebraic Structures: Group Through Linear Space.

Linear Mappings and Matrices.

Metrics and Topological Properties.

Banach and Hilbert Spaces.

Orthonormal Bases and Fourier Series.

Operator Equations.

Fourier and Laplace Transforms.

Partial Differential Equations.

Topic Index. "The appearance of the book is pleasing and it readswell..." (The Mathematical Gazette, Nov 2002)

"From the preface: 'This book is written with the aim ofproviding students with a strong foundation in modern appliedmathematics.'" (Mathematical Reviews, 2001 I)

"...a useful account of basic ideas." (Mathematika,No.48, 2001)

"One should be grateful to the authors for having done a goodjob" (Zentrablatt Math, Vol.979, No.04, 2002)

"...textbook for a one-semester graduate course providingengineering students with a foundation in modern appliedmathematics." (SciTech Book News, Vol. 26, No. 2, June2002) VLADIMIR V. MITIN and DMITRI A. ROMANOV are both Professors in theDepartment of Electrical and Computer Engineering at Wayne StateUniversity.

MICHAEL P. POLIS is Professor in the School of Engineering andComputer Science at Oakland University in Michigan. A convenient single source for vital mathematical concepts, written by engineers and for engineers

Almost every discipline in electrical and computer engineering relies heavily on advanced mathematics. Modern Advanced Mathematics for Engineers builds a strong foundation in modern applied mathematics for engineering students, and offers them a concise and comprehensive treatment that summarizes and unifies their mathematical knowledge using a system focused on basic concepts rather than exhaustive theorems and proofs.

The authors provide several levels of explanation and exercises involving increasing degrees of mathematical difficulty to recall and develop basic topics such as calculus, determinants, Gaussian elimination, differential equations, and functions of a complex variable. They include an assortment of examples ranging from simple illustrations to highly involved problems as well as a number of applications that demonstrate the concepts and methods discussed throughout the book. This broad treatment also offers:

• Key mathematical tools needed by engineers working in communications, semiconductor device simulation, and control theory
• Concise coverage of fundamental concepts such as sets, mappings, and linearity
• Thorough discussion of topics such as distance, inner product, and orthogonality
• Essentials of operator equations, theory of approximations, transform methods, and
• partial differential equations
• A treatment that is adaptable for use with computer systems

Modern Advanced Mathematics for Engineers gives students a strong foundation in modern applied mathematics and the confidence to apply it across diverse engineering disciplines. It makes an excellent companion to less general engineering texts and a useful reference for practitioners.