具体描述
Fundamentals of Electromagnetics for Electrical and Computer Engineering, First Edition is appropriate for all beginning courses in electromagnetics, in both electrical engineering and computer engineering programs. This is ideal for anyone interested in learning more about electromagnetics. Dr. N. Narayana Rao has designed this compact, one-semester textbook in electromagnetics to fully reflect the evolution of technologies in both electrical and computer engineering. This book’s unique approach begins with Maxwell’s equations for time-varying fields (first in integral and then in differential form), and also introduces waves at the outset. Building on these core concepts, Dr. Rao treats each category of fields as solutions to Maxwell’s equations, highlighting the frequency behavior of physical structures. Next, he systematically introduces the topics of transmission lines, waveguides, and antennas. To keep the subject’s geometry as simple as possible, while ensuring that students master the physical concepts and mathematical tools they will need, Rao makes extensive use of the Cartesian coordinate system. Topics covered in this book include: uniform plane wave propagation; material media and their interaction with uniform plane wave fields; essentials of transmission-line analysis (both frequency- and time-domain); metallic waveguides; and Hertzian dipole field solutions. Material on cylindrical and spherical coordinate systems is presented in appendices, where it can be studied whenever relevant or convenient. Worked examples are presented throughout to illuminate (and in some cases extend) key concepts; each chapter also contains a summary and review questions. (Note: this book provides a one-semester alternative to Dr. Rao’s classic textbook for two-semester courses, Elements of Engineering Electromagnetics , now in its Sixth Edition.)
Title: Advanced Engineering Mathematics: A Comprehensive Guide for Modern Applications Book Description: This volume delves into the crucial mathematical foundations underpinning modern engineering disciplines, moving beyond introductory concepts to explore sophisticated analytical and computational techniques essential for tackling complex real-world problems. It is meticulously structured to provide both theoretical rigor and practical applicability, serving as an indispensable resource for advanced undergraduate and graduate students, as well as practicing engineers and researchers in fields requiring deep mathematical modeling capabilities. The text is organized into distinct, yet interconnected, modules, beginning with a robust treatment of Vector Calculus and Field Theory. This section meticulously revisits surface and volume integrals, line integrals, and curl and divergence theorems (Stokes’ and Gauss’), emphasizing their geometric interpretations and their utility in describing continuous media. A significant portion is dedicated to transforming coordinate systems beyond Cartesian, focusing intently on cylindrical and spherical coordinates, and introducing curvilinear coordinate systems relevant to specific engineering geometries. The inherent mathematical structure behind concepts like flux density and conservative fields is analyzed, preparing the reader for subsequent chapters on boundary value problems. Following the foundational calculus review, the book transitions into Partial Differential Equations (PDEs), the core language of continuous systems. The focus here is not merely on solving standard equations but on understanding the physical meaning embedded within their solutions. We provide comprehensive coverage of the wave equation, the heat equation, and, critically, Laplace's and Poisson's equations in multiple dimensions. Detailed methods for solving these equations are presented, including the method of separation of variables, Fourier series and transforms, and the crucial technique of Green's functions. The application of these techniques is grounded in physical scenarios such as transient heat conduction, vibrating strings and membranes, and steady-state potential distributions. Special attention is paid to handling non-homogeneous boundary conditions and internal sources, providing robust analytical tools for non-ideal systems. A significant section is dedicated to Complex Analysis for Engineering Systems. Complex variables are introduced not just as a mathematical tool, but as the natural domain for analyzing stability, transients, and frequency response in dynamic systems. The book rigorously covers Cauchy's integral theorem and formula, residue calculus for evaluating difficult real integrals encountered in signal processing and control theory, and conformal mapping techniques. The application of conformal mapping is explored in detail for solving two-dimensional potential problems where standard Cartesian solutions are intractable, demonstrating how geometric transformations simplify complex boundary interactions. Linear Algebra and Matrix Methods are treated with an emphasis on computational efficiency and system diagonalization. Beyond basic matrix operations, the book focuses heavily on eigenvalue problems, spectral decomposition, and the Singular Value Decomposition (SVD). These tools are directly applied to understanding system modes in structural dynamics, principal component analysis in data reduction, and the stability analysis of large systems of coupled linear ordinary differential equations (ODEs). Numerical stability and the computational complexity of different diagonalization methods are discussed, offering insight into software implementation choices. The text then bridges the gap between analytical solutions and practical simulation by introducing Numerical Methods for Engineering Computations. This module covers finite difference methods (FDM) for discretizing time-dependent PDEs, stability and convergence analysis for explicit and implicit schemes, and an introduction to the Finite Element Method (FEM) framework, focusing on variational principles underlying element formulation. Iterative techniques for solving large, sparse linear systems arising from discretized problems, such as the Gauss-Seidel, Jacobi, and Conjugate Gradient methods, are analyzed concerning their convergence rates and suitability for different problem classes. Finally, the volume incorporates a detailed exploration of Transform Methods in System Analysis. While Fourier series and transforms are revisited within the context of PDEs, this chapter focuses squarely on the Laplace Transform and its application to solving initial value problems for linear ODEs, particularly in control systems and circuit analysis where transient behavior is paramount. The properties of the two-sided Laplace transform and its use in analyzing stability margins and transfer functions are thoroughly covered. Furthermore, the Z-transform is introduced as the discrete-time analogue, essential for modern digital signal processing and digital control system design. Throughout the text, the integration of theory and practice is maintained through extensive worked examples drawn from diverse engineering fields—mechanical vibration, fluid dynamics (potential flow), heat transfer, and introductory continuum mechanics. End-of-chapter problems range from theoretical derivations designed to solidify mathematical proofs to complex modeling exercises requiring the selection and application of the appropriate analytical or numerical technique. The overall goal is to equip the reader with the mature mathematical fluency required to formulate, analyze, and solve the advanced engineering challenges that define contemporary technological development.
