Advance Engineering Mathematics By Dennis G. Zill & Warren S. Wright :: Now with a full-color design, the new Sixth Edition of Zill's Advanced Engineering Mathematics provides an in-depth overview of the many mathematical topics necessary for students planning a career in engineering or the sciences. A key strength of this text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fourth Sixth Edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. Numerous new projects contributed by esteemed mathematicians have been added. New modern applications and engaging projects makes Zill's classic text a must-have text and resource for Engineering Math students!
CONTENTS:
Part 1: Ordinary Differential Equations (Chapters 1 – 6)
Part 2: Vectors, Matrices, and Vector Calculus (Chapters 7 – 9)
Part 3: Systems of Differential Equations (Chapters 10 and 11)
Part 4: Fourier Series and Partial Differential Equations (Chapters 12 – 16)
Part 5: Complex Analysis (Chapters 17 – 20)
Content of the Text::
For flexibility in topic selection, the current text is divided into five major parts. As can be seen from the titles of these various parts, it should be obvious that it is our belief that the backbone of science/engineering-related mathematics is the theory and application of ordinary and partial differential equations.
Part 1: Ordinary Differential Equations (Chapters 1-6)
The six chapters in Part 1 constitute a complete short course in ordinary differential equations. These chapters, with some modifications, correspond to Chapters 1, 2, 3, 4, 5, 6, 7, and 9 in the text A First Course in Differential Equations with Modeling Applications, Tenth Edition by Dennis G. Zill (Brooks/Cole Cengage Learning). In Chapter 2 we cover methods for solving first-order differential equations, and in Chapter 3 the focus is mainly on linear second-order differential equations and their applications. Chapter 4 is devoted to the important Laplace transform.
Part 2: Vectors, Matrices, and Vector Calculus (Chapters 7-9)
Chapter 7, Vectors, and Chapter 9, Vector Calculus, include the standard topics that are usually covered in the third semester of a calculus sequence: vectors in 2- and 3-space, vector functions, directional derivatives, line integrals, double and triple integrals, surface integrals, Green's theorem, Stokes' theorem, and the Divergence theorem. In Section 7.6, the vector concept is generalized; by defining vectors analytically, we lose their geometric interpretation but keep many of their properties in n-dimensional and infinite-dimensional vector spaces. Chapter 8, Matrices, is an introduction to systems of algebraic equations,
determinants, and matrix algebra with special emphasis on those types of matrices that are useful in solving systems of linear differential equations. Sections on cryptography, error correcting codes, the method of least squares, and discrete compartmental models are presented as applications of matrix algebra.
Part 3: Systems of Differential Equations (Chapters 10 and 11)
There are two chapters in Part 3. Chapter 10, Systems of Linear Differential Equations, and Chapter 11, Systems of Nonlinear Differential Equations, draw heavily on the matrix material presented in Chapter 8 of Part 2. In Chapter 10, systems of linear first-order equations are solved utilizing the concepts of eigenvalues and eigenvectors, diagonalization, and by means of a matrix exponential function. In Chapter 11, qualitative aspects of autonomous linear and nonlinear systems are considered in depth.
Part4: Fourier Series and Partial Differential Equations (Chapters 12-16)
The core material on Fourier series and boundary-value problems was originally drawn from the text Differential Equations with Boundary-Value Problems, Eighth Edition by Dennis G. Zill and Warren S. Wright (Brooks/Cole Cengage Learning). In Chapter 12, Orthogonal Functions and Fourier Series, the fundamental topics of sets of orthogonal functions and expansions of functions in terms of an infinite series of orthogonal functions are presented. These topics are then utilized in Chapters 13 and 14 where boundary value problems in rectangular, polar, cylindrical, and spherical coordinates are solved using the method of separation of variables. In Chapter 15, Integral Transform Method, boundary-value problems are solved by means of the Laplace and Fourier integral transforms.
Part 5: Complex Analysis (Chapters 17-20)
The final four chapters of the text cover topics ranging from the basic complex number system through applications of conformal mappings in the solution of Dirichlet's problem.
This material by itself could easily serve as a one-quarter introductory course in complex variables. This material was adapted from A First Course in Complex Analysis with Applications, Second Edition by Dennis G. Zill and Patrick D. Shanahan (Jones & Bartlett Learning).
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