This textbook is created from the author's successful, Advanced Engineering Mathematics. The previous volume is now split into two books to offer more flexibility. Reviewers have endorsed the split. The author's best-selling book, Green's Functions, is distilled here, as well as coverage of complex variables, Z and Hilbert transforms, probability and random processes, and a unique coverage of Ito's stochastic calculus. The topics are driven by applications and MatLab is used throughout. This book offers flexibility in a course where many competitors are now over 1000 pages and very expensive. This second book covers topics normally taught in the second or third term of an AEM course.

The new edition splits the coverage of the previous one into two books. This offers instructors more flexibility and offers the students a more affordable option as the author distills the previous comprehensive coverage into a more useful format. Advanced Engineering Mathematics is a course taught at every four-year school with an Engineering Department throughout the world and can be taught in both Mathematics and Engineering Departments.

Since publication of the first edition over a decade ago, Green's Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green's function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect the current state of the art. The book opens with necessary background information: a new chapter on the historical development of the Green's function, coverage of the Fourier and Laplace transforms, a discussion of the classical special functions of Bessel functions and Legendre polynomials, and a review of the Dirac delta function. The text then presents Green's functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. Detailing step-by-step methods for finding and computing Green's functions, each chapter contains a special section devoted to topics where Green's functions particularly are useful. For example, in the case of the wave equation, Green's functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Green's functions, worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas are featured throughout the text. A new chapter on numerical methods closes the book. Included solutions and hundreds of references to the literature on the construction and use of Green's functions make Green's Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering.

Methods for Solving Mixed Boundary Value Problems An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations. Straightforward Presentation of Mathematical Techniques The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve various mixed boundary value problems using separation of variables, transform methods, the Wiener-Hopf technique, Green's function, and conformal mapping. Decipher Mixed Boundary Value Problems That Occur in Diverse Fields Including MATLAB (R) to help with problem solving, this book provides the mathematical skills needed for the solution of mixed boundary value problems.

"Methods for Solving Mixed Boundary Value Problems"

An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations.

"Straightforward Presentation of Mathematical Techniques"

The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve various mixed boundary value problems using separation of variables, transform methods, the Wiener-Hopf technique, Green's function, and conformal mapping.

"Decipher Mixed Boundary Value Problems That Occur in Diverse Fields"

Including MATLAB(R) to help with problem solving, this book provides the mathematical skills needed for the solution of mixed boundary value problems.

Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found analytically, numeric and asymptotic techniques now exist for their inversion, and because the problem retains some of its analytic aspect, one can gain greater physical insight than typically obtained from a purely numerical approach. Transform Methods for Solving Partial Differential Equations, Second Edition illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. The author has expanded the second edition to provide a broader perspective on the applicability and use of transform methods and incorporated a number of significant refinements: New in the Second Edition: * Expanded scope that includes numerical methods and asymptotic techniques for inverting particularly complicated transforms * Discussions throughout the book that compare and contrast transform methods with separation of variables, asymptotic methods, and numerical techniques * Many added examples and exercises taken from a wide variety of scientific and engineering sources * Nearly 300 illustrations--many added to the problem sections to help readers visualize the physical problems * A revised format that makes the book easier to use as a reference: problems are classified according to type of region, type of coordinate system, and type of partial differential equation * Updated references, now arranged by subject instead of listed all together As reflected by the book's organization, content, and many examples, the author's focus remains firmly on applications. While the subject matter is classical, this book gives it a fresh, modern treatment that is exceptionally practical, eminently readable, and especially valuable to anyone solving problems in engineering and the applied sciences.

Since publication of the first edition over a decade ago, Green's Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green's function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect the current state of the art. The book opens with necessary background information: a new chapter on the historical development of the Green's function, coverage of the Fourier and Laplace transforms, a discussion of the classical special functions of Bessel functions and Legendre polynomials, and a review of the Dirac delta function. The text then presents Green's functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. Detailing step-by-step methods for finding and computing Green's functions, each chapter contains a special section devoted to topics where Green's functions particularly are useful. For example, in the case of the wave equation, Green's functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Green's functions, worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas are featured throughout the text. A new chapter on numerical methods closes the book. Included solutions and hundreds of references to the literature on the construction and use of Green's functions make Green's Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering.