Advanced Engineering Mathematics 8/e (SI Edition)
作者：Peter V. O'Neil
Now you can make rigorous mathematical topics accessible to your students by emphasizing visuals, numerous examples, and interesting mathematical models with O'Neil’s ADVANCED ENGINEERING MATHEMATICS, 8E. New "Math in Context" broadens the engineering connections for your students by clearly demonstrating how mathematical concepts are applied to current engineering problems. You have the flexibility to select additional topics that are best for your individual course, including many new web modules while minimizing the cost of the printed book.
AN INSTRUCTOR’S SOLUTIONS MANUAL OFFERS COMPLETE SOLUTIONS. You will find detailed solutions to virtually all problems in the book to save you time and effort.
ALL MATHEMATICS IS COMPLETED CORRECTLY. Although the approach is informal and proofs are included only when they offer a useful and straightforward insight into the ideas, you can trust all of the mathematics presented in this edition.
TABLES OF TRANSFORMS PROVIDE QUICK REFERENCE. Your students will find tables for Fourier, Laplace, Fourier cosine and sine for use in solving problems within the book.
A GUIDE TO POST-CALCULUS NOTATION ASSISTS STUDENTS. This helpful guide provides support for your students as they reference new terms and symbols
DETAILED EXAMPLES HIGHLIGHT BOTH MATHEMATICAL IDEAS AND THEIR APPLICATIONS. Valuable examples throughout develop and emphasize mathematical concepts as well as practical engineering uses.
TWO ADDITIONAL WEB CHAPTERS DETAIL STATISTICS AND PROBABILITY. These chapters are conveniently posted on the book’s website and include both problems and solutions.
STUDENT SOLUTIONS MANUAL CONTAINS WORKED-OUT SOLUTIONS TO HALF OF THE TEXT PROBLEMS. These solutions are specifically developed to assist your students in truly understanding the ideas involved, rather than simply listing the mechanical steps.
THE BOOK’S SEVEN-PART ORGANIZATION BEST FITS MOST COURSE ORGANIZATIONS. Seven distinctive parts clearly focus and differentiate the mathematical ideas and methods while giving you the flexibility to select the sections best suited for your course and student needs.
DETAILED EXAMPLES ILLUSTRATE THE USE OF NOTATION AND THE THEORY. The numerous examples clarify notation, theory and the underlying computations, followed by the numerical calculations themselves.
New to this Edition
SPECIALIZED AND ADVANCED TOPICS ADDED AS WEB MODULES. In order to broaden coverage while keeping the length and cost of the book down, certain topics have been added as convenient web modules rather than appearing in the printed text. These modules include applications of complex analysis to the Dirichlet problem and to inverses of Laplace transforms, Lyapunov functions, the discrete Fourier transform, Maxwell’s equations, numerical methods for solving differential equations, LU factoring of matrices, limit cycles for systems of differential equations, and models of plane fluid flow.
NEW “MATH IN CONTEXT” FEATURES CONNECT THE MATHEMATICAL APPLICATIONS TO CURRENT ENGINEERING PROBLEMS. These special features specifically relate mathematical concepts and methods to real world problems that students will find in the workplace.
THIS EDITION PRESENTS THE SOLUTION OF INITIAL VALUE PROBLEMS FOR WAVE MOTION AND DIFFUSION PHENOMENA UNDER A VARIETY OF CONDITIONS. This edition considers nonhomogeneous conditions, forcing terms, convection and insulation effects, and other conditions encountered in applications.
COVERAGE INCLUDES EXPANDED TREATMENT OF SPECIAL FUNCTIONS. This edition includes even more material about both special functions and their applications to help you better prepare your students.
THE BOOK OFFERS A GENERAL APPROACH TO THE SOLUTION OF PROBLEMS USING EIGENFUNCTION EXPANSIONS.
NEW ORGANIZATION CLARIFIES AND CLEARLY DIFFERENTIATES TOPICS. This edition’s refined organization allows your students to focus on a particular idea and its applications before progressing to new topics.
NEW EXAMPLES AND APPLICATIONS CLARIFY HOW TO SOLVE SPECIFIC TYPES OF PROBLEMS. These new examples apply the mathematical techniques that students are learning to real-world settings, such as the analysis of wave motion and diffusion processes.
Table of Contents
PART I: ORDINARY DIFFERENTIAL EQUATIONS.
1. First-Order Differential Equations.
2. Second-Order Differential Equations.
3. The Laplace Transform.
4. Series Solutions
Part II: MATRICES AND LINEAR ALGEBRA.
5. Vectors and the Vector Space Rn.
6. Matrices, Determinants and Linear Systems.
7. Eigenvalues, Diagonalization and Special Matrices.
Part III: PARTIAL DIFFERENTIAL EQUATIONS.
8. Nonlinear Systems and Qualitative Analysis.
9. Systems of Linear Differential Equations.
Part IV: VECTOR ANALYSIS.
10. Vector Differential Calculus.
11. Vector Integral Calculus.
Part V: Sturm-Liouville Problems, Fourier Analysis and Eigenfunction Expansions
12. Sturm-Liouville Problems, and Eigenfunction Expansions
13. Fourier Transform
PART VI: PARTIAL DIFFERENTIAL EQUATIONS.
14. The Wave Equation.
15. The Heat Equation.
17. Laplace’s Equation.
18. Special Functions and Applications.
19. Transform Methods of Solution.
PART VII: COMPLEX FUNCTIONS.
20. Complex Numbers and Functions.
22. Series Representations of Functions.
23. Singularities and the Residue Theorem.
24. Conformal Mappings.
Dr. Peter O’Neil has been a professor of mathematics at the University of Alabama at Birmingham since 1978. At the University of Alabama at Birmingham, he has served as chairman of mathematics, dean of natural sciences and mathematics, and university provost. Dr. Peter O’Neil has also served on the faculty at the University of Minnesota and the College of William and Mary in Virginia, where he was chairman of mathematics. He has been awarded the Lester R. Ford Award from the Mathematical Association of America. He received both his M.S and Ph.D. in mathematics from Rensselaer Polytechnic Institute. His primary research interests are in graph theory and combinatorial analysis.