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Advanced Engineering Mathematics
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Through previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more.
- Amazon Sales Rank: #252844 in Books
- Brand: Brand: Cengage Learning
- Published on: 2011-01-01
- Original language: English
- Number of items: 1
- Dimensions: 1.30" h x 8.20" w x 10.10" l, 3.48 pounds
- Binding: Hardcover
- 912 pages
- Used Book in Good Condition
PART I: 1. FIRST-ORDER DIFFERENTIAL EQUATIONS. Terminology and Separable Equations. Linear Equations. Exact Equations. Homogeneous, Bernoulli and Riccsti Equations. Additional Applications. Existence and Uniqueness Questions. 2. LINEAR SECOND-ORDER EQUATIONS. The Linear Second-Order Equations. The Constant Coefficient Case. The Nonhomogeneous Equation. Spring Motion. Euler's Differential Equation. 3. THE LAPLACE TRANSFORM Definition and Notation. Solution of Initial Value Problems. Shifiting and the Heaviside Function. Convolution. Impulses and the Delta Function. Solution of Systems. Polynomial Coefficients. Appendix on Partial Fractions Decompositions. 4. SERIES SOLUTIONS. Power Series Solutions. Frobenius Solutions. 5. APPROXIMATION OF SOLUTIONS Direction Fields. Euler's Method. Taylor and Modified Euler Methods. PART II: 6. VECTORS AND VECTOR SPACES. Vectors in the Plane and 3 - Space. The Dot Book. The Cross Book. The Vector Space Rn. Orthogonalization. Orthogonal Complements and Projections. The Function Space C[a,b]. 7. MATRICES AND LINEAR SYSTEMS. Matrices. Elementary Row Operations. Reduced Row Echelon Form. Row and Column Spaces. Homogeneous Systems. Nonhomogeneous Systems. Matrix Inverses. Least Squares Vectors and Data Fitting. LU - Factorization. Linear Transformations. 8. DETERMINANTS. Definition of the Determinant. Evaluation of Determinants I. Evaluation of Determinants II. A Determinant Formula for A-1. Cramer's Rule. The Matrix Tree Theorem. 9. EIGENVALUES, DIAGONALIZATION AND SPECIAL MATRICES Eigenvalues and Eigenvectors. Diagonalization. Some Special Types of Matrices. 10. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS Linear Systems. Solution of X'=AX for Constant A. Solution of X'=AX+G. Exponential Matrix Solutions. Applications and Illustrations of Techniques. Phase Portaits. PART III: 11. VECTOR DIFFERENTIAL CALCULUS. Vector Functions of One Variable. Velocity and Curvature. Vector Fields and Streamlines. The Gradient Field. Divergence and Curl. 12. VECTOR INTEGRAL CALCULUS. Line Integrals. Green's Theorem. An Extension of Green's Theorem. Independence of Path and Potential Theory. Surface Integrals. Applications of Surface Integrals. Lifting Green's Theorem to R3. The Divergence Theorem of Gauss. Stokes's Theorem. Curvilinear Coordinates. PART IV: 13. FOURIER SERIES. Why Fourier Series? The Fourier Series of a Function. Sine and Cosine Series. Integration and Differentiation of Fourier Series. Phase Angle Form. Complex Fourier Series. Filtering of Signals. 14. THE FOURIER INTEGRAL AND TRANSFORMS. The Fourier Integral. Fourier Cosine and Sine Integrals. The Fourier Transform. Fourier Cosine and Sine Transforms. The Discrete Fourier Transform. Sampled Fourier Series. DFT Approximation of the Fourier Transform. 15. SPECIAL FUNCTIONS AND EIGENFUNCTION EXPANSIONS. Eigenfunction Expansions. Legendre Polynomials. Bessel Functions. PART V: 16. THE WAVE EQUATION. Derivation of the Wave Equation. Wave Motion on an Interval. Wave Motion in an Infinite Medium. Wave Motion in a Semi-Infinite Medium. Laplace Transform Techniques. Characteristics and d'Alembert's Solution. Vibrations in a Circular Membrane I. Vibrations in a Circular Membrane II. Vibrations in a Rectangular Membrane. 17. THE HEAT EQUATION. Initial and Boundary Conditions. The Heat Equation on [0, L]. Solutions in an Infinite Medium. Laplace Transform Techniques. Heat Conduction in an Infinite Cylinder. Heat Conduction in a Rectangular Plate. 18. THE POTENTIAL EQUATION. Laplace's Equation. Dirichlet Problem for a Rectangle. Dirichlet Problem for a Disk. Poisson's Integral Formula. Dirichlet Problem for Unbounded Regions. A Dirichlet Problem for a Cube. Steady-State Equation for a Sphere. The Neumann Problem. PART VI: 19. COMPLEX NUMBERS AND FUNCTIONS. Geometry and Arithmetic of Complex Numbers. Complex Functions. The Exponential and Trigonometric Functions. The Complex Logarithm. Powers. 20. COMPLEX INTEGRATION. The Integral of a Complex Function. Cauchy's Theorem. Consequences of Cauchy's Theorem. 21. SERIES REPRESENTATIONS OF FUNCTIONS. Power Series. The Laurent Expansion. 22. SINGULARITIES AND THE RESIDUE THEOREM. Singularities. The Residue Theorem. Evaluation of Real Integrals. Residues and the Inverse Laplace Transform. 23. CONFORMAL MAPPINGS AND APPLICATIONS. Conformal Mappings. Construction of Conformal Mappings. Conformal Mappings and Solutions of Dirichlet Problems. Models of Plane Fluid Flow. APPENDIX: A MAPLE PRIMER. ANSWERS TO SELECTED PROBLEMS.
About the Author
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.
Most helpful customer reviews
2 of 2 people found the following review helpful.
Editor Didn't Do Their Homework
By Bruce I. Rivera
First of all, please note that I am reviewing the product and not Amazon who, as always, did a stellar job getting this item to me in great condition and on time (they get five stars from me).
I bought this book because it is a required text in one of my classes. As such, I must keep it but, if I had bought this as a personal reference text, I would send it right on back. I have thus far only read chapters 6 and 7 (still in the class now), but they have been an endless list of errors page after page. I'm not talking grammar or spelling (although certainly these should also be as correct as possible in any published text) but, more egregiously, there are mathematical errors to be found everywhere. You can find the wrong formula in a theorem here and the wrong answer to an example problem there. I shouldn't have to be better at math than my textbook in order to ensure that it does not lead me astray!
My best guess? The publisher was eager to get another edition out and keep selling the same book year after year at the same or higher price. So... do they add something of value to the text? Of course not! Instead, let's juggle around the examples, change the color scheme, maybe some spiffy looking graphics here. Well, along the way, errors get introduced, variables get switched, basic arithmetic is botched and the price tag remains. $160 for a math book that does not even bother to check its own math is unacceptable.
It gets three stars because it appears to be well put together, the print is good, and, provided you already know a thing or two, the point comes across despite its many flaws. That said, as a working professional, I expect industry and academia to hold themselves to a higher standard than this. And, in a freer market where this thing is not a required text at certain universities, I'd like to think this book would not survive in its current state.
3 of 3 people found the following review helpful.
Plagued by little errors = inexcusable for 7th edtition.
By D. C. Brown
There is a crucial difference between being concise (which I love when it's done well), and inconsistently stripping out details that in some cases would have actually *explained* a new concept or tied an idea or example problem together. Also, the book is plagued by little errors: in example problems, homework problems, occasionally even in formulas/theorems at the core of the topic being covered. Errors & typos can have a more devastating impact in a math book compared to any other textbook I can think of. If this were a 1st or 2nd edition, we could all give this book the benefit of the doubt. For a SEVENTH edition, however, this is just plain inexcusable. It's not a terrible book, but there have got to be more effective teaching tools out there than this for the same subject matter. Especially when you consider the price, which was around $200 when I enrolled in class this spring. I see no reason for any professor (other than the author) to assign the 7th edition: by all reviews the 6th edition was far better, and would now be a whole lot cheaper too.
19 of 20 people found the following review helpful.
Buy the sixth edition if you can.
I bought the seventh edition because it was required for a class. I borrowed the sixth edition from a friend that took the class a few years ago and was floored by the differences. The seventh edition is exactly the same, except they removed some entire sections, removed some very useful examples and information from some other sections, and rearranged some problems and some section numbers to make the sixth edition unusable for homework assignments.
If you can get a key that tells you which sections and problems correspond between the two editions, or you are just buying the book as a reference, get the sixth edition (significantly cheaper and better).
I am constantly appalled by the practices of these text book publishers. They charge outrageous amounts for the books, make easy and unnecessary changes, release a new edition and force students to buy the new ones so they can make more money.