Advanced Engineering Mathematics by Erin Kreyszig 10th Edition is published by Wiley, copyrighted in 2011. This is a college level text book focusing on mathematical applications for engineers but also for physics and computer science.
The text book is broken into 7 segments: ordinary differential equations, linear algebra and vector calculus, Fourier analysis, complex analysis, numeric analysis, optimization, graphs, probability and statistics. The only required prerequisite is elementary calculus which is provided as a review in summary form in appendix 3 and the inside cover.
Each of the 7 segments, in advanced engineering mathematics by Erwin Kreyszig 10th edition, are self-contained to permit independent ordering, according to the instructor’s preferences. The problems are provided at the end of each section and answers to odd numbered problems are available at the back of the text. The examples included are intentionally simple to encourage the teaching process. The process starts simple and increases in complexity and difficulty as in a building process.
The text is extremely comprehensive, providing all the tools needed for application of mathematical and statistical problems. It is also an excellent reference with 5 extensive appendices containing references, answers to the odd-numbered problems, formulas, additional theorems with proofs and tables of functions.
There are 4 themes that are built into the book’s overriding function. Technology drives many engineering problems that require mathematical solutions. In that context, modeling is the first of the 4 themes. This text takes the student from the concept to defining a model to addressing the problem. It can be a financial model for bond pricing, an environmental problem addressing pollutants, a population problem or any number of other engineering problems. Defining the mathematical model to address the problem is provided in advanced engineering mathematics by Erwin Kreyszig 10th edition.
Once the model is defined it must be solved mathematically. The next step is to clearly interpret the results and then decide the correct action based on the results. This is what engineers do across a range of specializations.
The second theme is the use of software powerful enough to provide numeric analysis accommodating thousands or equations. Large industrial engineering projects require numeric analysis, building models that solve problems of significant magnitude. This text focuses on teaching the ability to address problems and build solutions of this size and complexity.
The third theme addresses the beauty of engineering mathematics and the few basic components within it. The fourth and final theme is to understand the combination of different approaches that go into the engineering mathematical methods.
The author makes suggestions concerning formatting classroom courses using the book as course ware over 4 semesters or as independent study in a one semester course.
The textbook, advanced engineering mathematics by Erwin Kreyszig 10th edition also provides the Wiley Plus. Wiley Plus is an online set of tools to advance student studies. Feedback to questions and special problems is provided promptly and to assist in success on exams.
This complete and comprehensive approach to engineering mathematics is well organized and supremely laid out and ordered. It is left for instructors and students to make use of the tools provided.