Engineering Mathematics

The book "Engineering Mathematics" by Amit K. Awasthi is a comprehensive textbook designed for students of engineering, particularly those in the III Semester B.Tech program of UPTU (Uttar Pradesh Technical University). Here is a detailed overview of the book:

Key Themes

1. Complex Variables:

   • The book begins with an introduction to functions of complex variables, covering topics such as analytic functions, Cauchy's integral theorem, Cauchy's integral formula, Taylor's and Laurent's series, singularities, and the residue theorem.

2. Statistical Techniques:

   • It includes two units on statistical techniques, covering moments, moment generating functions, skewness, kurtosis, curve fitting, method of least squares, fitting of straight lines and polynomials, exponential curves, correlation, linear and non-linear regression analysis, probability theory, binomial, Poisson, and Normal distributions, sampling theory, tests of significance (Chi-square test, t-test, Analysis of Variance), and statistical quality control methods.

3. Numerical Techniques:

   • The book covers numerical techniques in two units. The first unit deals with the solution of transcendental and polynomial equations using methods like Bisection, Regula-Falsi, and Newton-Raphson. It also covers interpolation techniques including finite differences, difference tables, Newton's forward and backward interpolation, and Lagrange's and Newton's divided difference formulas for unequal intervals. The second unit focuses on the solution of systems of linear equations using Gauss-Seidal and Crout methods, numerical differentiation and integration (Trapezoidal, Simpson's one-third and three-eighth rules), and the solution of ordinary differential equations (first order, second order, and simultaneous) using Euler's, Picard's, and fourth-order Runge-Kutta methods.

Plot Summary

The book is structured to provide a self-contained and comprehensive coverage of the course material for III Semester B.Tech students. Each topic is thoroughly covered in scope, content, and from the examination point of view. The book includes several worked-out examples carefully selected to cover all aspects of the topic, followed by practice exercises with answers to all the problems and hints to the difficult ones. The book aims to provide a framework into which the applications will fit, reflecting the importance of applied mathematics in engineering practices.

Critical Reception

While there is no specific critical reception available for this book, it is evident from the preface that the authors aimed to create a textbook that is lucid, easy to understand, and reflects the vibrant nature of applied mathematics. The book is designed to be useful for both students and teachers, with the authors encouraging feedback and suggestions for improving future editions.

Additional Information

• Authors: The book is authored by Amit K. Awasthi and Sanjay Chaudhary, both of whom are professors at PSIT Kanpur.
• Edition: The first edition was published in 2009.
• Format: The book is available in paperback and ebook formats.

Overall, "Engineering Mathematics" by Amit K. Awasthi is a well-structured textbook that provides a comprehensive coverage of the essential mathematical topics required for engineering students, making it a valuable resource for both students and instructors.