Re: Engineering Maths 3 By D K Jain
Edel Dieringer
Engineering Maths 3 By D K Jain
Engineering Maths 3 is a book that covers the topics of advanced engineering mathematics, such as special functions, Fourier series, partial differential equations, complex analysis, and numerical methods. The book is written by D K Jain, a professor of mathematics at the Indian Institute of Technology Delhi. The book is intended for students of engineering and science who want to learn the mathematical tools and techniques that are essential for solving engineering problems.
Special Functions
The book introduces some special functions that are frequently encountered in engineering applications, such as the gamma function, the beta function, and the Bessel functions. The book explains the properties, recurrence relations, and orthogonality of these functions, and shows how they can be used to evaluate improper integrals and series solutions to differential equations.
Fourier Series
The book discusses the concept of Fourier series, which are infinite series of trigonometric functions that can be used to represent periodic functions. The book derives the formulas for finding the Fourier coefficients of a given function, and shows how to use them to solve boundary value problems involving heat conduction, wave propagation, and vibration.
Partial Differential Equations
The book covers the methods of solving partial differential equations (PDEs), which are equations involving derivatives of a function with respect to more than one variable. The book explains the classification and characteristics of PDEs, and presents various techniques for finding their solutions, such as separation of variables, method of characteristics, Laplace transform, and Green's function.
Complex Analysis
The book explores the theory and applications of complex analysis, which is the study of functions of a complex variable. The book introduces the concepts of complex numbers, complex functions, analyticity, Cauchy-Riemann equations, contour integration, Cauchy's theorem, residues, and conformal mapping. The book also demonstrates how complex analysis can be used to solve problems in fluid mechanics, electrostatics, and potential theory.
Numerical Methods
The book presents some numerical methods that can be used to approximate the solutions of mathematical problems that cannot be solved analytically. The book covers the topics of numerical solution of algebraic and transcendental equations, interpolation and curve fitting, numerical differentiation and integration, numerical solution of ordinary and partial differential equations, and numerical linear algebra.
Conclusion
Engineering Maths 3 By D K Jain is a comprehensive and rigorous book that covers the essential topics of advanced engineering mathematics. The book provides clear explanations, worked examples, and graded exercises that help students understand the concepts and apply them to engineering problems. The book is suitable for undergraduate and postgraduate students of engineering and science who want to enhance their mathematical skills and knowledge.
References
- [Advanced Engineering Mathematics - R.K. Jain, S.R.K. Iyengar - Google Books]
- [Advanced Engneering Maths By R. K. Jain, S.R.K. Iyengar]
- [Engineering Mathematics 3 (M 3) Pdf Notes - 2020 SW - Smartzworld]