Engineering Mathematics 4 by Dr Ksc: A Comprehensive Textbook for VTU Students
Engineering Mathematics 4 by Dr Ksc is a textbook designed for the fourth semester engineering course of VTU (Visvesvaraya Technological University) under the CBCS (Choice Based Credit System) scheme. The book covers topics such as complex analysis, linear algebra, numerical methods, probability and statistics, and Laplace transforms. The book aims to provide a clear and concise exposition of the concepts and methods of engineering mathematics, with numerous examples, exercises, and solved problems.
The book is written by Dr Ks. Chandrashekhar, who is a former professor and head of the department of mathematics at The National Institute of Engineering, Mysuru. He has over four decades of teaching experience and has authored several books on engineering mathematics. He is also a recipient of the VTU Best Teacher Award in 2010.
Engineering Mathematics 4 by Dr Ksc is available as a PDF document on Scribd[^1^], where students can download it for free. The book is also available in print format from various online and offline bookstores. The book is suitable for students who want to learn the applications of mathematics in engineering and prepare for their examinations.
The book is divided into five chapters, each covering a major topic of engineering mathematics. The first chapter deals with complex analysis, which is the study of functions of complex variables. The chapter introduces the concepts of complex numbers, analytic functions, Cauchy-Riemann equations, harmonic functions, conformal mappings, complex integration, Cauchy's theorem, Cauchy's integral formula, Taylor and Laurent series, residue theorem, and contour integration. The chapter also discusses some applications of complex analysis in engineering problems such as potential theory, fluid flow, heat conduction, and electrostatics.
The second chapter covers linear algebra, which is the study of vector spaces, matrices, determinants, linear transformations, eigenvalues and eigenvectors, diagonalization, and canonical forms. The chapter also explains some applications of linear algebra in engineering problems such as systems of linear equations, linear differential equations, stability analysis, and linear programming.
The third chapter focuses on numerical methods, which are techniques for solving mathematical problems using computers. The chapter covers topics such as interpolation, numerical differentiation and integration, numerical solutions of algebraic and transcendental equations, numerical solutions of systems of linear equations, numerical solutions of ordinary differential equations, and numerical solutions of partial differential equations. The chapter also illustrates some applications of numerical methods in engineering problems such as curve fitting, optimization, and finite element analysis.
The fourth chapter deals with probability and statistics, which are branches of mathematics that deal with uncertainty and data analysis. The chapter introduces the concepts of probability theory such as sample space, events, axioms of probability, conditional probability, Bayes' theorem, random variables, probability distributions, expectation, variance, and moment generating functions. The chapter also covers topics of statistics such as descriptive statistics, sampling distributions, point and interval estimation, hypothesis testing, correlation and regression analysis, and analysis of variance. The chapter also discusses some applications of probability and statistics in engineering problems such as reliability analysis, quality control, and design of experiments.
The fifth and final chapter covers Laplace transforms, which are a powerful tool for solving linear differential equations with constant coefficients. The chapter covers topics such as definition and properties of Laplace transforms, inverse Laplace transforms, convolution theorem, initial value and boundary value problems, transfer functions and impulse response functions. The chapter also explains some applications of Laplace transforms in engineering problems such as electrical circuits,