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Engineering Mathematics 4 by Dr. KSC: A Comprehensive Guide for VTU Students

If you are looking for a reliable and easy-to-understand textbook for engineering mathematics 4, you might want to check out Engineering Mathematics 4 by Dr. KSC. This book is specially designed for the fourth semester engineering course of VTU (CBCS scheme) and covers all the topics in the syllabus.

Dr. KSC is a former professor and head of the department of mathematics at The National Institute of Engineering, Mysuru. He has a rich experience of teaching engineering mathematics and has authored several books on the subject. His books are known for their clarity, simplicity and practical examples.

Engineering Mathematics 4 by Dr. KSC is divided into five modules, each covering a different area of mathematics. The modules are:

Module 1: Complex Analysis

Module 2: Numerical Methods

Module 3: Conformal Mapping and Applications

Module 4: Probability and Statistics

Module 5: Z-Transforms and Difference Equations

The book also contains numerous solved problems, exercises, multiple choice questions and previous year question papers to help students prepare for the exams. The book is available in both print and digital formats.

If you want to download a free PDF version of Engineering Mathematics 4 by Dr. KSC, you can find it on Scribd[^2^]. However, we recommend that you buy the original book from a reputed online or offline store to support the author and get the best quality.

Engineering Mathematics 4 by Dr. KSC is a must-have book for every VTU student who wants to ace their engineering mathematics exams. It will help you understand the concepts, apply them to real-world problems and score high marks in your tests.

In this section, we will give you a brief overview of each module and some of the key topics covered in them.

Module 1: Complex Analysis

Complex analysis is the study of functions of complex variables. It has many applications in engineering, physics, chemistry and other fields. In this module, you will learn about:

Complex numbers and their properties

Complex functions and their derivatives

Cauchy-Riemann equations and analytic functions

Harmonic functions and their conjugates

Line integrals and Cauchy's integral theorem

Cauchy's integral formula and its applications

Taylor's series and Laurent's series

Singularities and residues

Residue theorem and its applications

Module 2: Numerical Methods

Numerical methods are techniques for solving mathematical problems using numerical approximations. They are useful when exact solutions are difficult or impossible to obtain. In this module, you will learn about:

Solution of algebraic and transcendental equations using bisection method, Newton-Raphson method and Regula-Falsi method

Solution of system of linear equations using Gauss elimination method, Gauss-Jordan method and Gauss-Seidel method

Interpolation using Newton's forward and backward difference formulae, Lagrange's interpolation formula and Newton's divided difference formula

Numerical differentiation using forward, backward and central difference formulae

Numerical integration using Trapezoidal rule, Simpson's 1/3 rule and Simpson's 3/8 rule

Solution of ordinary differential equations using Euler's method, Modified Euler's method, Runge-Kutta method and Predictor-Corrector method

Module 3: Conformal Mapping and Applications

Conformal mapping is a technique for transforming one complex plane into another while preserving angles. It has many applications in fluid mechanics, electrostatics, heat transfer and other fields. In this module, you will learn about:

Bilinear transformation and its properties

Mapping of standard regions using bilinear transformation

Cross ratio and invariant property of cross ratio

Mobius transformation and its properties

Mapping of standard regions using Mobius transformation

Schwarz-Christoffel transformation and its properties

Mapping of polygons using Schwarz-Christoffel transformation

Module 4: Probability and Statistics

Probability and statistics are branches of mathematics that deal with uncertainty, variability and data analysis. They have many applications in engineering, science, business and social sciences. In this module, you will learn about:

Basic concepts of probability theory such as sample space, events, probability axioms, conditional probability, Bayes' theorem, independence etc.

Random variables and their types such as discrete and continuous random variables

Probability distributions and their properties such as mean, variance, standard deviation etc.

Some common discrete distributions such as binomial distribution, Poisson distribution, geometric distribution etc.

Some common continuous distributions such as uniform distribution, exponential distribution, normal distribution etc.

Moments and moment generating functions of random variables

Chebyshev's inequality and its applications

Central limit theorem and its applications

Sampling theory such as sampling distribution, standard error etc.

Point estimation and interval estimation of population parameters such as mean, proportion etc.

Hypothesis testing for population parameters such as mean, proportion etc.

Correlation and regression analysis for bivariate data such as scatter diagram, correlation coefficient etc.

Module 5: Z-Transforms and Difference Equations

Z-transforms are a tool for analyzing discrete-time signals and systems. They are analogous to Laplace transforms for continuous-time signals and systems. Difference equations are equations involving differences of a function. They are used to model discrete-time systems. In this module, you will learn about:

Z-transforms and their properties such as linearity, shifting etc.

Inverse Z-transforms using partial fraction ec8f644aee