Special Internshala Offer! Get Flat 80% Off on all Internshala Training Programs! All Courses @ Rs.999 Enroll Now!

# Engineering Mathematics-III Syllabus | Civil Engineering UTU

Unit 1: Fourier Transforms Fourier integral, Fourier Transform, Complex Fourier transform, Inverse Transforms, Convolution Theorem, Fourier sine and c

# Detailed Syllabus of Engineering Mathematics - III | Civil Engineering Second Year Syllabus

## Unit 1: Fourier Transforms

Fourier integral, Fourier Transform, Complex Fourier transform, Inverse Transforms, Convolution
Theorem, Fourier sine and cosine transform, Applications of Fourier transform to simple one-dimensional heat transfer equations.

## Unit 2: Laplace Transform

Definition of Laplace transform. Existence theorem, Laplace transforms of derivatives and integrals, Initial and final value theorems, Unit step function, Dirac-delta function, Laplace transform of the periodic function. Inverse Laplace transform, Convolution theorem, Application to solve linear differential
equations.

## Unit 3: Solution of Algebraic and Transcendental equations & Interpolation

Number and their accuracy, Solution of algebraic and transcendental equations: Bisection method, Iteration method, Newton-Raphson method and Regula-Falsi method. Rate of convergence of these
methods (without proof), Interpolation: Finite differences, Relation between operators, Interpolation using Newton's forward and backward difference formula. Interpolation with unequal intervals: Newton's divided difference and Lagrange's formula.

## Unit 4: Numerical differentiation, Integration & Solution of ODE

Numerical Differentiation, Numerical integration: Trapezoidal rule, Simpson's 1/3rd and 3/8 rule Runge Kutta method of fourth-order for solving first-order linear differential equations. Milne's predictor-corrector method.

## Unit 5: Statistical Techniques

Introduction: Measures of central tendency, Moments, Moment generating function (MGF), Skewness, Kurtosis, Curve Fitting: Method of least squares, Fitting of straight lines, Fitting of second-degree parabola, Exponential curves. Correlation and Rank correlation, Regression Analysis: Regression lines of y on x and x on y, regression coefficients, properties of regressions coefficients and non-linear regression.

## Reference Books:

### 10. J.N. Kapur: Mathematical Statistics: S. Chand & Sons Company Limited, New Delhi.

*Taken from the official website of Uttarakhand Technical University.

*Self Typed
*Source - Books, Internet, Self-Analysis

Getting Info...

## About the Author

This is Ashutosh Nautiyal. Currently, I'm pursuing my graduation from Bipin Tripathi Kumaon Institute Of Technology, Dwarahat, Almora and my branch is Civil Engineering. I have done my schooling at Omkarananda Saraswati Nilayam, Rishikesh.