__Detailed Syllabus of Engineering Mathematics - III | Civil Engineering Second Year Syllabus __

## Unit 1: Fourier Transforms

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.

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.

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.

## Unit 5: Statistical Techniques

## Reference Books:

### *Click on the book to open.

### 1. E. Kreyszig: Advanced Engineering Mathematics; John Wiley & Sons

### 2. B.V. Ramana: Higher Engineering Mathematics; Tata McGraw-Hill Publishing Company Limited, New Delhi.

### 3. Peter V.O' Neil. Advanced Engineering Mathematics, Thomas (Cengage) Learning

### 4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2000.

### 6. R.K. Jain and S.R.K. Iyenger: Advance Engineering Mathematics; Narosa Publishing House, New Delhi.

### 7. P. Kandasamy, K. Thilagavathy, K. Gunavathi, Numerical Methods, S. Chand & Company, 2nd Edition, Reprint 2012.

### 8. S.S. Sastry, Introductory methods of numerical analysis, PHI, 4a Edition, 2005.

9. N.P. Bali and Manish Goyal, Computer Based Numerical and Statistical Techniques, Laxmi Publications, Reprint, 2010.

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

*Source - Books, Internet, Self-Analysis