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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 







    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 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:

    *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. 











    *Taken from the official website of Uttarakhand Technical University.




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

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    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.

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