Engineering Mathematics - III syllabus
MDM-221-CVL · Second Year Civil Engineering, SPPU 2024 pattern. Every unit, the marks scheme, course outcomes and books, copied from the official syllabus PDF.
Unit-wise syllabus
Linear Differential Equations (LDE) and Applications
8 hoursLDE of nth order with constant coefficients, Complementary Function, Particular Integral, General method, Short cut methods, Method of Variation of parameters, Cauchy’s and Legendre’s DE, Simultaneous DE. Modelling of problems on bending of beams and whirling of shafts.
Statistics and Probability
8 hoursStatistics: Measures of central tendency, Measures of dispersion, Coefficient of variation, Moments, Skewness and Kurtosis, Correlation and Regression, Reliability of Regression estimates. Probability: Introduction, Probability density function, Probability distributions: Binomial, Poisson, Normal and Test of hypothesis: Chi-square test and t- test.
Numerical Methods for solving Algebraic and Transcendental Equations
8 hoursNumerical Solution of Algebraic and Transcendental equations: Bisection, Secant, Regula-Falsi, Newton–Raphson and Successive Approximation Methods, Convergence and Stability. Numerical Solutions of System of linear equations: Gauss elimination with partial pivoting, LU Decomposition, Jacobi and Gauss-Seidel Methods.
Numerical Interpolation and Solution of ODE
8 hoursInterpolation: Finite Differences, Newton’s and Lagrange’s Interpolation formulae, Numerical Differentiation. Numerical Integration: Trapezoidal and Simpson’s rules, Bound of truncation error. Solution of Ordinary differential equations (ODE): Euler’s, Modified Euler’s, Runge-Kutta 4th order methods and Predictor-Corrector methods
Vector Calculus
8 hoursVector differentiation, Gradient, Divergence, Curl, Directional derivative, Solenoidal & Irrotational fields, Vector identities. Line, surface and volume integrals, Green’s theorem, Gauss’s Divergence theorem and Stokes’ theorem.
Marks and credits
| Head | Marks | Credit |
|---|---|---|
| CCE (continuous comprehensive evaluation) | 30 | 3 |
| End-semester exam | 70 |
Prerequisite: Differential & Integral calculus, Differential equations of first order & first degree, Fourier series, Collection, Classification and Representation of data and Vector algebra..
Course outcomes
- CO1SOLVE higher order linear differential equations and its applications to model and analyze bending of beams and whirling of shafts.
- CO2APPLY Statistical methods like correlation, regression in analyzing and interpreting experimental data applicable to reliability engineering and probability theory in testing and quality control.
- CO3SOLVE Algebraic & Transcendental equations and System of linear equations using numerical techniques.
- CO4OBTAIN Interpolating polynomials, numerical differentiation and integration, numerical solutions of ordinary differential equations used in modern scientific computing applicable to Civil engineering.
- CO5PERFORM Vector differentiation & integration, ANALYZE the vector fields and APPLY to fluid flow problems.
Books
Text books
- Higher Engineering Mathematics – B. V. Ramana (Tata McGraw-Hill)
- Higher Engineering Mathematics – B.S. Grewal (Khanna Publication, Delhi)
Reference books
- Erwin Kreyszig, “Advanced Engineering Mathematics,” 10th Edition, by Wiley India, 2006.
- Michael D. Greenberg, “Advanced Engineering Mathematics, 2nd Edition, Pearson Education, 1998.
- Peter V. O'Neil, “Advanced Engineering Mathematics”, 8th Edition, Cengage Learning, 2023.
- Shepley L. Ross, “Differential Equations”, 3rd Edition, Wiley India, 2018.
- Sheldon M. Ross, “Introduction to Probability and Statistics for Engineers and Scientists”, 6th Edition, Elsevier Academic Press, 2021. e-Books
- https://archive.org/details/higher-engineering-mathematics-bs-grewal
- https://wp.kntu.ac.ir/dfard/ebook/em/Advanced%20Engineering%20Mathematics%2010 th%20Edition.pdf
- https://minerva.it.manchester.ac.uk/~saralees/statbook3.pdf
- https://plcsitemiz.files.wordpress.com/2009/04/the-laplace-transform-theory-andapplications.pdf
FAQ
How many units are in Engineering Mathematics - III?
Engineering Mathematics - III (MDM-221-CVL) has 5 units: Unit I Linear Differential Equations (LDE) and Applications (8 h); Unit II Statistics and Probability (8 h); Unit III Numerical Methods for solving Algebraic and Transcendental Equations (8 h); Unit IV Numerical Interpolation and Solution of ODE (8 h); Unit V Vector Calculus (8 h).
What is the marks scheme for Engineering Mathematics - III?
The official Civil Engineering 2024 pattern syllabus lists continuous comprehensive evaluation (CCE) for 30 marks and the end-semester exam for 70 marks, for 3 credits.
What should I know before Engineering Mathematics - III?
Prerequisite listed in the syllabus: Differential & Integral calculus, Differential equations of first order & first degree, Fourier series, Collection, Classification and Representation of data and Vector algebra..