Engineering Mathematics-III syllabus
MDM-221-MEC · Second Year Mechanical 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
7 hoursLDE of nth order with constant coefficients, Complementary Function, Particular Integral, General method, Short methods, Method of variation of parameters, Cauchy’s and Legendre’s DE, Simultaneous DE. Modelling of Mass-spring systems, Free & Forced damped and undamped systems
Statistics & Probability
8 hoursIntroduction to Data Science, Measures of central tendency, Measures of dispersion, Coefficient of variation, Moments, Skewness and Kurtosis, Correlation: Karl Pearson’s correlation, Spearman’s rank correlation, Regression analysis and Reliability of regression estimates. Probability, Probability density function, and Central limit theorem, 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 and Curl, Directional derivative, Solenoidal & Irrotational fields, Vector identities. Line, Surface and Volume integrals, Green’s Lemma, Gauss’s Divergence theorem and Stoke’s theorem.
Marks and credits
| Head | Marks | Credit |
|---|---|---|
| CCE (continuous comprehensive evaluation) | 40 | 3 |
| End-semester exam | 60 |
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 mass spring systems.
- 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 Mechanical engineering.
- CO5PERFORM Vector differentiation & integration, ANALYZE the vector fields and APPLY to fluid flow problems.
Books
Text books
- Higher Engineering Mathematics by B.V. Ramana (Tata McGraw-Hill).
- Higher Engineering Mathematics by B. S. Grewal (Khanna Publication, Delhi).
Reference books
- Advanced Engineering Mathematics, 10e, by Erwin Kreyszig (Wiley India).
- Advanced Engineering Mathematics, 7e, by Peter V. O'Neil (Cengage Learning).
- Differential Equations, 3e by S. L. Ross (Wiley India).
- Introduction to Probability and Statistics for Engineers and Scientists, 5e, by Sheldon M. Ross (Elsevier Academic Press)
- Steven C. Chapra, ‘Applied Numerical Methods with MATLAB for Engineers and Scientist’, (Tata Mc- Graw Hill Publishing Co. Ltd).
- Jason Brownlee, ‘Statistical Methods for Machine Learning’, Machine learning Mastery.
NPTEL and SWAYAM links
Listed in the official syllabus:
FAQ
How many units are in Engineering Mathematics-III?
Engineering Mathematics-III (MDM-221-MEC) has 5 units: Unit I Linear Differential Equations (LDE) and Applications (7 h); Unit II Statistics & 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 Mechanical Engineering 2024 pattern syllabus lists continuous comprehensive evaluation (CCE) for 40 marks and the end-semester exam for 60 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.