IMP QUESTIONS | M3 MECHANICAL | SPPU PUNE UNIVERSITY

For more such content and unit wise lectures as per SPPU Pune university, you can download our application named SIMPLIFYING ENGINEERING from google play store. Link is given below:- Application link:- https://play.google.com/store/apps/de... IOS App link:- https://apps.apple.com/in/app/classpl... ORG CODE:- KELYXQ Website link:- https://www.simplifyingengineering.com/ Telegram Channel Link:- https://t.me/+UzKUeLdwblUwNjBl Whatsapp link:- https://t.me/+UzKUeLdwblUwNjBl UNIT 1:- Linear Differential Equations (LDE) and Applications LDE 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 UNIT 2:- Statistics & Probability Introduction 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 UNIT 3:- Numerical methods for solving algebraic and transcendental equations Numerical 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. UNIT 4:- Numerical Interpolation and solution of ODE Interpolation: 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. UNIT 5:- Vector Calculus Vector 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