Mathematical Methods in Engineering syllabus

Initial and boundary value problems: introduction. Initial value problems: Ordinary differential equations (ODE): Taylor method, Euler method, Runge-Kutta 4th order, simultaneous equations using Runge-Kutta 2nd order method. Boundary value problems (BVP). Introduction. Partial differential equations (PDE): finite difference method to 1D problems, Rayleigh’s method, Galerkin’s method, Laplace equation in 2D.

Numerical Integration (1D): Trapezoidal rule, Simpson’s 1/3rd rule, Simpson’s 3/8th rule, Gauss quadrature for 2-point and 3-point method, double integration. Double integration: Trapezoidal rule, Simpson’s 1/3rd rule.

Curve fitting: least square technique; first order, quadratic, power equation, exponential equation. Regression analysis: linear regression, multiple regressions. Interpolation: Lagrange forward and inverse interpolation, Newton forward interpolation.

Measures of central tendency: arithmetic mean, median, mode. Measurement of variability and dispersion: range, interquartile range, variance, standard deviation, coefficient of variation. Measure of shape: definition of shape parameters, skewness, types of skewness, Karl Pearson’s coefficient of skewness, kurtosis, types of kurtosis, mesokurtic, leptokurtic, platykurtic. Correlation: concept of correlation, Karl Pearson’s coefficient of correlation, Spearman’s rank correlation. Probability: joint, conditional and marginal probability, Bayes’ theorem, Discrete and continuous probability distributions, normal, lognormal and Weibull distributions, applications.

Statistical inference: test of hypothesis, null and alternative hypotheses, type I and II errors, level of significance, p-value, chi-square test, t-test, ANOVA, ANCOVA, manufacturing process validation. Reliability: introduction to reliability, reliability definition, failure rate, repair rate, reliability function, and reliability models, exponential distribution, mean time to failure (MTTF), mean time between failures (MTBF). Failure Mode and Effects Analysis (FMEA): product life cycle prediction, preventive maintenance planning, system design optimization (theoretical treatment only).