Engineering Mathematics IV Syllabus

Numerical Methods
- Numerical solutions of ordinary differential equations (ODEs)
- Picard’s method, Taylor series method
- Modified Euler’s method, Runge-Kutta methods
- Predictor-corrector methods (Milne’s and Adams-Bashforth)
Partial Differential Equations (PDEs)
- Formation and solutions of PDEs
- Method of separation of variables
- Classification of second-order PDEs
- Wave equation, heat conduction equation, Laplace equation
Complex Analysis
- Functions of a complex variable
- Analytic functions, Cauchy-Riemann equations
- Complex line integrals, Cauchy’s theorem and integral formula
- Laurent series, residue theorem, and applications
Probability and Statistics
- Random variables (discrete and continuous)
- Probability distributions (Binomial, Poisson, Normal)
- Joint probability distributions
- Expectation, variance, covariance
- Hypothesis testing, confidence intervals
- Chi-square test, t-test, and F-test
Special Functions
- Bessel functions: properties, recurrence relations, orthogonality
- Legendre polynomials: properties, Rodrigue’s formula, orthogonality
Transformations
- Conformal mappings
- Bilinear transformations
- Applications of transformations in engineering problems
Stochastic Processes
- Introduction to stochastic processes
- Markov chains, transition probabilities
- Steady-state probabilities, applications in engineering

mechanical-engineering