B.Tech Mechanical Engineering · Sem 2 (Core) · B.Tech Automobile Engineering · Sem 2 (Core) · B.Tech Aeronautical Engineering · Sem 2 (Core) · B.Tech Mechanical & Industrial Engineering · Sem 2 (Core) · B.Tech Production & Industrial Production Engineering · Sem 2 (Core) · B.Tech Manufacturing Technology · Sem 2 (Core) · B.Tech Mining Engineering · Sem 2 (Core)
Linear differential equation of nth order with constant coefficients, Cauchy- Euler equation, solution of second order linear differential equations with variable coefficient by the method of variation of parameters, change of independent variable, normal form. Applications : Spring-mass-damper system modeling, Heat conduction in machine components, Mechanical control system modeling.
Laplace Transform: Definition of Laplace Transform, Existence Conditions, Linearity Property, Laplace Transform of some standard functions, I and II Shifting theorems (without proof), Change of Scale Property, Laplace transform of derivatives and integrals, Periodic Functions, Unit Step Function, Inverse Laplace Transform, Partial Fraction Method, Convolution theorem (without proof), Application of Laplace transform to solve ordinary differential equation. Applications: Transient response analysis of mechanical systems, Modelling of vibration and damping systems, Dynamic response of suspension systems.
Definition of a Sequence, Monotonic Sequence, Convergence and Divergent Sequence, Cauchy Sequence, Necessary Condition for Convergence, Tests of Convergence: Comparison Test, Ratio Test, Raabe’s Test, Logarithmic Test Applications: Convergence analysis of iterative engineering algorithms, Computational fluid dynamics (CFD) simulations, Numerical solutions of engineering equations.
Differentiation Functions of Complex Variables, Limit Continuity and Differentiability, Analytic Function, Cauchy- Riemann Equations (Cartesian and Polar Form), Harmonic Function, Milne-Thomson Method for constructing the Analytic Function. Applications : Two-dimensional fluid flow analysis, Stress analysis in elasticity.
Integration Complex integrals, Cauchy-Integral theorem (without proof), Cauchy integral formula (without proof),Taylor’s series and Laurent’s series, Singularities, Residue of a function, Cauchy Residue Theorem, Evaluation of the Real definite integrals. Applications: Evaluation of contour integrals in fluid mechanics, Frequency response analysis in mechanical vibration and control systems.
After completion of the course student will be able to:
This subject is on page 18, 19, 20, 21, 22 of the original AKTU PDF.
