Fundamental concepts in mathematical modeling: Abstraction-linearity and superposition-balance and conservation laws and the system boundary approach.
Lumped element modeling: Mechanical systems- Translational, rotational. Hydraulic systems. Thermal systems.RLC electrical systems. Modeling analogies.
Modeling of first order and second order systems: Governing equations for free and forced responses – transient response specifications – experimental determination of time constant and damping coefficient. Laplace Transforms. State space formulation.
Frequency response of Linear Time Invariant (LTI) systems: Frequency response of first order and second order systems – Transfer function – mathematical features – Bode plots-Relating time domain, frequency domain and state space.
Introduction to modeling and analysis of nonlinear engineering systems.
Introduction to linear system identification – time and frequency domain identification – discrete time input output models for LTI systems – linear least square parameter estimation.