By the end, students will be able to:

• Introduction to the concept of nonlinearity and nonlinear systems.
• Formal definition and properties of linearity.
• Solution of nonlinear differential equations; existence and uniqueness.
• Phenomena exhibited by nonlinear systems only; finite escape time, multiple equilibria, limit cycles, harmonic and subharmonic generation, multiple modes, resonance prevention, jump phenomenon, frequency entrainment, chaos.
• Graphical, analytical, and integral representation of nonlinearities.
• Direct integration method in nonlinear analysis.
• Method of local linearization; Jacobians, linearizability conditions.
• State and phase plane analysis; singular points, state trajectories, conservative systems, isoclines, Lienard's construction, delta method, Pell's method, Drobov's method, slopeline method, time construction.
• Behavior of singular points and global state/phase plane analysis; numerical integration, variable structure systems, piecewise linearization.
• Limit cycle analysis; amplitude, frequency, and stability of limit cycles, harmonic balance, existence theorems of limit cycles, Poincaré index, theorems of Poincaré, Bendixon, method of contact curves, Lienard sufficiency conditions.
• Approximation methods; singular perturbation method, regular perturbation method, Poisson's method, secular terms, nonautonomous systems, averaging methods, Krylov-Bogoliubov's method, Van der Pol's method, method of slowly varying parameters, existence and stability of limit cycles.
• Describing function analysis; definition and various forms of describing functions, connection with Krylov-Bogoliubov treatment, various examples including hysteresis, inertia- and friction-controlled backlash, piecewise nonlinearities, polynomial nonlinearities, implicitly dynamic nonlinearities, synthesis of describing functions,