chapter 1 Elements of mathematical modeling -- chapter 2 Expansion of function and mathematical methods -- chapter 3 Regular and singular perturbations -- chapter 4 Wave-impact processes -- chapter 5 Padé approximations -- chapter 6 Averaging of ribbed plates -- chapter 7 Chaos foresight -- chapter 8 Continuous approximation of discontinuous systems -- chapter 9 Nonlinear dynamics of a swinging oscillator.