Focusing on classical mechanics for performance, this work shows how applied mathematics is used in engineering areas. It explores the interplay between physical laws and mathematical methods as the basis for modeling natural phenomena and engineering devices. It discusses multilinear algebra, coordinate transformation, mass distributions, and tensors, covering numerous examples from particle physics, engine design, aeronautics, rigid body dynamics, and more. Each chapter includes problems and step-by-step solutions, encouraging readers to create their own mathematical-physical models.