Geometry of PDEs and Mechanics.

Algebraic Geometry: Algebraic Complements, Affine spaces, Differential Manifolds, Grassmann Manifolds, Spectral Sequences. 2. Differential Equations (PDES): Geometry of Differential Equations, Ordinary Differential Equations (ODEs), Characteristics of PDEs, Affine PDEs and Green Functions, Spectral Sequences in PDEs, Tunnel Effects in PDEs, Cobordism Groups in PDEs. 3. Mechanics: Structure of Galilean Space-Time, One-Body Dynamics, Important Formulas, Fundamental Theorems of Dynamics, Lagrangian Mechanics for Perfect Holonomic Systems, Rigid-Body Dynamics. 4. Continuum Mechanics: Flow, Stress Tensor and Moment of Stress Tensor, Local Dynamic Equations, Thermodynamics of Continuum Media, Rheological Classification of Materials, Rheoptics, Multicomponent Continuum Systems, Variational Field Theory. 5. Quantum Field Theory: Locally Convex Manifolds and Derivative Spaces, Differential Geometry of Quantum Situs, Mathematical Logic and Quantization of PDEs, Formal and Dirac Quantizations of PDEs, Canonical Quantization of PDEs. 6. Geometry of Quantum PDEs: Differential Geometry of Quantum Manifolds, Cohomology of Quantum Manifolds, Formal Theory of Quantum PDEs, Cartan Spectral Sequences of Quantum PDEs, Quantum Distribution Solutions and Singular Solutions of Quantum PDEs, Tunnel Effects in Quantum PDEs, Quantum PDEs Non-holonomic Connections, Gauge Quantum PDEs, Supergravity Quantum PDEs.