Projects from NC A&T (2017-2018) Doctoral Pre-requisites (Pre Qualifiers) Nanoengineering

Here's my summary of the subjects you studied during your first year of nanoengineering:

Overview: Numerical Analysis focuses on algorithms for solving mathematical problems numerically rather than symbolically. This includes techniques for approximating solutions to equations, integration, differentiation, and optimization.
Key Topics:
- Error analysis and numerical stability.
- Methods for solving linear and nonlinear equations.
- Numerical differentiation and integration.
- Numerical solutions of differential equations.
- Interpolation and approximation of functions.

Overview: Differential Equations involve equations that relate functions with their derivatives. These are essential for modeling real-world phenomena where changes over time or space are involved, such as in physics, engineering, and biology.
Key Topics:
- Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs).
- Initial and boundary value problems.
- Analytical and numerical solutions.
- Applications in modeling physical systems, such as heat conduction, wave propagation, and fluid dynamics.

Overview: Nano-materials are materials with structures on the nanoscale, typically between 1 and 100 nanometers. This field studies their unique properties, which differ significantly from those of bulk materials.
Key Topics:
- Synthesis and fabrication methods of nano-materials.
- Characterization techniques like electron microscopy and spectroscopy.
- Properties of nano-materials, including electrical, optical, and mechanical properties.
- Applications in electronics, medicine, energy storage, and catalysis.

Overview: Quantum Mechanics is the fundamental theory that describes the behavior of matter and energy on the atomic and subatomic scales. It provides the basis for understanding phenomena that classical physics cannot explain.
Key Topics:
- Wave-particle duality and the uncertainty principle.
- Schrödinger equation and its applications.
- Quantum states, operators, and observables.
- Quantum tunneling, superposition, and entanglement.
- Applications in nanotechnology, quantum computing, and materials science.

Overview: Chemistry is the study of matter, its properties, and the changes it undergoes. Biochemistry focuses on the chemical processes within and related to living organisms, essential for understanding biological systems at a molecular level.
Key Topics:
- Atomic and molecular structure.
- Chemical bonding and reactions.
- Thermodynamics and kinetics.
- Organic chemistry, including biomolecules like proteins, lipids, and nucleic acids.
- Metabolic pathways and enzyme kinetics.

Overview: Molecular Dynamics (MD) is a computer simulation technique that models the physical movements of atoms and molecules over time. It’s used to study the structure, dynamics, and thermodynamics of molecular systems.
Key Topics:
- Newtonian mechanics applied to molecular systems.
- Force fields and potential energy surfaces.
- Simulation algorithms, including integration methods and boundary conditions.
- Applications in materials science, biophysics, and chemistry.
- Analysis of simulation data, including thermodynamic properties and molecular interactions.

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