Description
COLLEGE Mathematics & Physics
MATHEMATICS
Calculus I, II, III
- Usual functions
- Limits, continuity
- Differentiation
- Integration techniques
- Improper integrals
- Sequences and series
- Multivariable calculus
- Partial derivatives
- Gradient, divergence, curl
- Laplacian, Jacobian
- Multiple integrals
- Line and surface integrals
- Green, Stokes, Gauss theorems
Linear Algebra
- Vector spaces
- Linear maps
- Matrices
- Determinants
- Eigenvalues, eigenvectors
- Diagonalization, trigonalization
- Orthogonality
- Spectral decomposition
- Other matrix reductions (Gauss-Jordan, LU, Choleski, polar…)
Differential Equations
- First and second-order ODEs
- Linear systems
- Stability analysis
- Phase space
- Fourier series
- Introduction to PDEs
Probability & Statistics
- Random variables
- Probability distributions
- Expectation, variance
- Central limit theorem
- Law of Large Numbers
- Continuous and discrete distributions
- Gaussian integrals
- Monte-Carlo, other methods
Geometry
- Planar and spatial analytic geometry
- Euclidean geometry
- Affine geometry
- Conic sections (geometric and algebraic approaches)
PHYSICS
Classical Mechanics
- Newtonian mechanics
- Lagrangian mechanics
- Variational principles
- Central force motion
- Oscillations
- Gravitation (non-relativistic)
- Rigid-body dynamics
Electromagnetism
- Electrostatics, electric fields and potentials
- Magnetostatics, magnetic fields and induction
- Gauss’s and Ampère’s laws
- Maxwell’s equations
- Faraday law
- Electromagnetic waves
Waves & Optics
- Wave equation
- Fourier analysis
- Diffraction, interference
- Geometrical optics: lenses, mirrors
- Physical optics
Thermodynamics
- Thermodynamic laws
- Entropy
- Statistical ensembles
- Partial functions
Fluid Mechanics
- Continuity equation
- Euler equations
- Navier-Stokes equations
- Laminar and turbulent flows, Rayleigh number
Special Relativity
- Lorentz transformations
- Minkowski spacetime
- Proper time
- Relativistic dynamics
- Spacetime diagram
- Introduction to general relativity
Introduction to Quantum Mechanics
- Particle-Wave duality, energy
- Schrödinger’s equation, Hamiltonian
- Simple applications: hydrogen atom model and quantum oscillator
CHEMISTRY – General Chemistry I & II
Atomic & Molecular Structure
- Quantum mechanics of the atom
- Atomic orbitals, periodic structure
- Valence bond theory
- Molecular orbital theory
- Hybridization
- Spectroscopy
Thermochemistry
- Three laws of thermodynamics
- Enthalpy, entropy, free energy
- Phase equilibria
- Chemical potential
Kinetics
- Reaction mechanisms
- Zeroth, First and Second order kinetics
- Arrhenius law
Equilibrium
- Acid-base equilibria
- Electrochemical equilibria