Physics 325 Syllabus (Spring 2011)
Course outline
0. Mathematics Background Assumed
- Series approximation
- Vectors, matrices, coordinate systems
- Basic complex analysis and functions (e.g. Euler's formula)
- Ordinary differential equations
- Vector calculus
1. Basic Notions of Classical Mechanics
- Galilean Invariance, Inertial Reference Frames
- Newton’s Laws
- One Dimensional Motion
- Conservative Fields, Potential Energy
- Conservative Laws, Center of Mass
- Momentum & Angular Momentum
- Rocket Motion
- Motion in Three Dimensions
2. Gravitation
- Central Forces
- Gravitational Force and Potential
- Motion in a Central Field and Planetary Orbits
3. Oscillations
- Harmonic Oscillators
- Damped Oscillations
- Driven Oscillations, Resonance
- Fourier Series and Periodic Driving
- Impulse Response and Green's Functions
4. Lagrangian and Hamiltonian Dynamics
- Calculus of Variations
- Hamilton's Principle, Euler-Lagrange Equations
- Generalized Coordinates and Constraints
- Lagrangian Dynamics
- Lagrange Multipliers, Generalized Forces and Momenta
- Conservation Laws
- Hamiltonian Dynamics
5. Motion in Noninertial Frames
- Transformation to Accelerated Reference Frames
- Rotating Reference Frames
- The Coriolis force and the Foucault Pendulum
- Principle of Equivalence
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