Reference books:

•       Classical Mechanics, J. R. Taylor (University Science Books, 2005)

•       Classical Dynamics of particles and systems, S. T. Thornton and J. B. Marion (2008)

•       Introduction to Classical Mechanics with problems and solutions, D. Morin (Cambridge UK, 2007)

•       Div, grad, curl and all that: an informal text on vector calculus, H. M. Schey (3rd ed., Norton and Co.)

Unit 1: Newton's laws of motion

1. Fundamental concepts – Space, time, mass, force, and the concept of a point particle

2. Properties of vectors, differentiation of vectors – Velocity and acceleration

3. Newton’s first and second laws, second law as a differential equation, solution for constant F with arbitrary initial conditions, forces in nature- fundamental vs empirical, inertial, non-inertial frames

4. Pseudo-forces, an example of a uniformly accelerating frame

5. Newton’s third law and conservation of momentum, validity of the third law, example(s) of breakdown

6. Newton’s second law in 2-D polar coordinates, examples of the second law: sliding block, planar (simple) pendulum + oscillating skateboard, circular pendulum

Unit 2: Oscillations

1. Simple harmonic motion – explicit solution of equation of motion

2. Damped oscillator- Solutions for under-damped, over-damped, and critically damped cases

3. Driven, damped harmonic motion, Resonance

Unit 3: Motion in One Dimension

1. Kinetic energy, potential energy, work-energy theorem

2. Energy in 1-d systems, time period – energy equation, turning points, stable, and unstable equilibrium

3. Introduction to phase space

4. Phase space of harmonic oscillator – undamped, damped, and critically damped (overdamped not included)

5. Phase diagram for non-linear systems, plane pendulum

Unit 4: Conservative forces

1. Work-energy theorem in higher dimensions, force as gradient of potential energy (introduce and discuss the notion of gradient in Cartesian coordinates)

2. Geometric interpretation of the gradient and properties of line integral, condition that F is conservative, introduction of the curl operator (Cartesian only)

3. Line element, gradient and kinetic energy in cylindrical and spherical coordinates

Unit 5: The Lagrangian method

1. Euler-Lagrange equations, forces of constraint

2. Generalized coordinates and conservation laws

Unit 6: Motion under central forces

1. Conservation of angular momentum, Lagrangian in plane polar coordinates, effective potential

2. Equations of orbit, bounded and unbounded orbits, Gravity (inverse-square law) and Kepler’s Laws, notion of reduced mass

Unit 7: Vector Calculus with Applications to Fluid Mechanics

1. Flux of a vector field, Gauss divergence theorem, divergence in cylindrical and spherical polar coordinates

2. Circulation and curl, Stokes’s theorem

3. Fluid flow, Bernoulli's principle, Continuity equation