1. Introduction and basic math (3 hrs)
(1) Introduction
(2) Scalars, vectors, and tensors

2. Kinematics (6 hrs)
(1) Lagrangian vs. Eulerian specifications, material derivatives
(2) Streamline, path line, and streak line
(3) Strain rate
(4) Vorticity and circulation

3. Conservation law (12 hrs)
(1) Reynolds transport theorem
(2) Conservation of mass, scalar, and heat
(3) Conservation of momentum: Navier-Stokes equation, viscous vs. inviscid flows
(4) Bernoulli equation

4. Vorticity dynamics (6 hrs)
(1) Kelvin’s circulation theorem
(2) Helmholtz vortex theorems
(3) Vorticity transport equation

5. Potential flow (6 hrs): Fundamentals and examples

6. Dynamic Similarity (2 hrs): Buckingham's PI theorem

7. Laminar flow (8 hrs)
(1) Examples of steady parallel flows
(2) Stokes’ first problem and similarity solution
(3) Stokes' second problem
(4) Creeping flow around a sphere

8. Boundary layers and related topics (5 hrs)
(1) Boundary layer approximation
(2) Measure of BL thickness
(3) Blasius solution
(4) Separation