Experience the most comprehensive and interactive way to learn fluid dynamics.

The AMMS (Advanced Maths Made Simple) app in fluid dynamics presents a thorough course designed to assist university and college mathematics students who, like myself, have encountered hurdles in understanding this subject. Conceived two decades ago during my time as a struggling mathematics student at Oxford, the app aims to offer straightforward explanations and abundant practice exercises, addressing the challenge of finding accessible resources for mastering fluid dynamics.

There are no ads in the app. I ask for a small contribution to access the full content - which I will use to build the next app, which will be a complete course in algebra [Starting at the basics, taking you all the way up to university/graduate school level algebra].
The app consists of lessons describing each topic and subtopic in an easy-to-digest questions and answers form.

Tests and quizzes contain 20 and 10 questions respectively - with the option of choosing what topics to include in your tests. Each question comes with a helpful hint in case you get stuck. There are thousands of questions in the app, and each time a random selection will be chosen to test you.

You can keep track of your progress on our progress page - the colours of the subtopics represent your average score - a low score is indicated in red and a high score in green. So the aim of the game is to keep working at it until you have a bright green page on your progress page.

The topics are divided into bite-sized subtopics. Nearly 20,000 words of course notes cover the following syllabus:

1. Fluid properties
- Density
- Viscosity
- Surface tension
- The equation of state
- Entropy
2. Fluid statics
- Pressure in a fluid at rest
- Pascal's law
- Hydrostatic pressure distribution
- Buoyancy and Archimedes' Princple
3. Fluid kinematics
- Velocity and acceleration fields
- Eulerian and Lagrangian descriptions of flow
- Streamlines, streaklines, and pathlines
- Boundary conditions
4. Fluid dynamics equations
- Continuity equation (Conservation of mass)
- Navier-Stokes equations (Conservation of momentum)
- Energy equation (Conservation of energy)
5. Incompressible flow
- Incompressible flows
- Steady vs. unsteady flow
- Laminar vs turbulent flow
- Flow through pipes and channels
6. Compressible flow
- Compressibility
- Shockwaves and expansion waves
- Speed of sound and Mach number
7. Boundary layer theory
- Boundary layer theory
- Boundary layer on a flat plate
- Flow on a wedge
- Boundary layer on a free surface
8. Flow around objects
- Unidirectional flows
- Stokes flows
- Flow past a sphere
- Flows in a corner
- Flow past a circular cylinder
9. Vortex dynamics
- Vorticity
- Shear layers
- Vortex rings
- Vortex interactions
10. Waves
- The wave equation
- One-dimensional waves
- Stokes waves
- Other wave models
- Linear waves
- Non-linear waves
11. Multiphase flows
- Gas-liquid flows
- Gas-solid flows
- Liquid-solid flows
- Porous flows
12. Turbulence
- Characteristics of turbulent flow
- Turbulence modelling
13. Environmental fluid dynamics
- Atmospheric and oceanic flows
- River and coastal flows
14. Industrial applications
- Fluid dynamics in engineering design
- Heat transfer and fluid flow in industrial processes
- Fluid dynamics in engineering design
- Heat transfer and fluid flow in industrial processes

It can be very difficult to find a one-stop-shop for higher level mathematics, so I hope that you find this compact source of information as well as quick tests and deeper dive tests very handy. We welcome any comments and suggestions and we will do our utmost to reflect it in the app and further development.

Advanced Maths Made Simple

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