Applied Maths

Topics

1. Vectors

Represent vectors in terms of i and j components and in polar form Apply and interpret vector algebra Calculate and interpret the dot product of vectors

2.Kinematics(Linear Motion with Constant Acceleration)

Describe the motion of a particle in 1D; position, displacement, velocity, acceleration and time. Graphical Representation of velocity-time graphs and displacement -time graphs. The kinematics formulae under constant acceleration • v = u +a t • s = ut + ½a t2 • v2 = u2 +2as • s = t(u+v)/2

3. Projectiles

Solve projectile motion problems involving displacement, velocity and time. Calculate time of flight, maximum height and maximum range on horizontal planes.

4. Dynamics(Connected Particles)

Draw force diagrams for particles on a horizontal or inclined planes Resolve forces along and perpendicular to inclined planes Solve dynamic problems on rough and smooth surfaces

5. Collisions

Solve dynamic problems involving particles that collide directly and obliquely. Apply the Principle of Conservation of Momentum Apply Newton’s Experimental Laws for collisions Calculate the Coefficient of Restitution for elastic and inelastic collisions.

6. Difference Equations

Identify real-world situations which can be modelled by difference equations. Derive difference equations for real-world phenomena involving incremental change. Analyse, interpret and solve 1st & 2nd order difference equations. 2nd Order: un=l(α)^n+m(β)^n

7. Networks and Graphs

Use and apply the following network terminology: vertex / node, edge/arc, weight, path, cycle. Distinguish between connected and disconnected graphs, and between directed and undirected graphs. Represent a graph using an adjacency matrix, and reconstruct a graph from its adjacency matrix. Perform multiplication of square matrices & interpret the product of adjacency matrices. Use Kruskal & Prim’s algorithm to find minimum spanning trees.

8. Dynamic Programming and Shortest Paths

Apply Bellman’s Principle of Optimality to find the shortest paths in weighted networks. Apply Dijkstra’s algorithm to find the shortest paths in a weighted network Apply the concepts of Critical Path, Early Times, Late Times and Floats to Project Scheduling.

9. Circular Motion

Solve problems involving the dynamics of a particle moving in a Horizontal or Vertical circle.

10. Differential Equations

Identify real-world situations which can be modelled by differential equations Solve differential equations • first order separable • second order which can be reduced to first order