ImperialX: Further Mathematics Year 13 course 2: Applications of Differential Equations, Momentum, Work, Energy & Power, The Poisson Distribution, The Central Limit Theorem, Chi Squared Tests, Type I and II Errors
by Imperial College London
Module 1: Applications of Differential Equations
- Kinematics modeling
- Understanding types of damping
- Methods of solving coupled differential equations
Module 2: Momentum and Impulse
- Conservation of momentum principles
- Effects of impulse in collisions
Module 3: Work, Energy, and Power
- Fundamentals of work-energy principles
- Study of conservative and non-conservative forces
Module 4: Oblique Impact
- Elastic and inelastic collisions in two dimensions
- Analysis of kinetic energy changes during collisions
Module 5: Expectation and Variance and the Poisson Distribution
- Deep dive into the properties of the Poisson distribution
- Statistical tests for the mean of a Poisson distribution
Module 6: The Central Limit Theorem
- Applications of the Central Limit Theorem in real-world datasets
Module 7: Chi-Squared Tests
- Conducting and interpreting chi-squared tests
- Fitting theoretical distributions
Module 8: Type I and Type II Errors
- Understanding and calculating type I and II errors in hypothesis testing
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