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

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