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MAS108: Mathematical Modelling

Lecture 1. The concept of mathematical modelling
Lecture 2. Introduction to Difference Equations
Lecture 3. Cycles, period-doubling, and chaos
Lecture 4. More examples of difference equation models
Lecture 5. From difference to differential equations
Lecture 6. First order linear ordinary differential equations
Lecture 7. The muddiest point: part I
Lecture 8. Nature’s non-linearity and the need for qualitative solutions
Lecture 9. Direction fields for non-autonomous ODEs
Lecture 10. From the second law of motion to second order ODEs
Lecture 11. Modelling damped oscillations with homogeneous second order ODEs
Lecture 12. Inhomogeneous second order ODEs
Lecture 13. Modelling oscillations with second order ODEs: a worked example
Lecture 14. The muddiest point: part II
Lecture 15. Motion in more than one dimension
Lecture 16. Relative motion
Lecture 17. Modelling the effect of gravity close to the Earth’s surface
Lecture 18. Modelling projectile motion
Lecture 19. More examples of motion with constant acceleration
Lecture 20. The muddiest point: part III

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By Alex Best / Jonathan Potts

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