Lecture 1. Mathematical models in chemistry: an overview.
Lecture 2. Complex numbers and their applications in physical sciences.
Lecture 3. Limits and their applications in physical sciences.
Lecture 4. What is a continuous function and why are most functions in chemistry continuous?
Lecture 5. Formal definition of the derivative and its basic properties.
Lecture 6. Partial derivatives and their properties.
Lecture 7. Derivatives in chemistry: reaction rate equations.
Lecture 8. Derivatives in chemistry: process optimisation.
Lecture 9. Derivatives in chemistry: the linear least squares method.
Lecture 10. Derivatives in chemistry: the non-linear least squares method.
Lecture 11. Derivatives in chemistry: constrained optimisation.
Lecture 12. Derivatives in chemistry: constrained optimisation.
Lecture 13. Approximations in chemistry: basics.
Lecture 14. Approximations in chemistry: power series.
Lecture 15. Data processing: statistical analysis.
Lecture 16. Data processing: errors and probabilities.
Lecture 17. Formal definition of the integral.
Lecture 18. Integrals in chemistry: simple cases.
Lecture 19. Integrals in chemistry: complicated cases.
Lecture 20. Using Mathematica to differentiate, integrate and solve equations.
Lecture 21. Numerical differentiation and integration.
Lecture 22. Mathematical methods in chemistry: artificial neural networks.
Lecture 23. Mathematical methods in chemistry: data integrity assurance.