# Mathematical Methods for Arts and Sciences

This is the course page for the UCL first year mathematics/BASc course MATH1403, Mathematical Methods for Arts and Sciences, which ran in the first term of the 2013–14 year.

I have no office hour in the second or third terms, but you are free to contact me to schedule a meeting at a mutually convenient time.

Handouts, coursework and useful resources are posted both here and on Moodle.

If you have any queries or problems, you can email me. I will also pick up anything on Twitter with the hashtag #MATH1403.

### Lecture topics

1. (30/09/2013) Differentiation: Introduction, definition of differentiation, standard results, chain rule, product rule, quotient rule.
2. (01/10/2013) Standard results using the quotient rule, implicit differentiation, standard results using implicit differentiation, evil test.
3. (03/10/2013) Stationary points, local and global maxima and minima, why we might not be able to differentiate a function.
4. (07/10/2013) Introduction to hyperbolic functions, hperbolic identities, inverse hyperbolic functions.
5. (08/10/2013) Differentiating hyperbolic functions.
6. (10/10/2013) Differentiating inverse hyperbolic functions. The theory behind partial differentiation.
7. (14/10/2013) A practical approach to partial differentiation
8. (15/10/2013) Finding tangent planes to 3D graphs.
9. (17/10/2013) Maclaurin series: intuition and how to find it.
10. (21/10/2013) Taylor series: definition and examples.
11. (22/10/2013) Using Taylor series to solve differential equations and perform otherwise hideous integrations. Integration: what is integration? Partial fractions.
12. (24/10/2013) Integration using substitution.
13. (27/10/2013) Integration by parts.
14. (29/10/2013) Integration using reduction formulae / recurrence relations.
15. (30/10/2013) Improper integrals (being careful with infinity)
16. (11/11/2013) Complex numbers: introduction, arithmetic, complex conjugates.
17. (12/11/2013) Argand diagram, modulus-argument form of a complex number. Multiplying complex numbers in modulus-argument form.
18. (14/11/2013) Dividing complex numbers in modulus-argument form. Exponential form of a complex number. Euler’s identity.
19. (19/11/2013) Exponential form of complex numbers, de Moivre’s theorem.
20. (20/11/2013) Roots of unity, roots of complex numbers.
21. (22/11/2013) Complex logarithms.
22. (25/11/2013) Differential equations: what is a differential equation?, separable equations, exact solutions, deriving the integrating factor.
23. (26/11/2013) Examples of solving first order ODEs using the integrating factor and substitution.
24. (28/11/2013) Second order ODEs: derivation of solution form, some easy examples.
25. (02/12/2013) Inhomogeneous second order ODEs, complementary function and particular integral, particular integral when it’s part of the complementary function, some examples.
26. (03/12/2013) Examples, (Cauchy–)Euler’s equation.
27. (05/12/2013) Fourier series: motivation, periodic functions, trigonometric series.
28. (09/12/2013) Expressions for an and bn, Fourier series of a square wave.
29. (10/12/2013) Fourier series of the sawtooth wave. Even and odd functions.
30. (12/12/2013) Revision discussion and chocolate fountains!