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.

Handouts

Problem sheets

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!

Relevant Khan Academy/MIT videos

 Exam papers

Exam papers for other relevant courses can be found on the library website, and solutions to MATH1401 and MATH1402 can be found on the MATH1403 Moodle page.

 What next?

For information on mathematics courses which follow on from here, see Maths after 1403.