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.
- Syllabus (29/05/2013)
- Handout 0: Something for the summer (26/06/2013)
- Handout 1: Syllabus and introduction (30/09/2013)
- Handout 2: Greek letters (30/09/2013)
- Handout 3: Number sets (07/10/2013)
- Handout 4: Hyperbolic identities (07/10/2013)
- Handout 5: Inverse functions (14/10/2013)
- Handout 6: Taylor series (17/10/2013)
- Handout 7: What is integration? (22/10/2013)
- Handout 8: Complex logarithms (21/11/2013)
- Handout 9: Second order ODE derivation (28/11/2013)
- Handout 10: Second order ODE cheatsheet (28/11/2013)
- Handout 11: Fourier series in pictures (05/12/2013)
- Handout 12: Fourier series orthogonality relations (09/12/2013)
- Handout 13: Revision advice (12/12/2013)
- Revision lecture handout (25/04/2014)
- Problem sheet 1 (due 5pm 09/10/2013)
- Problem sheet 2 (due 2.30pm 16/10/2013)
- Problem sheet 3 (due 5pm 23/10/2013)
- Problem sheet 4 (due 5pm 30/10/2013)
- Problem sheet 5 (due 5pm 13/11/2013)
- Problem sheet 6 (due 5pm 20/11/2013)
- Problem sheet 7 (due 5pm 27/11/2013)
- Problem sheet 8 (due 5pm 04/12/2013)
- Problem sheet 9 (due 5pm 11/12/2013)
- (30/09/2013) Differentiation: Introduction, definition of differentiation, standard results, chain rule, product rule, quotient rule.
- (01/10/2013) Standard results using the quotient rule, implicit differentiation, standard results using implicit differentiation, evil test.
- (03/10/2013) Stationary points, local and global maxima and minima, why we might not be able to differentiate a function.
- (07/10/2013) Introduction to hyperbolic functions, hperbolic identities, inverse hyperbolic functions.
- (08/10/2013) Differentiating hyperbolic functions.
- (10/10/2013) Differentiating inverse hyperbolic functions. The theory behind partial differentiation.
- (14/10/2013) A practical approach to partial differentiation
- (15/10/2013) Finding tangent planes to 3D graphs.
- (17/10/2013) Maclaurin series: intuition and how to find it.
- (21/10/2013) Taylor series: definition and examples.
- (22/10/2013) Using Taylor series to solve differential equations and perform otherwise hideous integrations. Integration: what is integration? Partial fractions.
- (24/10/2013) Integration using substitution.
- (27/10/2013) Integration by parts.
- (29/10/2013) Integration using reduction formulae / recurrence relations.
- (30/10/2013) Improper integrals (being careful with infinity)
- (11/11/2013) Complex numbers: introduction, arithmetic, complex conjugates.
- (12/11/2013) Argand diagram, modulus-argument form of a complex number. Multiplying complex numbers in modulus-argument form.
- (14/11/2013) Dividing complex numbers in modulus-argument form. Exponential form of a complex number. Euler’s identity.
- (19/11/2013) Exponential form of complex numbers, de Moivre’s theorem.
- (20/11/2013) Roots of unity, roots of complex numbers.
- (22/11/2013) Complex logarithms.
- (25/11/2013) Differential equations: what is a differential equation?, separable equations, exact solutions, deriving the integrating factor.
- (26/11/2013) Examples of solving first order ODEs using the integrating factor and substitution.
- (28/11/2013) Second order ODEs: derivation of solution form, some easy examples.
- (02/12/2013) Inhomogeneous second order ODEs, complementary function and particular integral, particular integral when it’s part of the complementary function, some examples.
- (03/12/2013) Examples, (Cauchy–)Euler’s equation.
- (05/12/2013) Fourier series: motivation, periodic functions, trigonometric series.
- (09/12/2013) Expressions for an and bn, Fourier series of a square wave.
- (10/12/2013) Fourier series of the sawtooth wave. Even and odd functions.
- (12/12/2013) Revision discussion and chocolate fountains!
Relevant Khan Academy/MIT videos
- (L1) KA: Definition of differentiation
- (L1) KA: Standard results: derivative of xn
- (L1) KA: Chain rule (more, even more)
- (L1) KA: Product rule
- (L1) KA: Quotient rule (note he argues that the quotient rule is unnecessary, since it comes directly from the product rule. I find that people tend to make mistakes with negative powers which the quotient rule avoids)
- (L2) KA: Implicit differentiation (more, even more, even more still)
- (L3) KA: Maxima and minima
- (L4-6) KA: Hyperbolic functions
- (L7-8) KA: Partial differentiation (more) (note he approaches the topic using vectors, which is a sensible thing to do but since vectors are not part of our course, I have avoided doing)
- (L9-11) KA: Taylor series: intuition, Maclaurin series of cos(x), of sin(x), of ex.
- (L11) KA: Partial fractions (more, even more)
- (L12) KA: Integration using substitution (more, even more, even more still)
- (L13) KA: Integration by parts
(L13) MIT: Integration by parts (up to example 2)
- (L14) MIT: Reduction formulae (examples 3 and 4)
- (L15) MIT: Improper integrals
- (L16) KA: Introduction to i, the square root of -1
- (L16) KA: Complex numbers (part 0, part 1, part 2)
- (L16) KA: Complex conjugate example
- (L17-19) KA: Argand diagram, modulus-argument form of complex numbers, exponential form of complex numbers
- (L20) KA: Roots of complex numbers
- (L22) KA: What is a differential equation?
- (L22) KA: Separable differential equations (more)
- (L22) KA: Solving first order ODEs using the integrating factor (more)
- (L23) KA: Solving first order ODEs using a change of variables (more)
- (L24) KA: Homogeneous second order ODEs: if y1 and y2 are solutions, showing that Ay1 + By2 is a solution
- (L24) KA: Homogeneous second order ODEs: general solution for real, distinct roots of the auxiliary equation (note the way he just chooses y = erx is a fudge: we derived it properly!)
- (L24) KA: Homogeneous second order ODEs: showing that the cos-sin form for complex roots of the auxiliary equation is equivalent to the eλx form (part 2 with an example) (note he calls the auxiliary equation the ‘characteristic equation’)
- (L25) KA: Homogeneous second order ODEs: specific solution for real, distinct roots of the auxiliary equation with two boundary conditions (more)
- (L25) KA: Homogeneous second order ODEs: specific solution for complex roots of the auxiliary equation with two boundary conditions
- (L25) KA: Homogeneous second order ODEs: specific solution for repeated real roots of the auxiliary equation with two boundary conditions
- (L25-26) KA: Inhomogeneous second order ODEs: derivation of particular integral + complementary function form of solution and example (more, even more, even more still) (note he calls this the method of undetermined coefficients—everything has to have a name, I guess. I’ve never heard it called this, though. Maybe an American thing.)
- (L26) YouTube: Euler’s method for solving second order equations of the form x2y” + axy’ + by = f(x)
- (L27) MIT: Deriving Fourier series
- (L28) MIT: Fourier series of a square wave
- (L28-29) MIT: Manipulating Fourier series
- Practice Paper A (solutions)
- Practice Paper B (solutions)
- January 2013 exam (solutions)
- May 2013 exam (solutions)
- January 2014 exam (solutions) (video solutions)
- May 2014 exam
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.
For information on mathematics courses which follow on from here, see Maths after 1403.