Covered so far
PART I Vector Calculus
Lecture 1 Introductary remarks, scalar fields, the Riemann integral for fxns.
Lecture 2 The Riemann integral for fxns of two-variables, iterated integrals, an example.
Lecture 3 No tutorial in the first week.
Lecture 4 Changes of coordinates, the Jacobian, polar coordinates.
Lecture 5 Deriving the Jacobian formula, three-d, not much is different: iterated integrals and changes of coordinates.
Lecture 6 Tutorial: PS1.
Lecture 7 Spherical and cylindrical coordinates, vector fields.
Lecture 8 Vector fields. Grad, definition, examples, the directional derivative.
Lecture 9 Tutorial: PS2.
Lecture 10 Bank holiday.
Lecture 11 The divergence, the continuity equation.
Lecture 12 Tutorial: PS3.
Lecture 13 Curl. Vector identities.
Lecture 14 More vector identities. The line integral, definition, parametric form, example.
Lecture 15 Tutorial: PS4.
Lecture 16 More line integral, conservative implies path-independence, irrotational.
Lecture 17 Path-independence implies conservative, mention of when irrotational implies path-independent.
Lecture 18 Tutorial: PS5.
Lecture 19 Surface integral; definition, parametric form.
Lecture 20 Parametric form, examples. The integral theorems, Stokes and Green.
Lecture 21 Tutorial: PS6.
Lecture 22 Proof of Green's theorem.
Lecture 23 Proof of Stokes' theorem, applications.
Lecture 24 Tutorial: PS7.
Lecture 25 Cancelled.
Lecture 26 Gauss Theorem, statement and proof.
Lecture 27 The Christmas quiz.
Lecture 28 Gauss Theorem, examples.
Lecture 29 Line and surface integrals of scalars.
Lecture 30 No tutorial.
PART II Fourier series and transforms
Lecture 31 Start of Fourier series.
Lecture 32 Fourier series, with example.
Lecture 33 Class survey. Tutorial: PS9.
Lecture 34 Fourier series, complex.
Lecture 35 Complex series, Parceval's theorem.
Lecture 36 Class survey. Tutorial: PS10.
Lecture 37 The Fourier integral.
Lecture 38 More on the Fourier integral. Plancherel's formula.
Lecture 39 Tutorial: PS11.
Lecture 40 Introduction to the Dirac delta function.
Lecture 41 The Dirac delta function and distributions; properties of the delta function.
Lecture 42 Tutorial: PS12.
Lecture 43 Properties of the delta function.
Lecture 44 Fourier integrals and the delta function.
Lecture 45 Tutorial: PS13.
PART III Ordinary Differential Equations
Lecture 46 Start of ODEs, terminology, first order.
Lecture 47 First order, start of second order: homogenous, constant coefficients..
Lecture 48 Tutorial: PS14.
Lecture 49 Homogenous, constant coefficients, start of inhomogeneous.
Lecture 50 Constant coefficients, inhomogeneous.
Lecture 51 Tutorial: PS15.
Lecture 52 Green's functions. Euler's Equation, start of series solutions.
Lecture 53 Lecturer absent.
Lecture 54 Tutorial: PS15.
Lecture 55 Start of series solutions.
Lecture 56 More series solutions.
Lecture 57 Easter Friday.
Lecture 58 Easter Monday.
Lecture 59 Froebenius and Bessel, not finished.
Lecture 60 Froebenius and Bessel. Tutorial PS 17.
Lecture 61 Sturm Liouville equations, start.
Lecture 62 More Sturm Liouville, the Legendre equation.
Lecture 63 Tutorial PS 18 q4.
PART IV Partial Differential Equations
Lecture 64 PDEs, introduction, existence proof.
Lecture 65 Existence, the Gauss Mean Value Theorem
Lecture 66 Tutorial, rest of PS 18.
Lecture 67 Start of seperation of variables.
Lecture 68 More seperation of variables.
Lecture 69 Tutorial, PS19.
Lecture 70 Bank holiday Monday.
Lecture 71 The heat equation.
Lecture 72 Tutorial, PS21.