| Day | Time | Location |
| Monday | 12pm | CG93 |
| Tuesday | 12pm | CLC202 |
| Thursday | 5pm | D110 |
Here is a table of intended lecture summaries. This will be updated as we go through the term. Numbers in bold square brackets give corresponding chapters of Riley, Hobson, Bence.
| Week | Monday 12pm (CG93) |
Tuesday 12pm
(CLC202) |
Thursday 5pm (D110) |
| 11 | 1. Functions of several variables. 1.1 Examples 1.2. Graphs of functions 1.3. Examples of graphs of functions. [Ch. 5 (intro)] | Collection Exam. | 2. Partial Derivatives 2.1. Examples [5.1] 2.2. Mathematical definition of the partial derivative. 2.3. Multivariable partial derivatives 2.4 The Total differential [5.2,5.3] |
| 12 | 2.4. Total differential. 2.5. Exact and inexact differentials. [5.2,5.3] | 2.5.1 The multi-variable case 2.6. The chain rule 2.6.1 Examples [5.5] | 2.7. Change of variables [5.6]2.8. Some useful theorems of partial differentiation [5.4] |
| 13 | 2.9 Thermodynamic example 3. Partial differential equations 3.1.(simple examples) | 3.2 Aside: 2d Laplace equation in polar co-ordinates. Changing variables. 3.3 More PDE examples [5.7] |
3.3 More PDE examples: wave equation, heat equation etc. |
| 14 | 4. Taylor expansions |
5. Critical points. 5.1. Local
maxima, minima and saddle points [5.8] |
5.2 Examples |
| 15 | 6. Double integrals. 6.1 Interpretation as
volume under a
surface 6.2 Explicit
example: integration over rectangles [6.1] |
6.3 Double integration over regions 6.4 More on changing the order of integration [6.1] | 6.4 More
on changing the order of
integration [6.1] |
| 16 | 6.5 Change of variables in multiple integration 6.7 Polar co-ordinates [6.3] | 7. Triple
integration. 7.1. Cylindrical polar coordinates
|
7.2 Applications: Volumes, Masses,
centres of masses and centroids. |
| 17 | 7.3.
Change of
variables: Spherical polar coordinates [6.2] |
8 Vector Calculus. 8.1 Differentiation of vectors [10.1] 8.2 Integration of vectors [10.2] | 8.3 Vector
functions of several
arguments [10.4] 8.4 Vector
fields [10.6]8.5 Vector operators:
Grad 8.5.1 Directional derivatives[10.7.1] |
| 18 | 8.5.1 Directional derivatives 8.6 Vector operators:
Div, Curl [10.7.2, 10.7.3] |
8.6 Vector operators:
Div 8.6.1 Laplacian 8.7 Vector operators: Curl [10.8] |
8.8 Vector operator formulae 8.9 Action on position vector |
| 19 | 8.10 Combinations of Grad, Div, Curl (Electromagnetic waves from Maxwell) 8.11 General curvilinear coordinates |
8.11 General curvilinear coordinates [10.10] |
8.11 General curvilinear coordinates [10.10] + review of term |