MATH1011 Summer 2017/18

Lectures and notes

Jump to Chapter 1 2 3 4 5 6 7 8 9 10

1 Vector valued functions and functions of several variables

notes skeleton notes

• Introduction
• 1.1a Vector spaces, subsets
• 1.1b Coordinate systems
• 1.2 Vector valued functions
• 1.3 Functions of two variables
• 1.4 Vector fields

2 Limits and continuity

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• 2.1 Limit at a point
• 2.2 Limit at infinity
• 2.3 Limit laws
• 2.4 Squeeze theorem
• 2.5* Precise definition of a limit -this is an advanced topic. It won’t be assessed but it’s worth knowing about, especially if you continue with maths in second year.
• 2.6 Limits of multivariable functions
• 2.7a Continuity
• 2.7b Continuous functions

3 Differentiation

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• 3.1 Differentiation revision
• 3.2 Inverse functions
• 3.3 Inverse trigonometric functions
• 3.4 Differentiation of vector valued functions
• 3.5 Differentiation rules
• 3.6a Partial derivatives introduction
• 3.6b Partial derivatives examples
• 3.7 Higher order partials
• 3.8 Tangent vectors
• 3.9 Tangent planes
• The cross product
• 3.10 Normal vectors
• 3.11 Chain rule for partial derivatives
• 3.12 Directional derivatives
• 3.13 Maximum rate of change
• 3.14 The Jacobian matrix

4 Maxima and minima

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• 4.1 Extrema of functions of one variable (mostly revision)
• 4.2 Identifying local maxima and minima
• 4.3 Extrema of functions of two variables
• 4.4 Critical points of functions of two variables
• 4.5 The second derivative test

5 Integration

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• 5.1 Integration review
• 5.2 Integration techniques
• 5.3 Integration by inverse substitution (no video, not for assessment)
• 5.4 Partial fractions
• 5.5 Integration by parts
• 5.6 Riemann sums and integrals
• 5.7a Applications of Riemann sums
• 5.7b Lengths of curves

6 Double and triple integrals

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• 6.1 Double integrals
• 6.2 Calculating double integrals, continued here
• 6.3 The integral as a weighted sum
• 6.4 Triple integrals continued here
• 6.5 Triple integrals - examples continued here and then here
• 6.6 Centre of mass continued here

7 Change of coordinates in double and triple integrals

The following are lecture captures and notes from 2017 Semester 2 (by Dr Miccal Matthews).

notes and examples

• 7.1 Change of coordinates
• 7.2 Integrals in polar, cylindrical and spherical coordinates

8 Path and surface integrals

The following are lecture captures and notes from 2017 Semester 2 (by Dr Miccal Matthews)

notes and examples

• 8.1 Paths and lengths of curves
• 8.2 Path integrals
• 8.3 Surface parametrization and integration

notes and skeleton notes on:

• 8.4 Path integrals of (components of) vector fields continued here

9 Differential equations

lecture captures and notes from 2017 Semester 2 (by Dr Miccal Matthews)

notes and examples

• 9.1 Differential equations, direction fields
• 9.2 First order ODE
• 9.3 First order ODE examples
• 9.4 Second order ODE
• 9.5 Method of undetermined coefficients
• 9.6 Variation of parameters