Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
SOEE1300 Inter Maths for Environmental Sciences: 2007/2008 session Additional D questions. D questions are at a more advanced level  they are either mathematically harder, or they apply the knowledge you already have in a more practical situation. Althou
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
Chapter 1 Functions of One Variable
Examples 1, Q1 Examples 1, Q2
1.1
Variables
Quantities which can take a range of values (e.g. the temperature of the air, the concentration of pollutant in a river, etc.) are called variables.
1.2
Functions of One Varia
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
Chapter 2 Limits and Differentiation
2.1 Definition of a Limit
For the present purposes we will use an intuitive definition of a limit of a function rather than a more strictly rigorous mathematical definition. Suppose that x is close to, but not exactly
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
SOEE1300 Inter Maths for Environmental Sciences: 2007/2008 session Examples 3: Deadline 22nd November "A" questions are for lectures. "B" questions are for practice and should not be handed in. "C" questions are for assessment and should be handed in on o
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
SOEE1300 Intro Maths for Environmental Sciences: 2007/2008 session Examples 2: Deadline 8th November A questions are for lectures. B questions are for practice and should not be handed in. C questions are for assessment and should be handed in on or befor
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
Chapter 5 Vectors
5.1 Definition of Vectors
Vectors are quantities which have both magnitude and direction. For example, a displacement from a fixed point A to a fixed point B is a vector because its magnitude is the distance between A and B and the direc
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
SOEE1300 Inter Maths for Environmental Sciences: 2007/2008 session Examples 1: Deadline 18th October A questions are for lectures. B questions are for practice and should not be handed in. C questions are for assessment and should be handed in on or befor
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
Chapter 4 Complex Numbers
4.1 Definition of Complex Numbers
z = a + ib where a and b are real numbers and i has the property that i2 = 1. (4.2) (4.1)
A complex number is a number of the form
a is called the real part of z and b is called the imaginary pa
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
Chapter 3 Integration
3.1 Indefinite Integration
Integration is the reverse of differentiation. Consider a function f (x) and suppose that there exists another function F (x) such that dF = f (x). dx (3.1)
For example, if f (x) = 2x, then F (x) = x2 satis
Intermediate Mathematics for Environmental Sciences
SOEE 1300

Spring 2014
Varieties 58
Cultural category 5 and 6
Art cinemas
It was not until after the Second World War that European art cinema became firmly
established, with the succession of movements such as Italian NeoRealism, the French Nouvelle
Vague, and the New German