Module title & Course code
Practical Calculus
MAS170
Lecturer
Dr N Dummigan
Course description
In this course we learn how to define and evaluate derivatives and integrals for functions which
depend on more than one variable, with an emphasis on functions of two variables, for which the
main ideas already appear. We also think about what it means to approach a limit or to add up a sum
with infinitely many terms, but throughout the emphasis is on explicit examples and getting answers.
Prerequisites: MAS100 (Mathematics with Maple)
University course content
A Level course content
Module
Inequalities - basic properties and examples.
Modulus.
Inequalities and their graphical solutions sets
Modulus function and its properties; solving equations using the modulus
function
C1
C3
Further
module
only?
no
no
Idea of a limit, including at infinity, compound
interest.
Sum to infinity of a geometric series, compound interest
C2
no
C4
no
C3
no
Formulae to be remembered: U n  ar
Differential equation for continuous compound
interest. Solution by inspection and by separation
of variables.
Partial derivatives
n 1
a
a(1  r n ) S   1  r
, Sn 
,
1 r
Separating variables and forming and solving differential equations
Implicit Differentiation. Formula to be remembered:
d
dy
( f ( y ))  f ( y )
dx
dx
Use of the Chain Rule. Formula to be remembered:
dy dy dt dy  1 dx

dy
dx dt dx , dx
Double integrals
Infinite series
Integrations to find areas and volumes
Integration by substitution, partial fractions and other means
Using polar co-ordinates
Geometric series. Formulae to be remembered:
Tn  ar
n 1
,
Sn 
a(1  r n )
1 r ,
a
S 
1 r
Power series: Maclaurin and Taylor expansions and understanding of radius of
convergence. Formula to be remembered:

f ( x)  
n 0
C1-C4
C4
FP1
no
no
yes
C2
no
FP2
yes
f n (a)
( x  a) n
n!
i
Euler’s identity. Formula to be remembered: e  cos   i sin 
FP2/FP3 yes