ES1830
THE UNIVERSITY OF WARWICK
First Year Examinations: Summer 2015
ENGINEERING MATHEMATICS AND SYSTEMS MODELLING
Candidates should answer the THREE COMPULSORY QUESTIONS.
Time Allowed : 3 hours.
Only calculators that conform to the list of models approved by the School of Engineering
may be used in this examination. The Engineering Databook and standard graph paper will
be provided.
Read carefully the instructions on the answer book and make sure that the particulars required are
entered on each answer book.
USE A SEPARATE ANSWER BOOK FOR EACH SECTION
, ES1830
SECTION A: ENGINEERING MATHEMATICS
_________________________________________________________________________________________
1.
(i) Two complex numbers are given by:
z1 2 4i z2 3 5i
(a) Find z3 z1 z 2 . (1 mark)
(b) Find z1 z2 . (1 mark)
5 3i
(c) Write the complex number z 4 in the form a ib . (2 marks)
3 2i
dy
(ii) Find the derivative for the functions
dx
(a) y 8 x 4 3 x 3 2 x 9 (2 marks)
(b) y sin cos 3x (4 marks)
3x3 2 x2 5
(c) y (4 marks)
cos x
dy
(iii) Use implicit differentiation to find when x and y are related through
dx
x2 y3 x2 3y 3 0 . (4 marks)
(iv) Two vectors are given as
a 3i 2 j 4k and b 5i 1j 6k
(a) Calculate the dot product: a b (3 marks)
(b) Calculate the cross product: a b (3 marks)
Question 1 Continued Overleaf
1
THE UNIVERSITY OF WARWICK
First Year Examinations: Summer 2015
ENGINEERING MATHEMATICS AND SYSTEMS MODELLING
Candidates should answer the THREE COMPULSORY QUESTIONS.
Time Allowed : 3 hours.
Only calculators that conform to the list of models approved by the School of Engineering
may be used in this examination. The Engineering Databook and standard graph paper will
be provided.
Read carefully the instructions on the answer book and make sure that the particulars required are
entered on each answer book.
USE A SEPARATE ANSWER BOOK FOR EACH SECTION
, ES1830
SECTION A: ENGINEERING MATHEMATICS
_________________________________________________________________________________________
1.
(i) Two complex numbers are given by:
z1 2 4i z2 3 5i
(a) Find z3 z1 z 2 . (1 mark)
(b) Find z1 z2 . (1 mark)
5 3i
(c) Write the complex number z 4 in the form a ib . (2 marks)
3 2i
dy
(ii) Find the derivative for the functions
dx
(a) y 8 x 4 3 x 3 2 x 9 (2 marks)
(b) y sin cos 3x (4 marks)
3x3 2 x2 5
(c) y (4 marks)
cos x
dy
(iii) Use implicit differentiation to find when x and y are related through
dx
x2 y3 x2 3y 3 0 . (4 marks)
(iv) Two vectors are given as
a 3i 2 j 4k and b 5i 1j 6k
(a) Calculate the dot product: a b (3 marks)
(b) Calculate the cross product: a b (3 marks)
Question 1 Continued Overleaf
1
