13.
Suggestions for the Formula Sheets
Below are some suggestions for many more formulae than can be placed easily on both
sides of the two standard 8"11" sheets of paper for the final examination. It is
strongly recommended that students compose their ow

Mid Term Test Solutions 2012 06 21
ENGI 4430
1)
Page 1 of 9
For the vector field F y x xyz k :
i
j
(a) Find the equations of the lines of force (you may assume x 0, y 0 and z 0 ).
(b) Why are the lines of force not well-defined on the z-axis?
(c) Find the

ENGI 4430 Advanced Calculus for Engineering
Faculty of Engineering and Applied Science
Problem Set 1 Solutions
[Parametric & Polar Curve Sketching; Parametric Vector Functions]
1.
For the curve in 2 that is given in parametric form by
x (t ) t 2
=
= 3

Mid Term Test 2014 06 18 Solutions
ENGI 4430
1.
Page 1 of 7
For a particle that travels along the path
[15]
t
r t 2 m
t2
(where t is the time in seconds), find, by any valid method,
the normal component aN t of acceleration and the curvature t .
t

ENGI 4430 Advanced Calculus for Engineering
Faculty of Engineering and Applied Science
Problem Set 2 Solutions
[Multiple Integration; Lines of Force]
1.
Evaluate
x y dA
3 2
D
over the triangular region D that is bounded by the lines y = x, y = x and
x=2.

Mid Term Test Solutions 2011 06 24
ENGI 4430
Page 1 of 7
Find the equations of the family of lines of force for the vector field F 2 y x
i
j
[8]
and find the equations of the line of force that passes through the point (1, 4, 2).
1)
[3]
dr
dx dy dz
The

ENGI 4430 Advanced Calculus for Engineering
Quiz 2 - Solution
2014 June 11 at 12:30
A thin plate D has the shape of a triangle on the x-y plane whose vertices are the points
(0, 0), (1, 0) and (1, 1). The surface density everywhere on D is
12y (kg / m2)

ENGI 4430 Advanced Calculus for Engineering
Faculty of Engineering and Applied Science
Problem Set 3 Solutions
[Numerical Methods]
1.
Use Simpsons rule with four intervals to estimate I =
a = 0 , b = , n = 4 h =
y ( a ) y0
= =
y1
=
y2
=
y3
=
sin=
4
0
sin

ENGI 4430 Advanced Calculus for Engineering
Quiz 1 - Solution
2014 May 28 at 12:30
Answer the following question on this sheet.
This also includes any rough work calculations.
No notes are to be used.
Calculators with programming, text storage, communicat

ENGI 4430 Advanced Calculus for Engineering
Faculty of Engineering and Applied Science
Problem Set 5 Solutions
[Non-Cartesian coordinates]
1.
Convert from Cartesian coordinates to cylindrical polar coordinates the vector
F = ( x y) + ( x + y) + e
i
j
x 2

ENGI 4430 Advanced Calculus for Engineering
Faculty of Engineering and Applied Science
Problem Set 4 Solutions
[Gradient, divergence and curl (Cartesian coordinates)]
1.
Find the divergence and curl of the vector field F = x y 2 + x 2 y + z k .
i
j
x y2

ENGI 4430
1)
Mid Term Test Solutions 2013 06 12
Page 1 of 7
A thin metal plate is in the shape of the unit square, as shown.
The surface density is ( x, y ) = x 2 kg/m2. Find the mass of the plate.
[12]
The elementary strips of area may be taken in either