Mathematical Backgrounds (NAN)
Higher Institute of Transport and Logistics (HITL)
Semester: First Semester
Level: 300
Year: 2018
THE UNIVERSITY OF BAMENDA
HIGHER INSTITUTE OF TRANSPORT AND LOGISTICS
TUTORIALS
COURSE: MATHEMATIC BACKGROUNDS
PART ONE: VECTORS, DIFFERENTIAL OPERATOR AND APPLICATIONS
Exercise 1: In an orthonormal basis (
) the vector
1) Calculate the magnitude of
2) Find the magnitude of the projection of
on the XOZ plan
3) Let
another vector so that
= -
a) Calculate
.
b) Calculate
X
c) Find two vectors
,
, perpendicular to
Exercise 2: Let us consider three vectors
,
, and
,
a) Demonstrate that
.(
) =
.(
) =
.(
)
b) Demonstrate that
(
) = (
)
.
)
c) Demonstrate that if
+
+
=
, then
=
=
Exercise 3: Let us consider two scalar functions f(x, y, z) and g(x, y, z) defined by
f(x, y, z)=
and g(x, y, z) =
a) Calculate the gradients of f(x, y, z) and g(x, y, z)
b) Demonstrate the !
"
# = # !$
"
!$
"
#
Exercise 4: Let
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