Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
The Fundamental Theorem of
Calculus and Integration
The Fundamental Theorem of Calculus, Part 1
If f is continuous on a, b , then the function
x
F x f t dt
a
has a derivative at every point in a, b , and
dF d x
f t dt f x
dx dx a
First Fundamental Theor
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
The reporting guideline is given below.
Reporting guidelines
Group Report
Page Margins
25mm on all sides (top, bottom, left, right)
Font
12pt. Times Roman or Courier. For figures, however, use a sans serif font such as
Arial.
Spacing
Doublespaced
Alignm
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
DESIGN REPORT FORMAT
The executive summary is used by decision makers (managers) to determine what action needs
to be taken as a result of a project. The typical size of the executive summary is one page. The
executive summary is independent of the body o
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
Sri Lanka Institute of Information Technology
Year 1 Semester I  2014
MA 130 Engineering Mathematics I
Q1.Use the definition of a derivative to examine the differentiability of following functions:
4 3x
2x
1
(iii ) f ( x)
x
(i ) G ( x)
(ii ) f ( x )
1
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
DIFFERENTIALS: LINEAR
AND QUADRATIC
APPROXIMATION
By Kenny Abitbol, Sam Mote, and Evan
Kirkland
Introduction of Linear
Approximation
= +
: point whose tangent line as an approximation of the function
: point whose value is being approximated
If () is
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
Faculty of Engineering
BSc in Engineering UGC +Curtin programme
Program Calendar
Week
1
Functions and limits
Real Number System, Mathematical logic and the principle of mathematical
induction, Supremum and Infimum, Completeness Axiom, Engineering
Function
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
Sri Lanka Institute of Information Technology
Year 1 Semester I  2014
Solutions
(1)
a)
b)
c)
MA 130 Engineering Mathematics I
d)
e)
f)
g)
h)
x lim
ln( x 2 1)
2x
x lim
x x
( x 2 1)(1
1
)
2 x1 2
2x
x lim
1
1
x 2 (1 )(1
)
2
1
2
x
2x
2
x lim
1
1
x(1 )(
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
Sri Lanka Institute of Information Technology
Year 1 Semester I  2014
MA 130 Engineering Mathematics I
(1)
Compute the following limits.
5 x 2 8 x 13
a) x lim 3
x2 5
1 1
x
c ) x lim 2 3 2
x 8
3 x 5
e) x lim 4
x 4
g ) x lim 0 x ln x
i)
(2)
x
b) x lim 0
si
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
Limits and Continuity
Definitions
Evaluation of Limits
Continuity
Limit
We say that the limit of f ( x) as x approaches a is L and write
lim f ( x) L
xa
if the values of f ( x) approach L as x approaches a.
y f ( x)
L
a
Example 01
a) Find
3x if x 2
lim f
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
Differentiability
Arches National Park
Photo by Vickie Kelly, 2003
Greg Kelly, Hanford High School, Richland, Washington
What is the derivative of something?
The derivative of a function f(x) is, mathematically
speaking, the slope of the line tangent to
Australian College of Business and Technology, Colombo
Design Process
ENGINEERIN EC344

Spring 2016
Creative Thinking
Madhawa Herath
B.Sc Eng. (Hons.), C. Eng., MBA (PIM Sri J.), PMP (PMI USA), MIESL, MIEEE, MIET
Source : Lecture notes by Prof. Chandana Perera
Creative Thinking
Imagination is more important than knowledge
Albert Einstein
The ultimate