Chemical Engineering

Topics: Derivative, Calculus, Product rule Pages: 50 (3654 words) Published: September 22, 2014
Year 1 / Semester 1

Notes:School of Engineering

August 2014 Intake

Dr. Abdulkareem Sh. Mahdi

Engineering Mathematics 1 (MTH60103)

Differentiation – part i
1

September 6, 2014

2

Learning outcomes

At the end of this lecture, you should be able to:

(1) Evaluate the limits of functions;
(2) Differentiate using the FIRST PRINCIPLES;
(3) Differentiate using the standard formulae
(4) Differentiate using the rules of

Dr. Abdulkareem Sh. Mahdi

September 6, 2014

i- Constant, ii- Power, iii- Constant multiple,
iv- Sum (Difference) v- Product Rule, vi- Quotient Rule.
vii- Chain Rule
https://www.khanacademy.org/math/differential-calculus
Notes:-

School of Engineering

Year 1 / Semester 1

Engineering Mathematics 1 (MTH60103)

August 2014 Intake

Differentiation – part i

Year 1 / Semester 1
August 2014 Intake

Rule 6

Notes:Dr. Abdulkareem Sh. Mahdi

Lecture Roadmap

School of Engineering

Engineering Mathematics 1 (MTH60103)

Differentiation – part i
3

September 6, 2014

4

Learning outcomes
At the end of this lecture, you should be able to:

(1) Evaluate the limits of functions;
(2) Differentiate using the FIRST PRINCIPLES;
(3) Differentiate using the standard formulae
(4) Differentiate using the rules of
i- Constant,
ii- Power,
iii- Constant multiple,
iv- Sum (Difference).
Notes:-

Dr. Abdulkareem Sh. Mahdi

September 6, 2014

School of Engineering

Year 1 / Semester 1

Engineering Mathematics 1 (MTH60103)

August 2014 Intake

Differentiation – part i

5

What is the function?

1)Function: a value of one variable
quantity, which we may call y,
depends on the value of another
variable quantity, which we may
call x. We say that

“y is a function of x”
Notes:-

Dr. Abdulkareem Sh. Mahdi

September 6, 2014

School of Engineering

Year 1 / Semester 1

Engineering Mathematics 1 (MTH60103)

August 2014 Intake

Differentiation – part i

September 6, 2014

What is the function?

August 2014 Intake

Dependent
variable

y = f (x)

Independent
variable

A function of a variable x is a rule that describes
how a value of the variable x is manipulated to
2) P = f (h)
generate a value of the variable y. The rule is
3) A= f (r)
often expressed in the form of an equation
4) P = f (V, I). y = f(x) with the proviso that “for any single input x there is just one output y” – the function
is said to be single valued.

1) T = f (H)

Notes:-

School of Engineering

Engineering Mathematics 1 (MTH60103)
Year 1 / Semester 1

6

Dr. Abdulkareem Sh. Mahdi

Differentiation – part i

7

What is the function?
2) Domain: All the input numbers x that a
function can process are collectively called
the function’s DOMAIN.

Dr. Abdulkareem Sh. Mahdi

September 6, 2014

Examples: What is the domain of the following functions?

1) y = x,

2) y = ln x,

3) R = 1/x

4) C = e-t

5) y = √x,

6) z = sin (x)

Notes:-

School of Engineering

Year 1 / Semester 1

Engineering Mathematics 1 (MTH60103)

August 2014 Intake

Differentiation – part i

3) Range: The complete collection of numbers y
that correspond to the numbers in the
domain is called the RANGE.

Dr. Abdulkareem Sh. Mahdi

September 6, 2014

What is the function?

Examples: What is the range of the following functions?
1- y = x,

2- y = ln x,

3- R = 1/x

4- C = e-t

5- y = √x,

6- z = sin (x)

Khan Academy
Year 1 / Semester 1

8

http://www.khanacademy.org/math/algebra/algebrafunctions/v/domain-and-range-of-a-function Notes:-

School of Engineering

Engineering Mathematics 1 (MTH60103)

August 2014 Intake

Differentiation – part i

9

What is the function?
If you are unclear what a function is, please
look at Stroud Programme F.12
I also strongly recommend you to use Microsoft
Excel Spreadsheet or any other Math Software
as mathematical tools to represent the...
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