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Upon completion of this course, the student should

be able to:  Develop critical thinking and problem solvingskills, in the context of algebra and calculus.Describe the algebraic and graphical propertiesof elementary functions (linear, polynomial,

exponential, logarithmic, trigonometric and theirinverses) and their applications to engineering,economics and sciences.Explain the significance of the derivative and

integration and be able to apply techniques for thederivative and integration to situations ineconomics, engineering and sciences. Demonstrate the use of proper mathematicalnotation 

8/3/2019 Lect 1 Vector Calculus-1

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 Quiz : 15 Marks(3) 

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 Assignment: 10 Marks(2) 

 Mid Term Exam: 25 Marks(1) 

 Final Exam: 50 Marks(1) 

8/3/2019 Lect 1 Vector Calculus-1

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A scalar quantity is a quantity that hasmagnitude only and has no direction in space

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Examples of Scalar Quantities: Length, i.e. 5m

Area

Volume

Time

Mass

Speed

Temperature

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A vector quantity is a quantity that has bothmagnitude and a direction in space

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Examples of Vector Quantities:

Displacement

Velocity

Acceleration

Force

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A vector is represented on paperby an arrow1. the length represents magnitude

2. the arrow faces the direction of motion

3. a vector can be “picked up” and moved on 

the paper as long as the length and

directionits pointing does not change

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If A is the point (a1,a2), as shown in figuregiven below, then is called positionvector for (a1,a2), or for point A.

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 AO

A(a1,a2)

Ox

y

a

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The magnitude of the vector a (a1,a2) isactually the length of its position vector

is given by:

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 AO

2

2

2

121,( aaaaa

Exercise:

Sketch the position vectors for a=(-3,5), b=(0,-find magnitude of each vector.

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To accurately draw a given vector, startat the second direction and move thegiven degrees to the first direction.

N

S

EW

30° N of E

Start on the Eastorigin and turn30° to the North

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5.0 m/s East(suggested scale: 1 cm = 1 m/s)

300 Newtons 60° South of East

(suggested scale: 1 cm = 100 N)

0.40 m 25° East of North(suggested scale: 5 cm = 0.1 m)

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4. Measure the magnitude of Resultant Vectorwith a ruler. Use your scale and convert thislength to its actual amount, and record withunits.

5. Measure the direction of Resultant Vectorwith a protractor and add this value alongwith the direction after the magnitude.

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5 Km

3 Km

Scale: 1 Km = 1 cm

Resultant Vector (red) = ?,

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Use a graphical representation to solve the

following: A hiker walks 1 km west, then 2

km south, then 3 km west. What is the sum of his distance traveled using a graphical

representation?

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Answer = ?

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Use a graphical representation to solve the

following: Another hiker walks 2 km south

and 4 km west. What is the sum of herdistance traveled using a graphical

representation? How does it compare to hiker

#1?

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Answer = ?

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Vector diagrams areshown using anarrow

The length of the

arrow represents itsmagnitude

The direction of thearrow shows its

direction

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Vectors in 3-D Space

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