MTH632 Slides Complete by Mahar Afaq Safdar Muhammadi

MTH632

Topic: ABC

Good school is that which most successfully achieves the targets set by the stakeholders by showing high grades and good results in exams.

Heading · 1. Instructional · Leadership · 2. Clear and · Focused Mission · 3. Safe and Orderly · Environment · 4. Climate of High · Expectations

A school is effective not because of the specific nature of what is taught (though it is important) but through the manner in which a positive, supportive, richly and frequently interactive atmosphere is created. Gammage, 1985.

• What is a good

school?

• And Effective

school?

What is the · difference · between ‘effective · school’ and ‘good

school’?

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And Effective school?

What is the difference between ‘effective school’ and ‘good school’?

END

Complex · Analysis & · Differential · Geometry · Topic No. 01 · Do we need more

Numbers?

We need one more number

𝒊= −𝟏

“Cardano was the first to introduce complex

numbers 𝒂+ −𝟏𝒃 into

algebra, but had misgivings about it”

“To divide 10 in two parts, the product of which is 40”. 𝟓+ −𝟓, 𝟓− −𝟓

Rafael Bombelli authored · l’Algebra (1572, and 1579) · a set of three books · “At first, the thing seemed · to me to be based more on · sophism than on truth, but · I searched until I found the · proof” · L. Euler (1707-1783) introduced the notation

𝒊= −𝟏 END

What are complex

numbers?

Topic No. 02 · A complex number 𝒛 can · be defined​ as an ordered pair · numbers · can interpreted as · points in the · complex plane · • When real numbers 𝒙 are · displayed · as · points

(𝒙, 𝟎) on the real axis the

set of complex numbers

includes the real numbers

as a subset.

• Complex numbers of the

form (𝟎, 𝒚) correspond to

points on the 𝒚-axis and · are · pure · imaginary · numbers when 𝒚≠𝟎. The · 𝒚-axis is then referred to

as the imaginary axis.

For complex number · are known as the real and · imaginary parts of 𝒛 · respectively; and we write · Equality of complex · numbers · Two complex Numbers 𝒛𝟏 · and 𝒛𝟐 are equal whenever · they have the same real · parts · and · the · same

imaginary parts.

correspond to the same

point in the complex, or z, plane.

end

Computations in · Topic No. 03 · Addition of two complex · number · For · The addition is defined as