DIFFERENTIAL CALCULUS EBOOK PDF

" calculus is the word used in the
Roman empire to describe a little pebble that was used in counting. But
today the word is used to describe that branch of mathematics that
extends the basic concept of elementary algebra and geometry into a
new tool used in solving a variety of real-life problems. Calculus is now
one of the important mathematical tools in solving most work of life.
For example you could use it in the prediction of the orbit of earth
satellites, in study of inertial navigation systems and radar systems.

In the modeling of economy, social and psychological behavior calculus

is widely used. Calculus is useful in solving problems in the field of

business, biology, medicine, animal husbandry and political science.

The history of discovery of differential calculus could be traced back to

2nd half of the seventeenth century, when Sir Isaac Newton (1642 -

1727) was able to explain the motion of the planets about the sun as a

consequent of the result known today as the Law of gravitational

attraction. In 1675 a German Mathematician Gottfried Whilhem Leibniz

(1646 - 1716) introduced the famous and basic notation dx andds which

you will use in this course and the second course respectively. Other

mathematicians since then have contributed to the growth and

development of differential calculus among such are Bernoulli of Busel,

Taylor, Lagrange and Maclaurin.

In this course you will learn how to use the limiting process to find the derivation of a function. You will combine the properties of numbers and functions to find the derivatives of special functions. You will extend these laws to finding derivatives of sum, difference, product, quotient and composite of differentiation to find the derivatives of transcendental functions such as sin x, cos x, ex , cu x, sin hx, cos hx etc. You will also be required to apply the skills acquired in techniques of differential to the following (i) Sketching graphs of curves (ii) Solving minimum and maximum problem (iii) finding approximate value of a quantity (iv) finding the equation of tangent and normal lines (v) finding velocity and acceleration of a moving body.

the conts of this course are

 There are ten study units in this course. It is given to you as follows:

Module 1

Unit 1 Basic Properties of Real Number

Unit 2 Functions

Unit 3 Limit

Unit 4 Continuity

Unit 5 Differentiation

Module 2

Unit 1 Rules of Differentiation

Unit 2 Higher Derivatives and Implicit Differentiation

Unit 3 Differentiation of Logarithmic and Exponential Function.

Unit 4 Differentiation of Trigonometric and Hyperbolic Function

Unit 5 Application of Differentiation

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DIFFERENTIAL CALCULUS