Table of Contents

**MTH101: Calculus And Analytical Geometry**

In ancient mathematics, analytical geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a linking system. This is contrary to artificial geometry. Analytic geometry is applied to physics and engineering, aerospace, rocketry, space science, and space science. MTH101 Handouts pdf

#### MTH101 Handouts pdf

**Course Category: Mathematics **MTH101 Handouts pdf

**Course Outline**

Absolute value, Coordinates plane and graphs, Distance; Circles, Quadratic Equations, Limits, Continuity, Differentiation, Tangent Lines, Rates of Change, The Derivative, Derivatives of Trigonometric Functions Maximum and Minimum Values of Functions, Newton’s Method, Rolle’s Theorem and the Mean Value Theorem, Integration by Substitution, Sigma Notation, Definite Integral, First and Second Fundamental Theorem of Calculus, Applications of the Definite Integral:,.The area between two curves, Volumes by Cylindrical Shells, Length of Plane Curves, Improper Integral, L”Hopital”s Rule, Improper Integral, Infinite Series, Sequence and Monotone Sequences, Alternating Series; Conditional Convergence, Taylor and Maclaurin Series. MTH101 Handouts pdf

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### MTH101 HANDOUTS

**MTH101: Calculus And Analytical Geometry**

#### What is Calculus ??

Well, it is a study of ongoing rates of exchange rates. It is a study of how different values change in relation to other values. For example, one would like to know how distance changes in relation (from now on we will use the abbreviation w.r.t), how time changes the speed of w.r.t, how the flow of water changes time, etc. You want to know how this happens continuously. We will see what it always means.

#### Natural Numbers

1, 2, 3, 4, 5,…

They are called natural numbers because they are the opposite of human intelligence. think about it: these are the numbers we count. So, our ancestors used these numbers first to calculate, and they came to us naturally! Hence the word NATURAL !!!

Natural numbers are from a subset of a larger class of numbers called integers. I used the word subset. from now on we will consider the set as a collection of things.

**Is 0 a Natural Number Digit?**

We do not have 0 in natural numbers because this number has a fascinating story, ranging from the writing of DEVIL’s concept in ancient Greece to the easy acceptance of Indian philosophy to the promotion of its use of trade and science by Arabs and Europeans. But here, we welcome you with an open heart to the set of integers.

**Sequence**

A sequence in math is a succession of numbers e.g 2,4,6,8, ……. & 1,2,3,4, ……. Consecutive numbers are called sequential terms Each term has a place name, such as the first term, 2nd term, etc. and we can write them as a1, a2, etc. It is easy to write a sequence as a formula 2, 4, 6, 8,… can be written as a formula by {} 1 2 n n + ∞

#### An Intuitive View of Convergence

The implication of a random, cohesive or divisive sequence is not based on the behavior of the “first words” of the sequence, but rather on the behavior of the “end of the tail.” So in order for the sequence {an} to meet the boundary L, it does not matter if the first terms are from L, just so that the consecutive words are closer to L. If so, one can add, remove, or change many words without touching the conjunction, the separation. , or limit (if any).

**0 a Natural Numbers?**

We do not have 0 in natural numbers because this number has a fascinating story, ranging from the writing of DEVIL’s concept in ancient Greece to the easy acceptance of Indian philosophy to the promotion of its use of trade and science by Arabs and Europeans. But here, we welcome you with an open heart to the PRICES SET.