Engineering Maths

Petroleum Engineering

Engineering Mathematics

January 2012

Contenido

INTRODUCTION 3
1. Algebra 4
1.1 Elementary Algebra 4
1.2 Linear Algebra 10
1.2.1 Vectors and vector spaces 10
1.3 Modern Algebra 13

INTRODUCTION

Petroleum Engineering is primarily concerned with the economic extraction of oil, gas, and other natural resources from the earth. Producing oil and gas isaccomplished through the design, drilling and operation of wells and well systems, and the integrated management of the underground reservoirs in which the resources are found.

One of the basic area as an Engineering is mathematics, so Petroleum Engineering needs Math to develop most of concepts, systems and programs.
Course Objective is understand and be able to use the language and methodsof mathematics in the description, analysis and design of engineering systems. Have a composite understanding of the modular elements: complex numbers, vectors, linear algebra, probability and statistics, functions and classical mathematical analysis, introduction to numerical methods, single variable differential and integral calculus, including the solution of ordinary differential equations,multiple variable differential calculus.

Basic mathematics is needed for engineering degree programs. This essay contains the well-recognized elements of classical engineering mathematics which universally underpin the formation of the professional engineer. There are four main sections:

Algebra (vectors, complex numbers, matrices); Calculus (differentiation and integration of functions ofone or more variables); Differential Equations; Probability (basic concepts, events, random variables, empirical discrete and continuous distributions).

1. Algebra

1.1 Elementary Algebra

Branch of mathematics that deals with the general properties of numbers and the relations between them. Algebra is fundamental not only to all further mathematics and statistics but to the naturalsciences, computer science, economics, and business. Along with writing, it is a cornerstone of modern scientific and technological civilization. Earlier civilizations—Babylonian, Greek, Indian, Chinese, and Islamic—all contributed in important ways to the development of elementary algebra. It was left for Renaissance Europe, though, to develop an efficient system for representing all real numbers and asymbolism for representing unknowns, relations between them, and operations.

Elementary algebra is concerned with the following topics:
* Real and complex numbers, constants, and variables—collectively known as algebraic quantities.
* Rules of operation for such quantities.
* Geometric representations of such quantities.
* Formation of expressions involving algebraicquantities.
* Rules for manipulating such expressions.
* Formation of sentences, also called equations, involving algebraic expressions.
* Solution of equations and systems of equations.

1.1.1 Algebraic quantities

The principal distinguishing characteristic of algebra is the use of simple symbols to represent numerical quantities and mathematical operations. Following a system thatoriginated with the 17th-century French thinker René Descartes, letters near the beginning of the alphabet (a, b, c,…) typically represent known, but arbitrary, numbers in a problem, while letters near the end of the alphabet, especially x, y, and z, represent unknown quantities, or variables. The + and − signs indicate addition and subtraction of these quantities, but multiplication is simplyindicated by adjacent letters. Thus, ax represents the product of a by x. This simple expression can be interpreted, for example, as the interest earned in one year by a sum of a dollars invested at an annual rate of x. It can also be interpreted as the distance traveled in a hours by a car moving at x miles per hour. Such flexibility of representation is what gives algebra its great utility.
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