1. The use of knowledge and understanding of mathematics in engineering context.
Mathematics is science of pattern that engineers seek out whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Knowledge and use of basic mathematics have always been an inherent and integral part of engineering. In our previous semester, basic mathematics was applied in almost every module. From stress analysis of simple machine components to numerical description of various shapes of new gadgets( using CAD packages), from using FBDs(free body diagram) for solving out the problem in engineering mechanics to using Bernoulli equation or mass flow rate equation in fluid mechanics. From calculation of heat and mass flow in various systems to calculating of engine power or shaft power in engineering systems. From reliability in electrical power circuits in household or any other appliances to traffic in networks (tar roads and optical fibres ) , mathematics crosses boundaries in a way no other technical subject can. The examples mentioned above are subjects of many books. Yet, they collectively fail to convey that engineering applications of mathematics have. First semester was just revision and application of the topics covered in previous years of education and also to form a perfect base for more analytical and application based engineering principles. Mathematics and engineering go hand to hand. Without application of mathematics, engineering problem cannot be solved.
2. The application of engineering analysis to understand the behavior of physical systems.
Everything working in this universe has some or the other kind of engineering principle involved in it. Engineering analysis, when applied in the context of engineering systems, involves the application of scientific analytic principals and processes to reveal the properties and the state of the system. To understand the behavior of any physical systems, application of various...
...article, we present the concept of mathematical application projects as a means to enhance the capabilities of engineering students to use mathematics for solving problems in larger projects as well as to communicate and present mathematical content. As opposed to many case studies, we concentrate on stating criteria and project classes from which instructors can build instances (i.e. specific projects). The main goal of this paper is to facilitate the definition of new „good“ projects in a certain curricular setting. 1. INTRODUCTION Learning and training mathematical concepts and algorithms in engineering departments of German Universities of Applied Sciences ("Fachhochschulen") usually consists of a sequence of "small steps" with "smallsized" assignments. This is necessary in order to gain familiarity without overloading students with too much complexity. But in the end, an engineer is required to use mathematics (models, software) for solving problems in larger projects as well as to communicate and present mathematical content. Without also learning this further step in mathematics education for engineers, mathematical knowledge often remains "inert" (Mandl), i.e. small chunks of knowledge are existing, but the capability of how to apply them for solving a problem is missing. As a remedy, we introduced mathematical application projects in the third semester...
...10 MAT 21
Dr. V. Lokesha
2012
EngineeringMathematics – II
(10 MAT21)
LECTURE NOTES
(FOR II SEMESTER B E OF VTU)
VTUEDUSAT Programme16
Dr. V. Lokesha
Professor of Mathematics
DEPARTMENT OF MATHEMATICS
ACHARYA INSTITUTE OF TECNOLOGY
Soldevanahalli, Bangalore – 90
Partial Differential Equation
1
10 MAT 21
Dr. V. Lokesha
2012
ENGNEERING MATHEMATICS – II
Content
CHAPTER
UNIT IV
PARTIAL DIFFERENTIAL EQUATIONS
Partial Differential Equation
2
10 MAT 21
Dr. V. Lokesha
2012
Unit‐IV
PARTIAL DIFFERENTIAL EQUATIONS
Overview:
In this unit we study how to form a P.D.E and various methods of obtaining solutions of P.D.E. This unit
consists of 6 sections. In section 1, we learn how to form the P.D.E. by eliminating arbitrary constants
and in section 2 we learn the formation of P.D.E by eliminating arbitrary functions. In section 3, the
solution of non homogeneous P.D.E by the method of direct integration is discussed. In section 4, the
solution of homogeneous equations is discussed. In section 5 we learn the method of separation of
variables to solve homogeneous equations. In section 6 we discuss the Lagrange’s linear equation and
the solution by the method of grouping and multipliers, at ...
...Chapter 2: THE NATURE OF MATHEMATICSMathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. Because mathematics plays such a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. To achieve this, students need to perceive mathematics as part of the scientific endeavor, comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills.
This chapter focuses on mathematics as part of the scientific endeavor and then on mathematics as a process, or way of thinking. Recommendations related to mathematical ideas are presented in Chapter 9, The Mathematical World, and those on mathematical skills are included in Chapter 12, Habits of Mind.
PATTERNS AND RELATIONSHIPS
Mathematics is the science of patterns and relationships. As a theoretical discipline, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have...
...ASSIGNMENT 2: ROBOTS
In this report I will write in detail about the uses and operations of industrial robots, flexible manufacturing systems, productivity loading and unloading systems and coordinated work schedules. I will show the benefits and disadvantages of the above and evaluate the consequences of such practices.
First of all robots have many applications such as: assembling products, handle dangerous material, spray finishes on, inspect parts/produce/livestock and cut/polish products. Robots are also used to do tasks that are too dull, dirty, or dangerous for humans. Industrial robots used in manufacturing lines used to be the most common form of robots, but that has recently been replaced by consumer robots cleaning floors and mowing lawns. The advantages of Industrial Robots are:
• Quality  Robots have the capacity to drastically improve product quality when compared to humans. Applications are performed with precision and mass repeatability every time. This level of consistency can be hard to achieve any other way.
• Production  With robots speeds increase, which directly increases the rate of production. Because robots have the ability to work at a constant speed without pausing for breaks, sleep, holidays, they have the potential to produce more than a human worker.
• Safety  Robots increase workplace safety as they’re less likely to cause accidents. Workers are moved to other roles, so they no longer have to perform dangerous applications in...
...1 EngineeringMathematics 1 (AQB10102)
CHAPTER 1: NUMBERS AND ARITHMETIC
1.1 TYPE OF NUMBERS
NEGATIVE INTEGER

POSITIVE
AND
REAL NUMBERS (R)
•
•
Numbers that can be expressed as
decimals
Real Number System:
•
Consist of positive and
negative natural numbers
including 0
Example:
…, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, …
•
All numbers including natural
numbers, whole numbers,
integers, rational numbers
and irrational numbers are
real numbers
Example:
4 = 4.0000...
−
5
= −0.8333...
6
1
= 0.5000...
2
• Classification of Real Numbers
Numbers
Example
Natural Numbers (N)
1, 2, 3, 4, 5, …
– counting numbers
Whole Numbers (W)
0, 1, 2, 3, 4, 5, …
– a set of zero together with
the natural numbers
Rational Numbers (Q)
– any number that can be
written in the form of
a
b
8 0 5
, , ,7
4 9 3
where a and b are integers
with b ≠ 0
a) Terminates: end in an
infinite string ‘0’
3
= −0.75
4
65
= 65
1
−
b) Repeats: end with a block
of digits that repeat over
and over
Irrational Numbers (I)
 the decimal represented of
irrational numbers do not
repeat in cycles (pattern)
10
= 3.3333...
3
5
= 0.8333...
6
0.1010010000100001...
3 = 1.7320508075...
log10 5 = 0.698970004336...
3 = 1.37050...
•
Real Numbers can be
represented geometrically as
points on a number line called
Real Line
Example
Prime Numbers
 any natural number,
greater than 1,...
...Context doesn’t always have to be truthful. It depends on what position the context is observed in. If context is supplemented with society, truth matters. If it is a personal observation, in most cases the truth will get you out of trouble. One area of knowledge that can be controversial and doesn’t have to be truthful is art. One area that involves consideration and can be involved controversially is science. This is one of the most factual that can be errored very easily.
Within art, there are many contentious topics that make a stair step to society. For example, the Shrewd of Turin is viewed in many ways based on the Christian beliefs. Even though this important part of history is talked about and is encased by the Catholic Church, there have been many scientists that have argued that it’s either made by a print or carbon dating to provide a sufficient solution to whether it’s true or a fallacy. The Da Vinci code is also significance towards whether it is a woman and all the clues hidden behind them or perhaps just Leonardo himself proposed as a woman. In the sense of subjective art this cannot be objective and cannot be gained by any knowledge. When context is thrown into this category it will not have anything to do with the artistic views because the drawings are made upon other’s experiences and perceptions. I may perceive that the shrewd of Turin is just an old man but others...
...Chemical Engineering
In the future I would like to become a chemical engineer. I really enjoy chemistry and hands on work “Chemical engineering is the application of chemistry to large scale industrial systems.” (Chemical engineering). I enjoy helping build different things like skateboards, ramps and, fixing parts on different things. When I took the sixteen personality quiz it said I was a virtuoso. The virtuoso likes hands on work and exploring ideas which I think fits my personality perfectly. The quiz also recommended jobs related to engineering. I really want to be a chemical engineer because I feel like I would really enjoy it and be good at it too.
There are a few requirements to become a chemical engineer. It requires at least a bachelor’s degree. It would be good to major in math and science classes because that’s what chemical engineering involves. There is no training course for chemical engineering, you get trained on the job. “To become a chemical engineer you would normally need an accredited BEng degree in chemical process or biochemical engineering.”(Chemical engineer). The need for chemical engineers is growing but at a slow rate. Some related jobs to chemical engineering are a chemist or any job relating to engineering. Becoming a chemical engineer would not be easy but I am willing to put in the time and effort to become...
...Mechanical engineering is a discipline of engineering that applies the principles of engineering, physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the design, production, and operation of machines and tools.[1] It is one of the oldest and broadest engineering disciplines.
The engineering field requires an understanding of core concepts including mechanics, kinematics, thermodynamics, materials science, structural analysis, and electricity. Mechanical engineers use these core principles along with tools like computeraided engineering, and product lifecycle management to design and analyze manufacturing plants, industrial equipment and machinery, heating and cooling systems, transport systems, aircraft, watercraft, robotics, medical devices, weapons, and others.
Mechanical engineering emerged as a field during the industrial revolution in Europe in the 18th century; however, its development can be traced back several thousand years around the world. Mechanical engineering science emerged in the 19th century as a result of developments in the field of physics. The field has continually evolved to incorporate advancements in technology, and mechanical engineers today are pursuing...