Systems of Units. Some Important Conversion Factors
The most important systems of units are shown in the table below. The mks system is also known as the International System of Units (abbreviated SI ), and the abbreviations sec (instead of s), gm (instead of g), and nt (instead of N) are also used.
System of units
Length
Mass
Time
Force
cgs system
centimeter (cm)
gram (g)
second (s)
dyne
mks system
meter (m)
kilogram (kg)
second (s)
newton (nt)
Engineering system
foot (ft)
slug
second (s)
pound (lb)
1 inch (in.)
2.540000 cm
1 foot (ft)
1 yard (yd)
3 ft
1 statute mile (mi)
5280 ft
1 mi2
2.5899881 km2
1 nautical mile
1 acre
91.440000 cm
6080 ft
4840 yd2
4046.8564 m2
1/128 U.S. gallon
1 U.S. gallon
4 quarts (liq)
231/128 in.3
8 pints (liq)
1 British Imperial and Canadian gallon
1.609344 km
640 acres
29.573730 cm3
3785.4118 cm3
128 fl oz
4546.087 cm3
1.200949 U.S. gallons
14.59390 kg
1 pound (lb)
4.448444 nt
1 British thermal unit (Btu)
1 calorie (cal)
°C • 1.8
1054.35 joules
1 joule
3414.4 Btu
105 dynes
107 ergs
3.6 • 106 joules
2542.48 Btu/h
1 horsepower (hp)
1 kilowatt (kW)
1 newton (nt)
4.1840 joules
178.298 cal/sec
1 kilowatthour (kWh)
°F
30.480000 cm
1.853184 km
1 fluid ounce
1 slug
12 in.
1000 watts
32
3414.43 Btu/h
0.74570 kW
238.662 cal/s
1°
60
3600
0.017453293 radian
For further details see, for example, D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics. 9th ed., Hoboken, N. J: Wiley, 2011. See also AN American National Standard, ASTM/IEEE Standard Metric Practice, Institute of Electrical and Electronics Engineers, Inc. (IEEE), 445 Hoes Lane, Piscataway, N. J. 08854, website at www.ieee.org.
...BAHRIA FOUNDATION HIGH SCHOOL SARGODHA
Paper: Mathematics 2nd PHASE PAPER.201 Class: 10th
Total Marks:15 Time Allowed: 2 :10 min
NOTE: You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; mark the correct options with tick. Cutting or overwriting or use of led pencil will in result in zero mark in that question.
Q # 1: MULTIPLE CHOICE QUESTIONS 15
1) Two liner factors of x215x+56 are
a) (x7)(x8) b) (x7)(x+8) c) (x+7)(x+8) d) (x+7)(x8)
2) Two square roots of the unity
a) 1,1 b)1,ω c) 1,ω d) ω, ω2
3) The third proportion of the x2 and y2 is
a) y2/x2 b) x2/y2 c)x2y2 d)y2x2
4) a fraction in which the degree of numerator is less than the degree of denominator is called
a) equation b) improper c) proper d) identity
5) A histogram is a set of adjustment
a) Square b) rectangular c)circle d)a,b both
6) The different ways of describing a set
a) 1 b) 2 c) 3 d) 4
7) 3π/4 radians=
a) 1150 b)1350 c)1500 d)300
8) +
a) 2sec2 b) 2cos2 c)sec2 d) cos2
9) The observation that divide a data into four equal parts are called
a) Median b) mode c) mean d) a, b both
10) If A and B are disjoint then AUB is equal to
a) A b) B c) null d) BUA
11) If =the componendo property is
a) = b) = c) d) none of these
12) If α , β are the roots of x2x1=0 the product of 2αβ is
a) 2 b)2 c) ±2 d) 4
13) The solution of equation of...
...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 ...
...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...
...ADVANCEDMATHEMATICS
MONASH UNIVERSITY FOUNDATION YEAR
1. INTRODUCTION
A student taking this course must also be concurrently enrolled in (or previously studied) MUFY Mathematics Part A as many of the topics in MUFY AdvancedMathematics require an understanding of the concepts in MUFY Mathematics Part A.
2. COURSE OBJECTIVES
AdvancedMathematics is designed to prepare students who wish to take tertiary courses with a high mathematical content, or which use a considerable amount of mathematical reasoning. In Part A, students study matrices, complex numbers, vectors, trigonometric functions and differentiation techniques. In Part B the topics covered are integration techniques and applications of definite integrals, differential equations and kinematics.
3. COURSE CONTENT
Semester A:
1. Matrices & Linear Algebra
The concept of a matrix; matrix algebra, including addition, subtraction, and multiplication of matrices, and multiplication of a matrix by a scalar. The conditions necessary for the sum or product of matrices to exist.
The unit matrix, I; the meaning of the inverse, A1, of a matrix A; the fact that AA1 = A1A = I.
Determinants; the determinant of a 2 x 2 matrix; the inverse of a 2 x 2 matrix.
The use of matrices to solve systems of two...
...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,...
...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...
...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...