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- Herausgeber: Packt Publishing
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This course serves as a comprehensive reference guide for engineers, mathematicians, scientists, and industry professionals, covering essential mathematical formulas and key scientific data. It is divided into two parts: mathematical formulas including algebra, trigonometry, analytic geometry, differential and integral calculus, and vectors; and scientific data covering units, properties of gases, elements, acoustics, materials, thermodynamics, radioactivity, and more.
Understanding these concepts is crucial for professionals, providing a solid foundation for their work. The course explains technical terms, theorems, and applicable laws in detail, ensuring clarity and practical understanding. Each chapter provides valuable insights and data fundamental for scientific and engineering applications.
Starting with algebra and geometry, the course advances through calculus and vectors, then explores scientific data in various fields. By the end, users will have a thorough reference of critical formulas and data, making it indispensable for students and professionals. This structured approach ensures learners gain both theoretical knowledge and practical applications essential for their careers.
Das E-Book können Sie in Legimi-Apps oder einer beliebigen App lesen, die das folgende Format unterstützen:
Seitenzahl: 117
Veröffentlichungsjahr: 2024
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MATHEMATICALFORMULASANDSCIENTIFIC DATA
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MATHEMATICALFORMULASANDSCIENTIFIC DATA
A Quick Reference Guide
C. P. KOTHANDARAMAN, PHD
MERCURY LEARNING AND INFORMATIONDulles, VirginiaBoston, MassachusettsNew Delhi
Reprint & Revision Copyright © 2023 by MERCURY LEARNINGAND INFORMATIONLLC.
All rights reserved. Original Copyright © 2021 by NEW AGE International Publishers.
This publication, portions of it, or any accompanying software may not be reproduced in any way, stored in a retrieval system of any type, or transmitted by any means, media, electronic display or mechanical display, including, but not limited to, photocopy, recording, Internet postings, or scanning, without prior permission in writing from the publisher.
Publisher: David PallaiMERCURY LEARNING AND INFORMATION22841 Quicksilver DriveDulles, VA [email protected](800) 232-0223
C. P. Kothandaraman.Mathematical Formulas and Scientific Data.ISBN: 978-1-68392-865-2
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Library of Congress Control Number: 2022952304
232425321 Printed on acid-free paper in the United States of America.
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CONTENTS
Preface
PART I: MATHEMATICAL FORMULAS
Chapter 1 Algebra
Chapter 2 Elementary Geometry
Chapter 3 Trigonometry
Chapter 4 Analytic Geometry
Chapter 5 Differential Calculus
Chapter 6 Integral Calculus—I
Chapter 7 Integral Calculus—II
Chapter 8 Vectors
PART II: SCIENTIFIC DATA FOR ENGINEERS
Chapter 1 SI Units
Chapter 2 The Fundamental Mechanical Units
Chapter 3 The Fundamental Electrical and Magnetic Units
Chapter 4 Relations Between the Systems of Electrical Units
Chapter 5 Rationalization of MKS Units
Chapter 6 Definitions of Electric and Magnetic Quantities in SI
Chapter 7 Definitions in the CGS Electromagnetic System of Units
Chapter 8 Heat Units and Definitions
Chapter 9 Photometric and Optical Units and Definitions
Chapter 10 Acoustical Units and Definitions
Chapter 11 Properties of the Elements
Chapter 12 Properties of Metallic Solids (at 293 K)
Chapter 13 Properties of Non-Metallic Solids (at 293 K)
Chapter 14 Properties of Liquids (at 293 K)
Chapter 15 Properties of Gases at STP
Chapter 16 Mechanical Data
Chapter 17 Relative Humidities From Wet-and Dry-Bulb Thermometers (Exposed in Standard Screen)
Chapter 18 Acoustic Data
Chapter 19 Astronomical Data
Chapter 20 Terrestrial and Geodetic Data
Chapter 21 Radioactivity
Chapter 22 Properties of Inorganic Compounds
Chapter 23 Properties of Organic Compounds (at 293 K)
Chapter 24 The Fundamental Constants
PREFACE
This will serve as an excellent reference for in-service professionals in the areas of mathematics, science, and engineering. It will also help students as a quick review for examinations.
Formulas from algebra to vectors are discussed in Part I of the book. Technical terms, theorems, and applicable laws are defined, and their uses are explained. Answers to standard equations in these areas are provided. Equations from straight lines to conics are derived and applications are provided. In the sections on differential and integral calculus, solutions are included for a large number of situations.
Part II is unique in providing numerical data in astronomical, acoustical, optical, and geophysical areas. Properties such as density, specific heat, thermal conductivity, and expansion coefficients are tabulated for a large number of metallic, nonmetallic, organic, and inorganic materials. This information and data will be particularly useful for practicing engineers.
C.P. Kothandaraman
PART I
MATHEMATICAL FORMULAS
CHAPTER 1
ALGEBRA
1 FUNDAMENTAL LAWS
2 LAWS OF EXPONENTS
3 OPERATIONS WITH ZERO
4 COMPLEX NUMBERS
A number of the form a + ib, where a and b are real.
5 LAWS OF LOGARITHMS
6 BINOMIAL THEOREM
7 EXPANSIONS AND FACTORS
8 RATIO AND PROPORTION
9 CONSTANT FACTOR OF PROPORTIONALITY (OR VARIATION), k
10 ARITHMETIC PROGRESSION
11 GEOMETRIC PROGRESSION
12 HARMONIC PROGRESSION
A sequence of numbers whose reciprocals form an arithmetic progression is called a harmonic progression. Thus
The harmonic mean of a and b is 2ab/(a + b).
13 PERMUTATIONS
14 COMBINATIONS
Each of the groups or relations which can be made by taking part or all of a set of things, without regard to the arrangement of the things in a group, is called a combination. The number of combinations of n different things taken r at a time is
15 PROBABILITY
If an event may occur in p ways and may fail in q ways, all ways being equally likely, the probability of its occurrence is p/(p + q), and that of its failure to occur is q/(p + q).
16 REMAINDER THEOREM
17 DETERMINANTS
Interest, Annuities, Sinking Funds.
In this section, n is the number of years, and r is the rate of interest expressed as a decimal.
18 AMOUNT
19 NOMINAL AND EFFECTIVE RATES
The rate of interest quoted in describing a given variety of compound interest is called the nominal rate. The rate per year at which interest is earned during each year is called the effective rate. The effective rate i corresponding to the nominal rate r, compounded q times a year is:
20 PRESENT OR DISCOUNTED VALUE OF A FUTURE AMOUNT
The present quantity P which in n years will accumulate to the amount A at the rate of interest r, is:
At simple interest:
At interest compounded annually:
At interest compounded q times a year:
P is called the present value of A due in n years at rate r.
21 TRUE DISCOUNT
The true discount is:
DA − P.
22 ANNUITY
A fixed sum of money paid at regular intervals is called an annuity.
23 AMOUNT OF AN ANNUITY
If an annuity P is deposited at the end of each successive year (beginning one year hence), and the interest at rate r, compounded annually, is paid on the accumulated deposit at the end of each year, the total amount N accumulated at the end of n years is
N is called the amount of an annuity P.
24 PRESENT VALUE OF AN ANNUITY
The total present amount P which will supply an annuity N at the end of each year for n years, beginning one year hence (assuming that in successive years the amount not yet paid out earns interest at rate r, compounded annually), is:
P is called the present value of an annuity.
25 AMOUNT OF A SINKING FUND
If a fixed investment N is made at the end of each successive year (beginning at the end of the first year), and interest paid at rate r, compounded annually, is paid on the accumulated amount of the investment at the end of each year, the total amount S accumulated at the end of n years is:
S is called the amount of the sinking fund.
26 FIXED INVESTMENT, OR ANNUAL INSTALLMENT
The amount N that must be placed at the end of each year (beginning one year hence), with compound interest paid at rate r on the accumulated deposit, in order to accumulate a sinking fund S in n years is:
N is called a fixed investment or annual installment.
Algebraic Equations
27 QUADRATIC EQUATIONS
28 CUBIC EQUATIONS
