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TABLE OF CONTENTS

Cover

Title Page

Copyright

Dedication

Preface

PART I UNITS

INTERNATIONAL SYSTEM OF UNITS

1.SI Base Units

2.SI Derived Units

3.SI Derived Units with Special Names and Symbols

4.SI Derived Units Whose Names and Symbols Include SI Derived Units with Special Names and Symbols

5.Units Outside the SI that Are Accepted for Use with the SI

6.SI Prefixes

METRIC UNITS OF MEASUREMENT

7.Units of Length

8.Units of Area

9.Units of Liquid Value

10.Units of Volume

11.Units of Mass

U.S. UNITS OF MEASUREMENT

12.Units of Length

13.Units of Area

14.Units of Liquid Volume

15.Units of Volume

16.Apothecaries’ Units of Liquid Volume

17.Units of Dry Volume

18.Avoirdupois Units of Mass

19.Apothecaries’ Units of Mass

20.Troy Units of Mass

TABLES OF EQUIVALENTS

21.Units of Length

22.Units of Area

23.Units of Volume

24.Units of Mass

PART II MATHEMATICS

ALGEBRA

1.Sets of Real Numbers

2.Properties of Real Numbers

3.Properties of Equality

4.Properties of Fractions

5.Division Properties of Zero

6.Real Number Line

7.Interval

8.Absolute Value

9.Distance between Two Points on the Number Line

10.Definition of Positive Integer Exponents

11.Definition of b0

12.Definition of b−n

13.Properties of Exponents

14.Definition of

15.Properties of Radicals

16.General Form of a Polynomial

17.Factoring Polynomials

18.Order of Operations

19.Adding and Subtracting Polynomials

20.Multiplying Polynomials

21.Dividing Polynomials

22.Rational Expressions

23.Complex Fractions

24.Definition of a Complex Number

25.Definition of a Linear Equation

26.Addition and Multiplication Properties of Equality

27.Systems of Linear Equations

28.Determinants

29.Quadratic Equations

30.Properties of Inequalities

31.Arithmetic Sequence

32.Arithmetic Series

33.Geometric Sequences

34.Geometric Series

35.Binomial Theorem

36.The Cartesian Coordinate System

37.Linear Functions

38.Forms of Linear Equations

39.Quadratic Functions

40.Basic Operation of Functions

41.Exponential Functions

42.Natural Exponential Function

43.Logarithmic Functions

GEOMETRY

1.Definition of an Angle

2.Unit Measurement of Angles

3.Acute Angles

4.Obtuse Angles

5.Right Angles

6.Complementary Angles

7.Supplementary Angles

8.Vertical Angles

9.Alternate Interior Angles

10.Alternate Exterior Angles

11.Corresponding Angles

12.Angle Bisector

13.Perpendicular Angles

14.Thales’ Theorem

15.Oblique Triangle

16.Geocenter of a Triangle

17.Orthocenter

18.Similarity of Triangles

19.The Law of Cosines

20.The Law of Sines

21.Right Triangle

22.Ratio of the Sides of a Right Triangle

23.Pythagorean Theorem

24.Equilateral Triangles

25.Isosceles Triangle

26.Square

27.Rectangle

28.Parallelogram

29.Rhombus

30.Trapezoid (American definition)

31.Kite

32.Regular Polygons

33.Circle

34.Sector of a Circle

35.Segment of a Circle

36.Annulus (Circular Ring)

37.Ellipse

38.Cube

39.Cuboid

40.Right Prism

41.Pyramid

42.Frustum of Pyramid

43.Cone

44.Frustum of Cone

45.Cylinder

46.Hollow Cylinder

47.Sliced Cylinder

48.Sphere

49.Spherical Cap

50.Sector of a Sphere

51.Zone of a Sphere

52.Torus

53.Ellipsoid

54.Barrel

TRIGONOMETRY

1.Circular and Angular Measures

2.Trigonometric Circle

3.Basic Formulas

4.Trigonometric Ratios for Right Angled Triangles

5.Sum and Difference of Functions of Angles

6.Sum and Difference of Angles

7.Double Angle Formulas

8.Half Angle Formulas

9.Functions of Important Angles

10.Solving Trigonometric Equations

11.Verifying Trigonometric Identities

12.Graphs of the Sine and Cosine Functions

13.Graphs of the Tangent and Cotangent Functions

ANALYTICAL GEOMETRY

1.Distance between Two Points

2.Point of Division

3.Inclination and Slope of a Line

4.Parallel and Perpendicular Lines

5.Angle between Two Intersection Lines

6.Triangle

7.The Equation for a Straight Line through a Point

8.Slope-Intercept Form

9.Equation for a Straight Line through Two Points

10.Intercept Form Equation of a Straight Line

11.General Form of an Equation of a Straight Line

12.Normal Equation of a Straight Line

13.Distance from a Line to a Point

14.Circles

15.Ellipses

16.Parabolas

17.Hyperbolas

18.Polar Coordinates

19.Cartesian Coordinates

20.Distance between Two Points

21.Angle between Two Lines

22.Every Plane

23.Line Perpendicular to Plane

24.Parallel and Perpendicular Planes

25.Distance of a Point from a Plane

26.Normal Form

27.Intercept Form

28.Angle Between Two Planes

29.The Straight Line in Space

30.Parametric Form Equations of a Line

31.Symmetric Form Equations of a Line

32.Two Points Form Equations of a Line

33.Relative Directions of a Line and Plane

34.The Sphere

35.The Ellipsoid

36.Hyperboloid

37.Elliptic Paraboloid

38.Hyperbolic Paraboloid

39.Cylindrical Surface

MATHEMATICS OF FINANCE

1.Simple Interest

2.Compound Interest

3.Annuities

4.Amortization of Loans

5.Sinking Fund Payment

CALCULUS

1.Limits

2.Rule for Limits

3.Slope of Tangent Line

4.Definition of the Derivative

5.Basic Derivatives

6.Increasing and Decreasing Function y = f(x)

7.Maximum and Minimum Function y = f(x)

8.Solving Applied Problems

9.Integration

10.Basic Integration Rules

11.Integration by Substitution

12.Basic Integrals

13.Arc Length

14.Finding an Area and a Volume

15.Finding the Area between Two Curves

STATISTICS

1.Definition of Set and Notation

2.Terms and Symbols

3.Venn Diagrams

4.Operations on Sets

5.De Morgan’s Laws

6.Counting the Elements in a Set

7.Permutations

8.Combinations

9.Probability Terminology

10.Basic Probability Principles

11.Random Variable

12.Mean Value x or Expected Value µ

13.Variance

14.Standard Deviation

15.Normal Distribution

16.Binomial Distribution

17.Poisson Distribution

18.Exponential Distribution

19.General Reliability Definitions

20.Exponential Distribution Used as Reliability Function

PART III PHYSICS

MECHANICS

1.Scalars and Vectors

2.Distance and Displacement

3.Acceleration

4.Speed and Velocity

5.Frequency

6.Period

7.Angular Displacement

8.Angular Velocity

9.Angular Acceleration

10.Rotational Speed

11.Uniform Linear Motion

12.Uniform Accelerated Linear Motion

13.Rotational Motion

14.Uniform Rotation about a Fixed Axis

15.Uniform Accelerated Rotation about a Fixed Axis

16.Simple Harmonic Motion

17.Pendulum

18.Free Fall

19.Vertical Projection

20.Angled Projection

21.Horizontal Projection

22.Sliding Motion on an Inclined Plane

23.Rolling Motion on an Inclined Plane

24.Newton’s First Law of Motion

25.Newton’s Second Law

26.Newton’s Third Law

27.Momentum of Force

28.Impulse of Force

29.Law of Conservation of Momentum

30.Friction

31.General Law of Gravity

32.Gravitational Force

33.Centrifugal Force

34.Centripetal Force

35.Torque

36.Work

37.Energy

38.Conservation of Energy

39.Relativistic Energy

40.Power

41.Resolution of a Force

42.Moment of a Force about a Point O

43.Mechanical Advantage of Simple Machines

44.The Lever

45.Wheel and Axle

46.The Pulley

47.The Inclined Plane

48.The Wedge

49.The Screw

MECHANICS OF FLUID

1.Density

2.Viscosity

3.Pressure of Solid

4.Pressure of Liquids

5.Force Exerted by Liquids

6.Pascal’s Principle

7.Archimedes’ Principle

8.Buoyant Force

9.Flow Rate

10.Conservation of Mass

11.Bernoulli’s Equation

TEMPERATURE AND HEAT

1.Pressure

2.Temperature

3.Density

4.Specific Volume

5.Molar Mass

6.Molar Volume

7.Heat

8.Specific Heat

9.Heat Conduction

10.Expansion of Solid Bodies

11.Expansion of Liquids

12.Expansion of Water

13.Fusion

14.Vaporization

15.Equation of State

16.The Charles Law for Temperature

17.Boyle’s Law for Pressure

18.Gay-Lussac’s Law for Temperature

19.Dalton’s Law of Partial Pressures

20.Combined Gas Law

21.The First Law of Thermodynamics

22.The Second Law of Thermodynamics

23.The Third Law of Thermodynamics

ELECTRICITY AND MAGNETISM

1.Coulomb’s Law

2.Electric Fields

3.Electric Flux

4.Gauss’ Law

5.Electric Potential

6.Electric Potential Energy

7.Capacitance

8.Capacitor

9.Electric Current

10.Current Density

11.Potential Difference

12.Resistance

13.Ohm’s Law

14.Series Circuits

15.Parallel Circuits

16.Series-Parallel Circuit

17.Joule’s Law

18.Kirchhoff’s Junction Law

19.Kirchhoff’s Loop Law

20.Resistors

21.Internal Resistance

22.Magnetic Forces on Moving Charges

23.Force on a Current-Carrying Wire

24.Magnetic Field of a Moving Charge

25.Magnetic Field of a Loop

26.Faraday’s Law

27.Properties of Alternating Current

28.Period

29.Frequency

30.Wavelength

31.Instantaneous Current and Voltage

32.Effective Current and Voltage

33.Maximum Current and Voltage

34.Ohm’s Law of AC Current Containing Only Resistance

35.AC Power

36.Changing Voltage with Transformers

37.Inductive Reactance

38.Inductance and Resistance in Series

39.Capacitance

40.Capacitance and Resistance in a Series

41.Capacitance, Inductance, and Resistance in Series

42.Power in AC Circuits

43.Parallel Circuit

LIGHT

1.Visible Light

2.Speed of Light

3.Light as a Particle

4.Luminous Intensity

5.Luminous Flux

6.Luminous Energy

7.Illuminance

8.Luminance

9.Laws of Reflection

10.Refraction

11.Polarization

12.Plane Mirrors

13.Concave Mirrors

14.Convex Mirrors

15.Mirror Formula

16.Lens Equation

WAVE MOTION AND SOUND

1.Definition and Graph

2.Wavelength

3.Amplitude

4.Velocity

5.Frequency

6.Period

7.Wave on a Stretched String

8.The Sinusoidal Wave

9.Electromagnetic Waves

10.Electromagnetic Energy

11.The Electromagnetic Spectrum

12.Sound Waves

13.Speed of Sound in Air

14.Sound Speed in Gases

15.The Doppler Effect

APPENDIX

1.Fundamental Physics Constants

INDEX

Applied Mathematical and Physical Formulas Pocket Reference

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