Читать книгу Applied Mathematical and Physical Formulas - Vukota Boljanovic - Страница 5
ОглавлениеTABLE OF CONTENTS
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
16. Apothecaries’ Units of Liquid Volume
18. Avoirdupois Units of Mass
19. Apothecaries’ Units of Mass
20. Troy Units of Mass
21. Units of Measure in Precious Metals
TABLES OF EQUIVALENTS
22. Units of Length
23. Units of Area
24. Units of Volume
25. Units of Mass
PART II MATHEMATICS
ARITHMETIC
1. Natural Numbers
2. Integers
3. Divisibility of Numbers
4. Prime and Composite Numbers
5. Decomposing Composite Numbers into their Prime Factors
6. Greatest Common Divisor (GCD)
7. Least Common Multiple (LCM)
8. Fractions
9. Proportionality
10. Percentages
11. Calculation for Mixtures
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. Intervals
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 Sequences
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 Operations 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. Ratios of the Sides of a Right Triangle
23. Pythagorean Theorem
24. Equilateral Triangle
25. Isosceles Triangle
26. Square
27. Rectangle
28. Parallelogram
29. Rhombus
30. Trapezoid (American definition)
31. Kite
32. Regular Polygon
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 Intersecting 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. General Form of an Equation of a Straight Line
11. Normal Equation of a Straight Line
12. Distance from a Line to a Point
13. Circles
14. Ellipses
15. Parabolas
16. Hyperbolas
17. Polar Coordinates
18. Cartesian Coordinates
19. Distance between Two Points
20. Angle between Two Lines
21. Planes
22. Line Perpendicular to a Plane
23. Parallel and Perpendicular Planes
24. Distance of a Point from a Plane
25. Normal Form
26. Intercept Form
27. Angle Between Two Planes
28. Straight Line in Space
29. Parametric Form Equations of a Line
30. Symmetric Form Equations of a Line
31. Two-Point Form Equations of a Line
32. Relative Directions of a Line and Plane
33. Sphere
34. Ellipsoid
35. Hyperboloid
36. Elliptic Paraboloid
37. Hyperbolic Paraboloid
MATHEMATICS OF FINANCE
1. Simple Interest
2. Compound Interest
3. Annuities
4. Amortization of Loans
5. Sinking Fund Payment
CALCULUS
1. Limits
2. Rules for Limits
3. Slope of Tangent Line
4. Definition of the Derivative
5. Basic Derivatives
6. Increasing and Decreasing Functions
7. Maximum and Minimum of a Function
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 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
MATHEMATICAL FUNDAMENTALS OF COMPUTER SCIENCE
1. Binary Data Representation
2. Number Systems
3. Decimal Number System
4. Binary Number System
5. Decimal to Binary Number Conversion
6. Counting in Binary
7. Octal Number System
8. Decimal to Octal Number Conversion
9. Binary to Octal Number Conversion and Its Converse
10. Counting in Octal
11. Hexadecimal Number System
12. Binary to Hexadecimal Number Conversion and Its Converse
13. Counting in Hexadecimal
14. Comparison of Number Systems
15. Binary Logic
16. Binary Arithmetic
17. Representation of Signed Numbers in Computers
18. Range of Numbers Written with n Digits
19. Representation of Real Numbers
20. Representation of Character Data Types
21. Information in Binary Form
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 0
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 FLUIDS
1. Density
2. Viscosity
3. Pressure of Solids
4. Pressure in 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’s 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 for 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 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. Definitions and Graphs
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: Fundamental Physical Constants
Index
About the Author
