GREEK LETTERS AB Alpha Beta Gamma Delta βY8EsnθLxauvgoπpotu中X zHe Zeta Lambda AMN三OnPETrΦx Omicron P Rho Sigma Psi Omega THE NUMBERS汇ANDe 213 320 2653589793 4481903252 2.302585092994046
Greek Letters α Α Alpha β Β Beta γ Γ Gamma δ Δ Delta ε Ε Epsilon ζ Ζ Zeta η Η Eta θ Θ Theta ι Ι Iota κ Κ Kappa λ Λ Lambda μ Μ Mu ν Ν Nu ξ Ξ Xi ο Ο Omicron π Π Pi ρ Ρ Rho σ Σ Sigma τ Τ Tau υ ϒ Upsilon ϕ Φ Phi χ X Chi ψ Ψ Psi ω Ω Omega The Numbers π and e π = 3.14159 26535 89793 e = 2.71828 18284 59045 log10e = 0.43429 44819 03252 loge10 = 2.30258 50929 94046
PRIME NUMIBERS 2357111317192329 3137414347535961677 7379 127131137139149151157163167 17918l191193197199211223227 233239241251257263269271277281 Important Numbers in Science(Physical Constants) Avogadro constant(NA) 6.02 x 1026 kmole-I Boltzmann constant(k)1.38×10-23J°K- Electron charge(e) 1602×10C Electron, charge/mas 1.760×10Ckg-l (elm Electron rest mass(m) 9. 11 x 10- kg(0.511 Mev araday constant( 9.65×104 C mole-1 8.31×103J°K-1km (ideal)normal volume 22. 4 m3.kmole-l onal constant(G) 6.67 x 10-lN-m2kg 1.673×102kg(9388Mev (rest mass)(mH) Neutron(rest mass)(m) 1.675 x 10-27 kg(939.6 Mev 663×1034J Proton(rest mass)(m,) 1.673 x 10-27 kg(938.3 Mev) Speed of light(c) 3.00×105ms-1
Prime Numbers 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 … … … Important Numbers in Science (Physical Constants) Avogadro constant (NA) 6.02 × 1026 kmole–1 Boltzmann constant (k) 1.38 × 10–23 J⋅°K–1 Electron charge (e) 1.602 × 10–19 C Electron, charge/mass (e/me) 1.760 × 1011 C⋅kg–1 Electron rest mass (me) 9.11 × 10–31 kg (0.511 MeV) Faraday constant (F) 9.65 × 104 C⋅mole–1 Gas constant (R) 8.31 × 103 J⋅°K–1 kmole–1 Gas (ideal) normal volume (Vo) 22.4 m3⋅kmole–1 Gravitational constant (G) 6.67 × 10–11 N⋅m2⋅kg–2 Hydrogen atom (rest mass) (mH) 1.673 × 10–27 kg (938.8 MeV) Neutron (rest mass) (mn) 1.675 × 10–27 kg (939.6 MeV) Planck constant (h) 6.63 × 10–34 J⋅s Proton (rest mass) (mp) 1.673 × 10–27 kg (938.3 MeV) Speed of light (c) 3.00 × 108 m⋅s–1
Contents 1 Elementary Algebra and geometry 1. Fundamental Properties (Real Numbers) 2. Exponents 3. Fractional Exponents 4. Irrational Exponents 5. Logarithms 6. Factorials 7. Binomial theorem 8. Factors and Expansion 9. Progression 10. Complex Numbers 1. Polar Form 12. Permutations 13. Combinations 14. Algebraic Equations 22233445677899 15. Geomet 16. Pythagorean Theorem 2 Determinants, Matrices, and Linear Systems of Equations 1. Determinants Evaluation by Cofactors es of Determinants 4. Matrices 5. Operations 67889 6. Properties 7. Transpose 8. Identity matrix
Contents 1 Elementary Algebra and Geometry 1. Fundamental Properties (Real Numbers) 1 2. Exponents 2 3. Fractional Exponents 2 4. Irrational Exponents 2 5. Logarithms 2 6. Factorials 3 7. Binomial Theorem 3 8. Factors and Expansion 4 9. Progression 4 10. Complex Numbers 5 11. Polar Form 6 12. Permutations 7 13. Combinations 7 14. Algebraic Equations 8 15. Geometry 9 16. Pythagorean Theorem 9 2 Determinants, Matrices, and Linear Systems of Equations 1. Determinants 15 2. Evaluation by Cofactors 16 3. Properties of Determinants 17 4. Matrices 18 5. Operations 18 6. Properties 19 7. Transpose 20 8. Identity Matrix 20
10. Inverse matrix 21 l1. Systems of Linear Equations 12. Matrix Solution 3 Trigonometry 1. Triangle 2. Trigonometric functions of an angle 26 3. Trigonometric Identities 4. Inverse Trigonometric functions 4 Analytic Geometry 1. Rectangular Coordinates 2. Distance between Two Points: Slope 33 3. Equations of Straight Lines 4. Distance from a point to a line 5. Circle 6. Parabola 7. Ellipse 39 8. Hyperbola(e> 1) 9. Change of Axes 10. General Equation of Degree 2 11. Polar Coordinates 47 12. Curves and Equations 50 13. Exponential Function(Half-Life) 5 Series, Number Facts, and Theory 1. Bernoulli and euler numbers 2. Series of functions 3. Error Function 4. Fermat's Little Theorem
9. Adjoint 21 10. Inverse Matrix 21 11. Systems of Linear Equations 23 12. Matrix Solution 24 3 Trigonometry 1. Triangles 25 2. Trigonometric Functions of an Angle 26 3. Trigonometric Identities 28 4. Inverse Trigonometric Functions 31 4 Analytic Geometry 1. Rectangular Coordinates 32 2. Distance between Two Points: Slope 33 3. Equations of Straight Lines 34 4. Distance from a Point to a Line 37 5. Circle 37 6. Parabola 37 7. Ellipse 39 8. Hyperbola (e > 1) 43 9. Change of Axes 44 10. General Equation of Degree 2 47 11. Polar Coordinates 47 12. Curves and Equations 50 13. Exponential Function (Half-Life) 56 5 Series, Number Facts, and Theory 1. Bernoulli and Euler Numbers 57 2. Series of Functions 58 3. Error Function 63 4. Fermat’s Little Theorem 64
5. Fermats last Theorem 6. Beatty's Theorem 7. An Interesting prime 8. Goldbach Conjecture 9. Twin Primes 466 10. Collatz Conjecture 6 Differential Calculus 1. Notation 2. Slope of a Curve 3. Angle of Intersection of Two Curves 69 4. Radius of curvature 5. Relative Maxima and minima 6. Points of inflection of a curve 7. Taylor's Formula 8. Indeterminant Forms 9. Numerical Methods 6000012356 10. Functions of Two variables 1. Partial Derivatives 7 Integral Calculus 2. Definite Integra 3. Properties 4. Common Applications of the 788 Definite Integral 5. Cylindrical and Spherical Coordinates 80 6. Double Integration 7. Surface Area and Volume by Double Integration 8. Centroid
5. Fermat’s Last Theorem 64 6. Beatty’s Theorem 64 7. An Interesting Prime 66 8. Goldbach Conjecture 66 9. Twin Primes 67 10. Collatz Conjecture 67 6 Differential Calculus 1. Notation 68 2. Slope of a Curve 68 3. Angle of Intersection of Two Curves 69 4. Radius of Curvature 69 5. Relative Maxima and Minima 70 6. Points of Inflection of a Curve 70 7. Taylor’s Formula 71 8. Indeterminant Forms 72 9. Numerical Methods 73 10. Functions of Two Variables 75 11. Partial Derivatives 76 7 Integral Calculus 1. Indefinite Integral 77 2. Definite Integral 77 3. Properties 78 4. Common Applications of the Definite Integral 78 5. Cylindrical and Spherical Coordinates 80 6. Double Integration 82 7. Surface Area and Volume by Double Integration 83 8. Centroid 83