Page 13 - Standard Handbook Of Petroleum & Natural Gas Engineering

Patricia Duettra
Consultant
Applied Mathematics and Computer Analysis
Albuquerque, New Mexico
Geometry ..... , ............................................................................................ 3
Sets and Functions 3. Angles 3. Polygons 3. Triangles 3. Quadrilaterals 4. Circles and Spheres 4.
Arcs of Circles 4. Concurrency 5. Similarity 5. Prisms and Pyramids 5. Coordinate Systems 6.
Graphs 6. Vectors 6. Lengths and Areas of Plane Figures 7. Surfaces and Volumes of Solids 12.
Algebra .................................................................................................... 18

Operator Precedence and Notation 18. Rules of Addition 19. Fractions 20. Exponents 21.
Logarithms 21. Binomial Theorem 22. Progressions 23. Summation of Series by Difference
Formulas 23. Sums of the first n Natural Numbers 24. Solution of Equations in One Unknown 24.
Solutions of Systems of Simultaneous Equations 25. Determinants 26.
Trigonometry .......................................................................................... 27
Directed Angles 27. Basic Trigonometric Functions 28. Radian Measure 28. Trigonometric
Properties 29. Hyperbolic Functions 33. Polar Coordinate System 34.
Differential and Integral Calculus .......................................................... 35
Derivatives 35. Maxima and Minima 37. Differentials 38. Radius of Curvature 39. Indefinite
Integrals 40. Definite Integrals 41. Improper and Multiple Integrals 44. Second Fundamental
Theorem 45. Differential Equations 45. Laplace Transformation 48.
Analytic Geometry .................... . ............................................................. 50
Symmetry 50. Intercepts 50. Asymptotes 50. Equations of Slope 51. Tangents 51. Equations of a
Straight Line 52. Equations of a Circle 53. Equations of a Parabola 53. Equations of an Ellipse of
Eccentricity e 54. Equations of a Hyperbola 55. Equations of Three-Dimensional Coordinate Systems
56. Equations of a Plane 56. Equations of a Line 57. Equations of Angles 57. Equation of a Sphere 57.
Equation of an Ellipsoid 57. Equations of Hyperboloids and Paraboloids 58. Equation of an Elliptic
Cone 59. Equation of an Elliptic Cylinder 59.
Numerical Methods ............ . . ....................... ...... . . . ........... . . ....... . ............ . 60
Expansion in Series 60. Finite Difference Calculus 60. Interpolation 64. Roots of Equations 69.
Solution of Sets of Simultaneous Linear Equations 71. Least Squares Curve Fitting 76. Numerical
Integration 78. Numerical Solution of Differential Equations 83.
Applied Statistics ................................................ . ............ . ...................... 92
Moments 92. Common Probability Distributions for Continuous Random Variables 94. Probability
Distributions for Discrete Random Variables. Univariate Analysis 102. Confidence Intervals 103.
Correlation 105. Regression 106.
Computer Applications ......................................................................... 108
Problem Solving 109. Programming Languages 109. Common Data Types 110. Common Data
Structures 110. Program Statements 112. Subprograms 113. General Programming Principles 113.
FORTRAN Language 114. Pascal Language 124. System Software 131. System Hardware 132.
References...... ....................................................................................... 133

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