TABLE OF CONTENTS Bruce A. Finlayson, Ph.D. Rehnberg Professor, Department of Chemical Engineering, University of Washington; Member, National Academy of Engineering (Section Editor, numerical methods and all general material)
Lorenz T. Biegler, Ph.D. Bayer Professor of Chemical Engineering, Carnegie Mellon University (Optimization)
| MATHEMATICS | |
| General | 3-3 |
| Miscellaneous Mathematical Constants | 3-4 |
| The Real-Number System | 3-4 |
| Algebraic Inequalities | 3-5 |
| MENSURATION FORMULAS | |
| Plane Geometric Figures with Straight Boundaries | 3-6 |
| Plane Geometric Figures with Curved Boundaries | 3-6 |
| Solid Geometric Figures with Plane Boundaries | 3-7 |
| Solids Bounded by Curved Surfaces | 3-7 |
| Miscellaneous Formulas | 3-8 |
| Irregular Areas and Volumes | 3-8 |
| ELEMENTARY ALGEBRA | |
| Operations on Algebraic Expressions | 3-8 |
| The Binomial Theorem | 3-9 |
| Progressions | 3-9 |
| Permutations, Combinations, and Probability | 3-10 |
| Theory of Equations | 3-10 |
| ANALYTIC GEOMETRY | |
| Plane Analytic Geometry | 3-11 |
| Solid Analytic Geometry | 3-13 |
| PLANE TRIGONOMETRY | |
| Angles | 3-16 |
| Functions of Circular Trigonometry | 3-16 |
| Inverse Trigonometric Functions | 3-17 |
| Relations between Angles and Sides of Triangles | 3-17 |
| Hyperbolic Trigonometry | 3-18 |
| Approximations for Trigonometric Functions | 3-18 |
| DIFFERENTIAL AND INTEGRAL CALCULUS | |
| Differential Calculus | 3-18 |
| Multivariable Calculus Applied to Thermodynamics | 3-21 |
| Integral Calculus | 3-22 |
| INFINITE SERIES | |
| Definitions | 3-25 |
| Operations with Infinite Series | 3-25 |
| Tests for Convergence and Divergence | 3-26 |
| Series Summation and Identities | 3-26 |
| COMPLEX VARIABLES | |
| Algebra | 3-27 |
| Special Operations | 3-27 |
| Trigonometric Representation | 3-27 |
| Powers and Roots | 3-27 |
| Elementary Complex Functions | 3-27 |
| Complex Functions (Analytic) | 3-28 |
| DIFFERENTIAL EQUATIONS | |
| Ordinary Differential Equations | 3-29 |
| Ordinary Differential Equations of the First Order | 3-30 |
| Ordinary Differential Equations of Higher Order | 3-30 |
| Special Differential Equations | 3-31 |
| Partial Differential Equations | 3-32 |
| DIFFERENCE EQUATIONS |
