Handbook of Mathematical Formulas
Published on 10. May 2014
528 pages
978-1-4832-6742-5 (ISBN)
Description
Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.
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Hans-Jochen Bartsch
Handbook of Mathematical Formulas
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Academic Press
€79.86
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Content
0. Mathematical Signs and Symbols 0.1. Mathematical Signs 0.2. Symbols Used in the Theory of Sets 0.3. Symbols of Logic1. Arithmetic 1.1. Set Theory 1.1.1. Fundamental Notions 1.1.2. Set Operations 1.1.3. Mappings, Cardinality 1.2. Real Numbers 1.2.1. General 1.2.2. Irrational Numbers 1.2.3. Binomial Coefficients, Binomial Theorem 1.3. Imaginary or Complex Numbers 1.3.1. Imaginary Numbers 1.3.2. Complex Numbers in Arithmetical Form 1.3.3. Complex Numbers in a Goniometric Form 1.3.4. Complex Numbers in Exponential Form 1.3.5. Natural Logarithms of Complex and Negative Numbers 1.3.6. Graphical Methods 1.4. Proportions 1.5. Logarithms 1.5.1. General 1.5.2. Rules for Calculating with Logarithms 1.5.3. The Use of Logarithm Tables for Finding Common Logarithms 1.6. Combinatoric Analysis 1.6.1. Permutations 1.6.2. Variations 1.6.3. Combinations 1.7. Per Cent Calculation, Interest Calculation 1.7.1. Per Cent (Per Mille) Calculation 1.7.2. Interest Calculation 1.8. Sequences and Series 1.8.1. General 1.8.2. Arithmetic Sequences and Series 1.8.3. Geometric Sequences and Series 1.8.4. Compound Interest Calculation 1.8.5. Annuities 1.9. Determinants 1.9.1. General 1.9.2. Theorems on Determinants 1.9.3. Applications of Determinants 1.10. Matrices 1.10.1. General 1.10.2. Theorems on Matrices 1.10.3. Applications2. Equations, Functions, Vectors 2.1. Equations 2.1.1. General 2.1.2. Algebraic Equations in One Variable 2.1.3. Transcendental Equations 2.1.4. Approximation Methods for Determining the Roots of an Equation 2.1.5. Systems of Equations 2.2. Inequalities 2.3. Functions 2.3.1. General 2.3.2. Further Methods of Analytic Representation 2.3.3. Graphical Representation of Functions 2.4. Vector Calculus 2.4.1. General 2.4.2. Multiplication of Vectors 2.4.3. Geometrical Applications of Vector Calculus 2.5. Reflection in a Circle, Inversion3. Geometry 3.1. General 3.2. Planimetry 3.2.1. Triangle ABC 3.2.2. Quadrilaterals 3.2.3. Polygons (n-Sided Polygons) 3.2.4. Circle 3.3. Stereometry 3.3.1. General Theorems 3.3.2. Solids Bounded by Plane Surfaces 3.3.3. Solids Bounded by Curved Surfaces 3.4. Goniometry, Plane Trigonometry, Hyperbolic Functions 3.4.1. Goniometry 3.4.2. Trigonometric Formulas for Oblique-Angled Triangles 3.4.3. Goniometric Equations 3.4.4. Inverse Trigonometric Functions 3.4.5. Hyperbolic Functions 3.4.6. Inverse Hyperbolic Functions 3.5. Spherical Trigonometry 3.5.1. General 3.5.2. Right Spherical Triangle 3.5.3. Oblique Spherical Triangle 3.5.4. Mathematical Geography4. Analytical Geometry 4.1. Analytical Geometry of the Plane 4.1.1. The Various Systems of Coordinates 4.1.2. Points and Line Segments 4.1.3. Straight Line 4.1.4. Circle 4.1.5. Parabola 4.1.6. Ellipse 4.1.7. Hyperbola 4.1.8. The General Equation of the Second Degree in x and y 4.2. Analytical Geometry of Space 4.2.1. The Various Systems of Coordinate 4.2.2. Points and Line Segments in Space 4.2.3. Planes in Space 4.2.4. Straight Lines in Space 4.2.5. Surfaces of the Second Order 4.2.6. The General Equation of the Second Degree in x, y and z5. Differential Calculus 5.1. Limits 5.2. Difference Quotient, Differential Quotient, Differential 5.3. Rules for Differentiation 5.4.
