Handbook of Mathematics
Published on 10. July 2014
794 pages
978-1-4831-4924-0 (ISBN)
Description
International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examples), Rolle's theorem, and the logarithmic function. The book also discusses extensively the functions of two variables in partial differentiation and multiple integrals. The book then describes the theory of functions, ordinary differential functions, special functions and the topic of sequences and series. The book explains vector analysis (which includes dyads and tensors), the use of numerical analysis, probability statistics, and the Laplace transform theory. Physicists, engineers, chemists, biologists, and statisticians will find this book useful.
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L. Kuipers | R. Timman
Handbook of Mathematics
Book
11/1969
Pergamon
€43.33
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Content
ForewordI. Glimpses of the History of Mathematics 1. The First Numbers 2. The Continuation of the Sequence of Numbers 3. The Infinite 4. The Irrational 5. The Infinitely Small 6. The Evolution of the Calculus 7. Some Later DevelopmentsII. Number Systems 1. The Natural Numbers 2. The Integers 3. The Rational Numbers 4. The Real Numbers 5. Complex NumbersIII. Linear Algebra 1. Vectors, Vector Space 2. Dependence, Dimension, Basis 3. Subspace 4. The Scalar Product 5. Linear Transformation, Matrix 6. Multiplication of Linear Transformations 7. Multiplication of Matrices 8. Row Matrices, Column Matrices 9. Rank of a Matrix 10. Determinants 11. Solution of a Non-homogeneous System of Equations 12. Solution of a Homogeneous System of Equations 13. Latent Roots 14. Latent Roots and Characteristic Vectors of Symmetric (Real) Matrices 15. Transformation of the Main Axes of Symmetric MatricesIV. Analytical Geometry 1. Coordinates 2. The Geometry of the Plane and of the Straight Line 3. Homogeneous Coordinates 4. Circle and Sphere 5. Conic Sections 6. Curves of the Second Degree 7. Polar Theory for Conic Sections 8. Surfaces of the Second Degree 9. Investigation of Surfaces of the Second Degree 10. Polar Theory of Quadratic SurfacesV. Analysis Differential and Integral Calculus 1. The Concept of Function - Interval - Neighborhood 2. The Concept of Limit 3. Algebra of Limits 4. The Concept of Continuity 5. Theorem on Continuous Functions - Examples of Continuous Functions 6. Derivative 7. First Derivative - Continuity and Differentiability - Higher Derivatives 8. Algebra of Derivatives 9. The Concept of Arc Length of a Circle - Continuity of the Trigonometric Functions - Trigonometric Inequalities 10. The Derivatives of the Trigonometric Functions 11. Limit Properties of Composite Functions 12. Differentiation of a Composite Function - The Chain Rule 13. Rolle's Theorem and the Mean Value Theorem of Differential Calculus 14. Generalized Mean Value Theorem 15. Extreme Values 16. Points of Inflection 17. Primitive Functions 18. Change of Variables - Differentials - Integration by Parts 19. The Concept of Area 20. Fundamental Theorem of Integral Calculus 21. Properties of Definite Integrals 22. Method of Integration by Parts and Method of Substitution 23. Mean Value Theorem 24. Logarithmic Function 25. Inverse Function 26. The Exponential Function 27. The General Power and the General Exponential Function 28. Some Logarithmic and Exponential Limits 29. The General Logarithm 30. The Cyclometric Functions 31. Leibniz's Formula 32. The Hyperbolic Functions 33. The Primitives of a Rational Function - Partial Fractions 34. The Primitives of Cosn x and Sinn x (n is an Integer) 35. The Primitives of a Rational Function of Sin x and Cos x 36. The Primitives of Irrational Algebraic Functions 37. Improper Integrals Functions of Two Variables-Partial Differentiation 38. The Concept of Function 39. The Concept of Limit 40. Continuity 41. Partial Differentiation 42. Partial Derivatives of the Second Order 43. Composite Functions-Total Differential 44. Change of the Independent Variables 45. Functions of More Than Two Variables 46. Extreme Values of Functions of Two Variables 47. Taylor's Formula for a Function of Two Variables - The Mean Value Theorem 48. Sufficient Conditions for Extreme Values of Functions of Two Variables Multiple Integrals 49.
