Outline Course of Pure Mathematics
Published on 16. May 2014
594 pages
978-1-4831-4790-1 (ISBN)
Description
Outline Course of Pure Mathematics presents a unified treatment of the algebra, geometry, and calculus that are considered fundamental for the foundation of undergraduate mathematics. This book discusses several topics, including elementary treatments of the real number system, simple harmonic motion, Hooke's law, parabolic motion under gravity, sequences and series, polynomials, binomial theorem, and theory of probability. Organized into 23 chapters, this book begins with an overview of the fundamental concepts of differential and integral calculus, which are complementary processes for solving problems of the physical world. This text then explains the concept of the inverse of a function that is a natural complement of the function concept and introduces a convenient notation. Other chapters illustrate the concepts of continuity and discontinuity at the origin. This book discusses as well the significance of logarithm and exponential functions in scientific and technological contexts. This book is a valuable resource for undergraduates and advanced secondary school students.
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A.F. Horadam
Outline Course of Pure Mathematics
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02/1969
Pergamon
€11.45
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Content
Greek AlphabetSelect BibliographyChapter 1. Differential Calculus 1. Differentiation (Revision) 2. Differentials 3. Maxima and Minima (Revision) Exercises 1 Chapter 2. Inverse Trigonometrical Functions 4. Nature of Inverse Functions 5. Special Properties of Inverse Trigonometrical Functions Exercises 2 Chapter 3. Elementary Analysis 6. Limits (Revision). The Symbol 7. Concept of the Limit of a Function 8. Concept of Continuity 9. The Mean Value Theorem. Rolle's Theorem 10. l'Hospital's Rule Exercises 3 Chapter 4. Expotential and Logarithmic Functions 11. Exponential Function. Exponential Number 12. Graphs of the Exponential and Logarithmic Functions 13. Differentiation of the Exponential and Logarithmic Functions Exercises 4 Chapter 5. Hyperbolic Functions 14. The Hyperbolic Functions 15. Differentiation of the Hyperbolic Functions 16. Graphs of the Hyperbolic Functions 17. Inverse Hyperbolic Functions 18. The Gudermannian and Inverse Gudermannian Exercises 5 Chapter 6. Partial Differentiation 19. n-Dimensional Geometry 20. Polar Coordinates 21. Partial Differentiation 22. Total Differentials Exercises 6 Chapter 7. Indefinite Integrals 23. The Indefinite Integral 24. Standard Integrals 25. Techniques of Integration: Change of Variable (Substitution, Transformation) 26. Techniques of Integration: Trigonometric Denominator 27. Techniques of Integration: Integration by Parts 28. Techniques of Integration: Partial Fractions 29. Techniques of Integration: Quadratic Denominator Exercises 7 Chapter 8. Definite Integrals 30. Elementary First-order Differential Equations (Method of Separation of Variables) 31. The Definite Integral 32. Improper Integrals 33. The Definite Integral as an Area and as the Limit of a Sum 34. Properties of f (x) dx 35. Reduction Formula 36. An Integral Approach to the Theory of Logarithmic Functions Exercises 8 Chapter 9. Infinite Series and Sequences 37. Sequences 38. Convergence and Divergence of Infinite Series 39. Tests for Convergence 40. Alternating Series. Absolute and Conditional Convergence 41. Maclaurin's Series 42. Leibniz's Formula Exercises 9 Chapter 10. Complex Numbers 43. The Real Number System 44. Number Rings and Fields 45. Intuitive Approach to Complex Numbers 46. Formal Development of Complex Numbers 47. Geometrical Representation of Complex Numbers. The Argand Diagram 48. Euler's Theorem (1742) 49. Complex Numbers and Polynomial Equations 50. Elementary Symmetric Functions 51. Some Typical Problems Involving Complex Numbers 52. Hypercomplex Numbers (Quaternions) Exercises 10 Chapter 11. Matrices 53. Linear Transformations and Matrices 54. Formal Definitions 55. Matrices and Vectors 56. Matrices and Linear Equations 57. Matrices and Determinants Exercises 11 Chapter 12. Determinants 58. Formal Definitions and Basic Properties 59. Minors and Cofactors. Expansion of a Determinant 60. Adjoint Determinant 61. Inverse of a Matrix 62. Solution of Simultaneous Linear Equations 63. Elimination and Eigenvalues 64. Determinants and Vectors Exercises 12 Chapter 13. Sets and Their Applications. Boolean Algebra 65. The Language of Set Theory 66. Transfinite Numbers 67. Venn Diagrams 68. Boolean Algebra and Sets 69. Number of Elements in a Set Exercises 13 Chapter 14. Groups 70. Intuitive Approach to Groups 71. Formal Definitions and Basic Properties 72. Survey of Groups of Order 2, 3, 4, 5, 6 73. Concepts of Subgroup and Generators 74. Isomorphism 75. Typical Problems in Elementary Group Theory 2 76. Abstract Rings and Fields Exercises 14 Chapter 15.
