Analysis in MathML

Foundations in Mathematical Analysis

(Safari Webkit 17.1)

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CONTENTS

Part 1	Prologue
	1. Basic Properties of Numbers   3
	2. Numbers of Various Sorts   21
Part 2	Foundations
	3. Functions   39   Appendix. Ordered Pairs   54
	4. Graphs   56   Appendix 1. Vectors   75   Appendix 2. The Conic Sections   80   Appendix 3. Polar Coordinates   84
	5. Limits   90
	6. Continuous Functions   113
	7. Three Hard Theorems   120
	8. Least Upper Bounds   131   Appendix. Uniform Continuity   142
Part 3	Derivatives and Integrals
	9. Derivatives   147
	10. Differentiation   166
	11. Significance of the Derivative   185    Appendix. Convexity and Concavity   216
	12. Inverse Functions   227    Appendix. Parametric Representation of Curves   241
	13. Integrals   250    Appendix. Riemann Sums   279
	14. The Fundamental Theorem of Calculus   282
	15. The Trigonometric Functions   300
	16. π is Irrational   321   ⚐
	17. Planetary Motion   327   ⚐
	18. The Logarithm and Exponentail Functions   336
	19. Integration in Elementary Terms   359    Appendix. The Cosmopolitan Integral   397
Part 4	Infinite Sequences and Infinite Series
	20. Approximation by Polynomial Functions   405
	21. e is Transcendental   435   ⚐
	22. Infinite Sequences   445
	23. Infinite Series   464
	24. Uniform Convergence and Power Series   491
	25. Complex Numbers   517
	26. Complex Functions   532
	27. Complex Power Series   546
Part 5	Epilogue
	28. Fields   571
	29. Construction of the Real Numbers   578
	30. Uniqueness of the Real Numbers   591   Suggested reading   599   Answers (to Selected Problems)   609   Glossery of Symbols   655   Index   659

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Specification

This page framework is Webkit–centric. The layout design is an eleventh–order quaternion prismplex, with eight dynamic relational-fields. It may also be described as a complete frame, meaning that every field has slide and scroll fucntionality. The frame's memory is accesible through conventional menus and search. Each slide has autonomous search, whose query returns remain loaded in the RAM while seperate fields are active. The directory is licensed for use under the terms outlined in the MIT License / BSD (C4)License bundle.