| 1 |
Chapter01 |
Fourth/Chapter01 |
Basic Properties of Numbers: P1–P12, Theorem 1, Problems 1–25 |
| 2 |
Chapter02, Chapter02ProblemsB |
Fourth/Chapter02 |
Numbers of Various Sorts: induction, binomial theorem, irrationality |
| 3 |
Chapter03, Chapter03ProblemsB, Chapter03Audit |
Fourth/Chapter03 |
Functions; appendix on ordered pairs |
| 4 |
Chapter04, Chapter04ProblemsB, Chapter04Audit, Chapter04Answers |
Fourth/Chapter04 |
Graphs; vectors, conic sections, polar coordinates |
| 5 |
Chapter05, Chapter05Problems, Chapter05ProblemsB, Chapter05Text, Chapter05Audit |
Fourth/Chapter05 |
Limits (Spivak's ε–δ); the 4th edition's rewritten text |
| 6 |
Chapter06, Chapter06Problems, Chapter06ProblemsB, Chapter06Text, Chapter06Audit |
Fourth/Chapter06 |
Continuous Functions; ContinuousOnIccS |
| 7 |
Chapter07, Chapter07Problems, Chapter07ProblemsB, Chapter07Text, Chapter07Audit |
Fourth/Chapter07 |
Three Hard Theorems, also under Spivak's continuity |
| 8 |
Chapter08, Chapter08Problems, Chapter08ProblemsB, Chapter08Text, Chapter08Audit |
Fourth/Chapter08 |
Least Upper Bounds; appendix on uniform continuity |
| 9 |
Chapter09, Chapter09Problems, Chapter09ProblemsB, Chapter09Audit |
— |
Derivatives |
| 10 |
Chapter10, Chapter10Problems, Chapter10ProblemsB, Chapter10Audit, Chapter10Answers |
Fourth/Chapter10 |
Differentiation, the Chain Rule |
| 11 |
Chapter11, Chapter11Problems, Chapter11ProblemsB, Chapter11Appendix, Chapter11AppendixB, Chapter11Audit, Chapter11ContS |
Fourth/Chapter11, Fourth/Chapter11Appendix |
Rolle, MVT, l'Hôpital; convexity |
| 12 |
Chapter12, Chapter12Problems, Chapter12ProblemsB, Chapter12Appendix, Chapter12AppendixB, Chapter12Audit, Chapter12ContS |
Fourth/Chapter12, Fourth/Chapter12Appendix |
Inverse functions; parametric curves |
| 13 |
Chapter13, Chapter13Problems, Chapter13ProblemsB, Chapter13Audit, Chapter13AuditB, Chapter13ContS |
Fourth/Chapter13 |
Spivak's integral; Riemann sums |
| 14 |
Chapter14, Chapter14Problems, Chapter14ProblemsB, Chapter14Audit, Chapter14ContS |
Fourth/Chapter14 |
Fundamental Theorem; improper integrals |
| 15 |
Chapter15, Chapter15Problems |
Fourth/Chapter15 |
Trigonometric functions constructed |
| 16 |
Chapter16, Chapter16Problems |
Fourth/Chapter16 |
π is irrational; Viète |
| 17 |
Chapter17, Chapter17Area |
Fourth/Chapter17 |
Planetary motion: Kepler's laws, with the ellipse's area derived |
| 18 |
Chapter18, Chapter18Problems |
Fourth/Chapter18 |
log, exp constructed |
| 19 |
Chapter19, Chapter19Text, Chapter19Problems, Chapter19ProblemsB, Chapter19Appendix, Chapter19ContS, Chapter19Liouville, Liouville |
Fourth/Chapter19 |
Integration in elementary terms; Liouville's theorem; the cosmopolitan integral |
| 20 |
Chapter20, Chapter20Text, Chapter20Problems, Chapter20Audit, Chapter20ContS |
Fourth/Chapter20, Fourth/Chapter20B |
Taylor's Theorem, e irrational; the 4th edition's rewritten text |
| 21 |
Chapter21, Chapter21Problems, Chapter21ContS, TranscendenceE |
Fourth/Chapter21 |
e is transcendental (two proofs) |
| 22 |
Chapter22, Chapter22Problems, Chapter22ProblemsB, Chapter22Audit, Chapter22ContS |
Fourth/Chapter22 |
Sequences, Bolzano–Weierstrass, Cauchy |
| 23 |
Chapter23, Chapter23Problems, Chapter23ProblemsB |
Fourth/Chapter23 |
Series, rearrangements; Kempner's series |
| 24 |
Chapter24, Chapter24Problems, Chapter24ProblemsB, Chapter24ProblemsC, Chapter24Audit, Chapter24ContS |
Fourth/Chapter24 |
Uniform convergence, power series |
| 25 |
Chapter25, Chapter25Problems |
Fourth/Chapter25 |
Complex numbers as ordered pairs |
| 26 |
Chapter26, Chapter26Problems, Chapter26Audit |
Fourth/Chapter26 |
Complex functions, Fundamental Theorem of Algebra |
| 27 |
Chapter27, Chapter27Problems, Chapter27ProblemsB, Chapter27ProblemsC, Chapter27Audit |
Fourth/Chapter27 |
Complex power series, e^{iπ} = −1, Liouville's theorem, Stirling's formula |
| 28 |
Chapter28, Chapter28Problems |
— |
Fields |
| 29 |
Chapter29, Chapter29Problems, Chapter29Direct, Chapter29DirectB |
— |
Reals as Dedekind cuts; Cauchy sequences and decimals, all from ℚ |
| 30 |
Chapter30, Chapter30Problems |
— |
Uniqueness of the reals |
| — |
TranscendencePi, TranscendencePiAux |
— |
π is transcendental |
| — |
ChapterFigures, ChapterFiguresB |
— |
the problems given only by a figure |
| — |
AppendixAudit |
— |
the text results of the nine appendices |
| — |
Bridge |
— |
Spivak's derivative and continuity agree with Mathlib's |
| — |
Verify |
— |
axioms of 148 representative results |
| — |
AuditAll |
— |
full axiom audit of every Spivak declaration |
| — |
docs/fourth/*.md |
— |
the 4th-edition concordance, one file per chapter |