Course Materials
Notes and derivations from my coursework, typeset in LaTeX.
18.100BReal Analysis
23 notes
- Lecture 1 NotesReal Numbers
- Lecture 2 NotesReal Numbers Ctd.
- Lecture 3 NotesProofs
- Lecture 4 NotesSequences
- Lecture 5 NotesMonotone Convergence Theorem
- Lecture 6 NotesCauchy Convergence Theorem
- Lecture 7 NotesBolzano-Weierstrass Theorem; Series
- Lecture 8 NotesConvergence Tests & Power Series
- Lecture 9 NotesLimsup, Liminf; Power Series (Cont); Continuous Functions; Exponential Function
- Lecture 10 NotesContinuous Functions; Exponential Function (Cont)
- Lecture 11 NotesExtreme & Intermediate Value Theorem; Metric Spaces
- Lecture 12 NotesConvergence in Metric Spaces; Operations on Sets
- Lecture 13 NotesOpen and Closed Sets; Coverings; Compactness
- Lecture 14 NotesSequential Compactness; Bolzano-Weierstrass Theorem in a Metric Space
- Lecture 15 NotesDerivatives; Laws for Differentiation
- Lecture 16 NotesRolle's Theorem; Mean Value Theorem; Taylor Expansion
- Lecture 17 NotesTaylor Polynomials; Remainder Term; Riemann Integrals
- Lecture 18 NotesIntegrable Functions
- Lecture 19 NotesFundamental Theorem of Calculus
- Lecture 20 NotesPointwise Convergence; Uniform Convergence
- Lecture 21 NotesIntegrals and Derivatives Under Uniform Convergence
- Lecture 22 NotesDifferentiating and Integrating Power Series; Ordinary Differential Equations
- Lecture 23 NotesExistence and Uniqueness for ODE's: Picard-Lindelof Theorem