Syllabus · Lecture Notes
MIT OpenCourseWare
Calculus with Theory
Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain
- Instructor
- Christine Breiner
- Term
- Fall 2010
- Level
- Undergraduate
- What's inside
- 1 reading · 57 other files · 5 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.014 Calculus with Theory, Fall 2010, Christine Breiner — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- A lecture sequence of 39 items is confirmed. Assignment and exam materials exist too, but MIT's own order for them could not be verified, so they're shown as materials below rather than a sequence.
Not included here
3 items from the source could not be safely included:
- Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (3 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Course Notes
21 files
- This resource contains information about all course notes (MIT18_014F10_course_notes.pdf) Download
- Integers and exponents Download
- Square roots, and the existence of irrational numbers Download
- The Riemann condition Download
- Properties of integrals Download
- Integrability of bounded piecewise-monotonic functions Download
- Continuity of the square root function Download
- Rational exponents – an application of the intermediate-value theorem Download
- The small span theorem and the extreme-value theorem Download
- Theorem and proof Download
- Exercises on derivatives Download
- The fundamental theorems of calculus Download
- The trigonometric functions Download
- The exponential and logarithm functions Download
- Integration Download
- Taylor’s formula Download
- L’Hopital’s rule for 0/0 Download
- Notes on error estimates Download
- The basic theorems on power series Download
- A family of non-analytic functions Download
- Fourier Series Download
Assignments
23 files
- Problem set 1 Download
- Problem set 1 · Solutions Download
- Problem set 2 Download
- Problem set 2 · Solutions Download
- Problem set 3 Download
- Problem set 3 · Solutions Download
- Problem set 4 Download
- Problem set 4 · Solutions Download
- Problem set 5 Download
- Problem set 5 · Solutions Download
- Problem set 6 Download
- Problem set 6 · Solutions Download
- Problem set 7 Download
- Problem set 7 · Solutions Download
- Problem set 8 Download
- Problem set 8 · Solutions Download
- Problem set 9 Download
- Problem set 9 · Solutions Download
- Problem set 10 Download
- Problem set 10 · Solutions Download
- Problem set 11 - part I Download
- This resource contains problem about partII of problems set 11 (MIT18_014F10_pset11b.pdf) Download
- Parts I and II Download
Exams
13 files
- Practice exam 1 Download
- Practice exam 1 solutions Download
- Exam 1 Download
- Exam 1 solutions Download
- Practice exam 2 Download
- Practice exam 2 solutions Download
- Exam 2 Download
- Exam 2 solutions Download
- Practice exam 3 Download
- Practice exam 3 solutions Download
- Exam 3 Download
- Exam 3 solutions Download
- Practice problems for the final exam Download
Course outline
Syllabus · Lecture Notes
Lecture 1: Axioms for the real numbers
Syllabus · Lecture Notes
Lecture 2: Integers, induction, sigma notation
Syllabus · Lecture Notes
Lecture 3: Least upper bound, triangle inequality
Syllabus · Lecture Notes
Lecture 4: Functions, area axioms
Syllabus · Lecture Notes
Lecture 5: Definition of the integral
Syllabus · Lecture Notes
Lecture 6: Properties of the integral, Riemann condition
Syllabus · Lecture Notes
Lecture 7: Proofs of integral properties
Syllabus · Lecture Notes
Lecture 8: Piecewise, monotonic functions
Syllabus · Lecture Notes
Lecture 9: Limits and continuity defined
Syllabus · Lecture Notes
Lecture 10: Proofs of limit theorems, continuity
Syllabus · Lecture Notes
Lecture 11: Hour exam I
Syllabus · Lecture Notes
Lecture 12: Intermediate value theorem
Syllabus · Lecture Notes
Lecture 13: Inverse functions
Syllabus · Lecture Notes
Lecture 14: Extreme value theorem and uniform continuity
Syllabus · Lecture Notes
Lecture 15: Definition of the derivative
Syllabus · Lecture Notes
Lecture 16: Composite and inverse functions
Syllabus · Lecture Notes
Lecture 17: Mean value theorem, curve sketching
Syllabus · Lecture Notes
Lecture 18: Fundamental theorem of calculus
Syllabus · Lecture Notes
Lecture 19: Trigonometric functions
Syllabus · Lecture Notes
Lecture 20: Logs and exponentials
Syllabus · Lecture Notes
Lecture 21: IBP and substitution
Syllabus · Lecture Notes
Lecture 22: Inverse trig; trig substitution
Syllabus · Lecture Notes
Lecture 23: Hour exam II
Syllabus · Lecture Notes
Lecture 24: Partial fractions
Syllabus · Lecture Notes
Lecture 25: Taylor’s Formula
Syllabus · Lecture Notes
Lecture 26: Proof of Taylor’s formula
Syllabus · Lecture Notes
Lecture 27: L’Hopital’s rule and infinite limits
Syllabus · Lecture Notes
Lecture 28: Sequences and series; geometric series
Syllabus · Lecture Notes
Lecture 29: Absolute convergence, integral test
Syllabus · Lecture Notes
Lecture 30: Tests: comparison, root, ratio
Syllabus · Lecture Notes
Lecture 31: Hour exam III
Syllabus · Lecture Notes
Lecture 32: Alternating series; improper integrals
Syllabus · Lecture Notes
Lecture 33: Sequences of functions, convergence
Syllabus · Lecture Notes
Lecture 34: Power series
Syllabus · Lecture Notes
Lecture 35: Properties of power series
Syllabus · Lecture Notes
Lecture 36: Taylor series
Syllabus · Lecture Notes
Lecture 37: Fourier series
Syllabus · Lecture Notes
Lecture 38: Final exam
MIT OpenCourseWare, Christine Breiner, 18.014 Calculus with Theory, Fall 2010.
License: CC BY-NC-SA 4.0 · Edition: Fall 2010 · Open the original course on OCW ↗
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