18.014 | Fall 2010 | Undergraduate

Calculus with Theory

Course Notes

This course is taught based upon the lecture notes of James Raymond Munkres, Professor of Mathematics, Emeritus. The notes are available as individual chapters, or as one file (PDF - 3.3MB).

A Integers and exponents (PDF)
B Square roots, and the existence of irrational numbers (PDF)
C The Riemann condition (PDF)
D Properties of integrals (PDF)
E Integrability of bounded piecewise-monotonic functions (PDF)
F Continuity of the square root function (PDF)
G Rational exponents – an application of the intermediate-value theorem (PDF)
H The small span theorem and the extreme-value theorem (PDF)
I Theorem and proof (PDF)
J Exercises on derivatives (PDF)
K The fundamental theorems of calculus (PDF)
L The trigonometric functions (PDF)
M The exponential and logarithm functions (PDF)
N Integration (PDF)
O Taylor’s formula (PDF)
P L’Hopital’s rule for 0/0 (PDF)
Q Notes on error estimates (PDF)
R The basic theorems on power series (PDF)
S A family of non-analytic functions (PDF)
T Fourier Series (PDF)

Course Info

As Taught In
Fall 2010
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions
Lecture Notes