MIT 18.01

Lecture 1

Definition of the Derivative

Graphing a Derivative Function

Smoothing a Piece-wise Function

Constant Multiple Rule

Tangent Line to a Polynomial

Lecture 3

Product Rule

Quotient Rule

Lecture 4

Chain Rule

Lecture 5

Implicit Differentiation

Graphing the Arctan Function

Arccos

Lecture 6

Log and Exponent Derivatives

Rules of Logs

Hyperbolic trig functions

Lecture 7

Lecture 9

Implicit Differentiation and Linear Approximation

Quadratic Approximation

Quadratic Approximation of a Product

Lecture 10

Sketching a curve

Closest Point to the Origin

Lecture 11

Minimum Triangle Area

Maximum Surface Area

Lecture 12

Related rates 1

Related rates 2

Lecture 13

Using Newton's Method

Lecture 14

Mean Value Theorem 1

Mean value theorem 2

Lecture 15

Antidiff. With Discontinuity

Computing Differentials

Linear approx. with differentials

Computing Antiderivatives

Antidifferentiation by substitution

Lecture 16

Differential Equation

Differential Equation With Graph

Summation Notation Practice

Riemann sum

Computing the Volume of a Paraboloid

4J3, Diffusion of a Chemical

Lecture 18

Definite Integrals of tan(x)

Definite Integral by Substitution

Lecture 19

Lecture 20

Applying the Second Fundamental Theorem

Second fundamental theorem and chain rule

Second fundamental theorem and quadratic approximation

Area Between the Graphs of Sine and Cosine

Area Between y=x^3 and y=3x-2

Lecture 21

Lecture 22

Volume of a Paraboloid via Disks

Volume of Revolution via Shells

Lecture 23

Average Velocity

Average x-Coordinate in a Region

Lecture 24

Explanation of Simpson's rule

Using the Trapezoid and Simpson's rules

Lecture 25

Lecture 27

Trig Integral Practice

Trig Integrals and a Volume of Revolution

Integral of tan^4 (theta)

Hyperbolic Trig Sub

Lecture 28

Integration by completing the square

Lecture 29

Partial Fractions Decomposition

Lecture 30

Finding u and v' When Integrating by Parts

Lecture 31

Integrating sin^n(x) Using Reduction

Lecture 32

Arc Length of y=x^(3/2)

Surface Area of a Torus

Parametric Arclength

Lecture 33

Polar to Cartesian

Graph of r = 1 + cos(theta/2)

Lecture 35

Integration Practice I

Integration Practice II

Integration Practice III

Integration Practice IV

l'Hospital Practice

Failure of L'Hospital's Rule

Lecture 36

Indeterminate forms

A Solid With Finite Volume and Infinite Cross Section

Improper Integrals

Integral of x^n e^(-x)

Lecture 37

Limit of a Series

Comparison Tests

Ratio Test for Convergence

Ratio Test -- Radius of Convergence

Integral Test

Integral Test as Estimation

Lecture 38

Power Series Practice

Finding Taylor's Series

Taylor's Series of a Polynomial

Taylor's Series for sec(x)

Integration of Taylor's Series

Series Calculation Using a Riemann Sum

Lecture 39