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Integral Calculus: notes and resources

http://gauss.vaniercollege.qc.ca/~kritchevski/cal2/

Eugene Kritchevski, Vanier College, last updated on April 18, 2016

This page contains links to freely available resources (notes, applets, videos, textbooks,...) that are useful for studying or teaching Integral Calculus.

Resources by topic

Generalities on summation (sigma notation, properties of sums, telescoping sums, sums of powers of integers)
notes on summation
Riemann sums
notes on Riemann Sums

worksheet on Riemann sums (Isaac Sabbah)
Fundamental Theorem of Calculus
Geogebra Applet - concept of the area function in FTC1

Substitution
notes on substitution, with practice problems

video on substitution (Selwin Hollis)

worksheet on integration by substitution (Isaac Sabbah)
Integration by Parts
notes on integration by parts, with practice problems

video on integration by parts (Selwin Hollis)

worksheet on integration by parts (Isaac Sabbah)
Areas Between Curves
notes on areas between curves - including applets, practice problems and link to a video
Volumes
notes on volume by disks

Geogebra applet - disk method example: volume of a cone

Geogebra applet - disk method example: volume of a sphere

Geogebra applet - cylindrical shells example: volume of a Torus

Geogebra applet - cylindrical shells example: rotating $\set{0 \leq x \leq \sqrt{\pi}, 0 \leq y \leq \sin(x^2)}$ about the $y$-axis

video on volumes by slicing in general (Selwin Hollis)

video on volumes by disks/washers (Selwin Hollis)

video on volumes by cylindrical shells (Selwin Hollis)

section on on volumes by cylindrical shells freely available from stewartcalculus.com

worksheet on volumes (Isaac Sabbah)
Trigonometric Integrals
section on trigonometric integrals freely available from stewartcalculus.com

Trigonometric Substitution
notes on arsin and on the substitution for $\sqrt{r^2-y^2}$

section on trigonometric substitution freely available from stewartcalculus.com

video on trigonometric substitution (Selwin Hollis)

worksheet on trigonometric substitution (Isaac Sabbah)
Partial Fractions
Geogebra Applet - 3 dictinct linear factors

GeoGebra Applet - repeated linear factors

video on partial fractions (Selwin Hollis)

worksheet on partial fractions (Isaac Sabbah)
Differential Equations
GeoGebra Applet - first order differential equations

worksheet on differential equations (Isaac Sabbah)
Note for questions 4.(4) and 4.(5) in the worksheet: replace $dy$ with $y'$ in the question.

L'Hospital's Rule
Improper Integrals
worksheet on improper integrals (Isaac Sabbah)
Sequences
Introductory examples of sequences - notes

video on Sequences - Part 1 (Selwin Hollis)

video on Sequences - Part 2 (Selwin Hollis)
Series
Watch the videos on series (Selwin Hollis) starting from video 49.

worksheet on series (Isaac Sabbah)

Review material

Strategy for Integration, section freely available from stewartcalculus.com

worksheet on integration review (Isaac Sabbah)

Appendices

proof of trigonometric identities

Other freely available resources on the web

A complete set of Video Lectures for Single-variable Calculus created by Selwin Hollis, Armstrong State University. These videos (and a set of videos on differential equations) are also available for free on iTunes U.

A list of open source textbooks (Calculus and other subjects) approved by the American Institute of Mathematics.

Paul's Online Math Notes.

Calculus notes used at the University of British Columbia, written by Joel Feldman and Andrew Rechnitzer.

Course materials from John Abbott College.