Math 201-203-RE
Integral Calculus

ANNOUNCEMENTS: 

Term Schedule
Office Hours
Offline Web Page
Academic Calendar 
Course Outline
Math Department Web Page

Tests
Test #1 -
Thursday, September 13.
Test #2 - Wednesday, October 17.

Test #3 - Monday, November 19.

Final Exam - Summary of Topics



MyYouTube
1.
Review of Differentiation - 1
- pdf
Review of Differentiation - 2
- pdf
Review of Differentiation - 3
- pdf
Review of Differentiation - 4
- pdf
Review of Differentiation - 5
- pdf
Review of Differentials
- pdf
Review of Limits at Infinity
- pdf
Review of L'H˘pital's Rule - 1
- pdf
Review of L'H˘pital's Rule - 2
- pdf
Review of L'H˘pital's Rule - 3
- pdf
2.
Antiderivatives - 1
- pdf
Antiderivatives - 2
- pdf
Simple Differential Equation - 1
- pdf
Simple Differential Equation - 2
- pdf
Indefinite Integrals - 1
- pdf
Indefinite Integrals - 2
- pdf
Indefinite Integrals - 3
- pdf
Indefinite Integrals - 4
- pdf
Indefinite Integrals - 5
- pdf
3.
Sigma Notation - 1
- pdf
Sigma Notation - 2
- pdf
Riemann Sum - 1
- pdf
Riemann Sum - 2
- pdf
Riemann Sum - 3
- pdf
The Definite Integral
- pdf
4.
The Fundamental Theorem of Calculus - Introduction
- pdf
The Fundamental Theorem of Calculus - Notation
- pdf
The Fundamental Theorem of Calculus - Proof
- pdf
The Fundamental Theorem of Calculus - Example 1
- pdf
The Fundamental Theorem of Calculus - Example 2
- pdf  (Additional)
  
(Example 2 is a slightly more elaborate example than 1.)
The Fundamental Theorem of Calculus - Example 3 -
pdf
Average Value of a Function
- pdf
Mean Value Theorem of Integration
- pdf  (Optional)
MVT of Integration - Comment
- pdf  (Optional)
Limits & the Fundamental Theorem of Calculus
- pdf  (Optional)
5.
U-Substitution - 1
- pdf
U-Substitution - 2
- pdf
U-Substitution - 3
- pdf
U-Substitution - 4
- pdf
U-Substitution - 5
- pdf
U-Substitution - 6
- pdf
U-Substitution - 7
- pdf
U-Substitution - 8
- pdf
U-Substitution & Trig. Functions - 1
- pdf
U-Substitution & Trig. Functions - 2
- pdf
6.
Integration by Parts - 1
- pdf
Integration by Parts - 2
- pdf
Integration by Parts - 3
- pdf
Integration by Parts - 4
- pdf
Integration by Parts - 5
- pdf
Integration by Parts - 6
- pdf (Optional)
7.
Area Between Curves - 1
(Solution 1) - pdf
Area Between Curves - 1
(Solution 2) - pdf
Area Between Curves - 2
(Solution 1) - pdf
Area Between Curves - 2
(Solution 2) - pdf
Area Between Curves - 3 -
pdf
Area Between Curves - 4 -
pdf  (Optional)
8.
Solids of Revolution - Disk -
pdf
Solids of Revolution - Washer -
pdf
Solids of Revolution - Shell -
pdf
Solids of Revolution - Problem 1
- pdf
Solids of Revolution - Problem 2
- pdf
Solids of Revolution - Problem 3
- pdf
Solids of Revolution - Problem 4
- pdf

Solids & Cross Sections - 1 -
pdf (Optional)
Solids & Cross Sections - 2 -
pdf (Optional)
Solids & Cross Sections - 3 -
pdf (Optional)
9.
Trigonometric Integrals - 1
- pdf
Trigonometric Integrals - 2
- pdf
Trigonometric Integrals - 3
- pdf
Trigonometric Integrals - 4
- pdf
Trigonometric Integrals - 5
- pdf
Trigonometric Integrals - 6
- pdf
Trigonometric Integrals - 7
- pdf
10.
Completing Squares
- pdf

11.
(Optional)
Trigonometric Substitutions - Introduction
- pdf
Trigonometric Substitutions - 1
- pdf
Trigonometric Substitutions - 2
- pdf
Trigonometric Substitutions - 3
- pdf
Trigonometric Substitutions - 4
- pdf
Trigonometric Substitutions - 5
- pdf
Trigonometric Substitutions - 6
- pdf
Trigonometric Substitutions - 7
- pdf

12.
Partial Fractions: Introduction - 1
- pdf
Partial Fractions: Introduction - 2
- pdf
Partial Fractions: Example 1
- pdf
Partial Fractions: Example 2
- pdf
Partial Fractions: Example 3
- pdf
Partial Fractions: Special Integral - 1
- pdf
Partial Fractions: Irreducibility & Discriminant
- pdf
Partial Fractions: Example 4
- pdf
Partial Fractions: Example 5
- pdf
Partial Fractions: Special Integral - 2
- pdf
Partial Fractions: Example 6
- pdf
13.
Rationalizing Substitutions - 1
- pdf
Rationalizing Substitutions - 2
- pdf
Rationalizing Substitutions - 3
- pdf
14.
Separable Differential Equations - 1
- pdf
The Slope of Orthogonal Lines
- pdf  (Optional)
Orthogonal Families of Curves - 1
- pdf  (Optional)
Orthogonal Families of Curves - 2
- pdf  (Optional)
15.
Arc Length - 1
- pdf  (Formula - Intuitive Derivation)
Arc Length - 2
- pdf  (Formula - Rigorous Derivation)
Arc Length - 3
- pdf
Arc Length - 4
- pdf

Surface Area - Introduction
- pdf  (Optional)
Surface Area - Example
- pdf  (Optional)
16.
Improper Integrals - Introduction -
pdf
Improper Integrals of Type 1 - Example 1
- pdf
Improper Integrals of Type 1 - Example 2
- pdf
Improper Integrals of Type 1 - Example 3
- pdf
Improper Integrals of Type 1 - Example 4
- pdf
Improper Integrals of Type 2 - Example 1
- pdf
Improper Integrals of Type 2 - Example 2
- pdf
Improper Integrals of Type 2 - Example 3
- pdf

The Comparison Theorem - Introduction
- pdf  (Optional)
The Comparison Theorem - Example 1
- pdf  (Optional)
The Comparison Theorem - Example 2
- pdf  (Optional)
The Comparison Theorem - Example 3
- pdf  (Optional)
The Comparison Theorem - Example 4
- pdf (Optional)
17.
Continuous Random Variables - PDF
- pdf
Continuous Random Variables - Mean
- pdf
Continuous Random Variables - Variance
- pdf
Continuous Random Variables: Example - Part 1
- pdf
Continuous Random Variables: Example - Part 2
- pdf
Continuous Random Variables: Example - Part 3
- pdf
18.
Sequences - Introduction
- pdf
Sequences - Convergence
- pdf
Sequences & L'H˘pital's Rule
- pdf
Geometric Sequences & Convergence - Intuition
- pdf
Geometric Sequences - Examples
- pdf
Geometric Sequences & Convergence - Proof
- pdf  (Optional)
The Factorial - Introduction
- pdf
The Factorial - Magnitude
- pdf  (Optional)
Hierarchy of Functions
- pdf
The Squeeze Theorem - 1
- pdf
The Squeeze Theorem - 2
- pdf
Bounded Sequences
- pdf
Monotonic Sequences
- pdf
Monotone Convergence Theorem - Intuition
- pdf
Monotone Convergence Theorem - Example
- pdf
The Harmonic Series
- pdf
19.
Introduction to Series - 1
- pdf
Introduction to Series - 2
- pdf
Properties of Convergent Series
- pdf
Geometric Series - Formula
- pdf
Geometric Series - Examples
- pdf
Finite Geometric Sums
- pdf
Geometric Series & Decimal Expansion
- pdf
Telescoping Series
- pdf
Divergence Theorem - Introduction -
pdf
Divergence Theorem - Proof -
pdf
Divergence Theorem - Examples
- pdf
20.
Geometric Series & Compounded Interests - 1
- pdf
Geometric Series & Compounded Interests - 2
- pdf
Geometric Series & Compounded Interests - 3
- pdf
Geometric Series & Compounded Interests - 4
- pdf
21.
Convergence & Ignoring Terms
- pdf
The Integral Test - Proof
- pdf
The Integral Test - Example 1
- pdf
The Integral Test - Example 2
- pdf
P-Series - Proof
- pdf
P-Series - Examples
- pdf
Series of Positive Terms - Intuition
- pdf
The Comparison Test - Intuition
- pdf
The Comparison Test - Example 1
- pdf
The Comparison Test - Example 2
- pdf
The Comparison Test - Example 3
- pdf
The Limit Comparison Test - Intuition
- pdf
The Limit Comparison Test - Proof
- pdf  (Optional)
The Limit Comparison Test - Example 1
- pdf
The Limit Comparison Test - Example 2
- pdf
The Limit Comparison Test - Example 3
- pdf
Alternating Series - Introduction
- pdf
Alternating Series Test - Introduction
- pdf
Alternating Series Test - Proof
- pdf  (Optional)
Alternating Series Test - Example 1
- pdf
Alternating Series Test - Example 2
- pdf
Alternating Series Test - Example 3
- pdf
Alternating Series & Error Estimate - Example
- pdf
Alternating Series & Error Estimate - Proof
- pdf  (Optional)
22.
Absolute Convergence - Introduction
- pdf
Absolute Convergence Test - Proof
- pdf
Absolute vs Conditional Convergence - Introduction
- pdf
Absolute vs Conditional Convergence - Example 1
- pdf
Absolute vs Conditional Convergence - Example 2
- pdf
The Ratio Test - Introduction
- pdf
The Ratio Test - Proof of Part (a)
- pdf  (Optional)
The Ratio Test - Proof of Part (b)
- pdf  (Optional)
The Ratio Test - Proof of Part (c)
- pdf  (Optional)
The Ratio Test - Example 1
- pdf
The Ratio Test - Example 2
- pdf
The Ratio Test - Example 3
- pdf
The Root Test - Introduction
- pdf
The Root Test - Proof of Part (a)
- pdf  (Optional)
The Root Test - Proof of Part (b)
- pdf  (Optional)
The Root Test - Proof of Part (c)
- pdf  (Optional)
The Root Test - Example 1
- pdf
The Root Test - Example 2
- pdf
The Root Test - Example 3
- pdf

Rearrangement - Introduction
- pdf  (Optional)
Riemann's Rearrangement Theorem - Introduction
- pdf  (Optional)
Riemann's Rearrangement Theorem - Example
- pdf  (Optional)
23.
Power Series: Introduction - 1
- pdf
Power Series: Introduction - 2
- pdf
Power Series: Introduction - 3
- pdf
Interval of Convergence - 1
- pdf
Interval of Convergence - 2
- pdf
Interval of Convergence - 3
- pdf
Differentiation & Integration - Introduction
- pdf
Differentiation & Integration - Part (a)
- pdf
Differentiation & Integration - Part (b)
- pdf
Differentiation & Integration - Part (c)
- pdf
24.
Maclaurin & Taylor Series - Introduction
- pdf
Maclaurin Series - Example 1
- pdf
Maclaurin Series - Example 2
- pdf
Maclaurin Series - Example 3
- pdf
Maclaurin Series & Limits - 1
- pdf (Optional)
Maclaurin Series & Limits - 2
- pdf (Optional)
Maclaurin Series & Higher Derivatives
- pdf  (Optional)
25.
Taylor Series - Example 1
- pdf
Taylor Series - Example 2
- pdf
Taylor Series - Example 3
- pdf  (Optional)
Taylor's Theorem - Introduction
- pdf  (Optional)
Taylor's Theorem - e^x
- pdf  (Optional)

Documents 
Summary of Differention Rules
Trigonometric Functions & Identities
9. Trigonometric Integrals - Help

12. Partial Fractions - Method
19-22. Series - Summary of Tests


Problem Sheets

1- Review
2- Antiderivatives
3-
Riemann Sums and the Definite Integral
4-
The Fundamental Theorem of Calculus
5-
U-Substitutions
6-
Integration by Parts
7-
Area Between Curves
8-
Solids of Revolution
9-
Trigonometric Integrals
10 - Completing Squares
11-
Trigonometric Substitutions (Optional)
12-
Partial Fractions
13-
Rationalizing Substitutions
14-
Differential Equations
15-
Arc Length
16-
Improper Integrals
17-
Probability
18-
Sequences
19-
Series (Part 1)
20-
Applications of Geometric Series
21- Series (Part 2)
22-
Series (Part 3)
23- Power Series
24- Maclaurin Series
25- Taylor Series