Math 201-NYA-05
Differential Calculus

ANNOUNCEMENTS: 

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

Tests
Test #1 - Friday, February 8.
Test #2 - Wednesday, March 13.
Test #3 - Thursday, April 11.

Final Exam - Summary of Topics




MyYouTube

0.  2
9:50
Adding Integers by Hand -
pdf   2:44
Adding Decimals by Hand -
pdf   1:50
Subtracting Integers by Hand -
pdf   3:32
Multiplying Integers by Hand -
pdf   9:31
Dividing Integers by Hand -
pdf   12:13

1. 
1:04:42
Fractions - Introduction -
pdf   6:03
Fractions - Cancelling Common Factors - pdf   7:17
Fractions - Multiplication -
pdf   9:14
Fractions - Addition - pdf   13:38
Fractions - Subtraction  - pdf   3:12
Fractions - Division - pdf   10:24

Fractions & Polynomials: Simplification - 1 - pdf   3:21
Fractions & Polynomials: Simplification - 2 - pdf   3:17
Fractions & Polynomials: Simplification - 3 -
pdf   8:16
2. 
1:03:47
Properties of Exponents - 1 -
pdf   2:53
Properties of Exponents - 2 - pdf   4:44
Properties of Exponents - 3 - pdf   7:02
Properties of Exponents - 4 - pdf   3:52
Properties of Exponents - 5 - pdf   4:11
Properties of Exponents - 6 - pdf   6:17
Simplifying Exponents - pdf   8:06
Simplifying Square Roots - pdf   6:42
Simplifying Cube Roots - pdf   6:05
Simplifying n-th Roots - pdf   3:38
Sketching the Graph of the Square Root - pdf   4:57
Sketching the Graph of the Cube Root -
pdf   5:20
3. 
1:38:05
Difference of Squares - 1
- pdf   4:17
Difference of Squares - 2
- pdf   4:18
Factoring & the Quadratic Formula -
pdf   15:00

Factoring by Inspection -
pdf   6:10
Factoring & Complex Numbers - pdf   6:00
Long Division -
pdf   17:00
The Factor Theorem -
pdf   19:15
The Factor Theorem - Proof - pdf   7:41 
The Factor Theorem - Proof - pdf   30:02 - Optional
Factoring Common Terms - 1 - pdf   4:30
Factoring Common Terms - 2 - pdf   8:14
Factoring Common Terms - 3 -
pdf   5:40
4. 
35:51
Functions & Substitutions -
pdf   17:36
Newton's Quotient -
pdf   18:15
5-7. 
1:08:04
Limits - Introduction - pdf   14:55
Limits - Properties - pdf   5:25
Limits - Piecewise Functions - pdf   7:45
Limits - Numerical Experimentation - pdf   12:50
Limits - Factoring - pdf   11:44
Limits - Conjugation - pdf   15:25
8.  2
7:59
Undefined Limits - Part 1 - pdf   15:52
Undefined Limits - Part 2 - pdf   12:07
9.  58:57
Limits at Infinity - Introduction 1
- pdf   2:27
Limits at Infinity - Introduction 2
- pdf   3:35
Limits at Infinity - Example 1
- pdf   3:29
Limits at Infinity - Example 2
- pdf   2:46
Limits at Infinity - Example 3
- pdf   3:10
Limits at Infinity - Example 4
- pdf   2:58
Limits at Infinity - Example 5
- pdf   3:17
Limits at Infinity - Remark
- pdf   6:31
Limits at Infinity - Example 6
- pdf   5:11
Limits at Infinity - Example 7
- pdf   4:41
Limits at Infinity - Example 8
- pdf   5:49
Limits at Infinity - Example 9
(attempt 1) - pdf   6:24
Limits at Infinity - Example 9
(
attempt 2) - pdf   8:32
10.  1:21:58
Continuity -
pdf   6:03
Discontinuity - Removable -
pdf   20:25
Discontinuity - Jump -
pdf   15:30
Discontinuity - Infinite -
pdf   11:46
Continuity - 2 Examples -
pdf   11:07
Continuity - Extensive Example -
pdf   17:07
11.
  12:36 
Average Velocity
- pdf   3:51
Instantaneous Velocity - Formula 1
- pdf   5:04
Instantaneous Velocity - Formula 2
- pdf   3:41
12. 
1:25:39
The Slope of a Line - 1
- pdf   4:09
The Slope of a Line - 2
- pdf   2:50
The Slope of a Line - 3
- pdf   4:17
The Derivative - Introduction - pdf   5:31
The Derivative - Definition - pdf   7:51  ( Animation)
The Derivative - Example 1 - pdf   13:54  
The Derivative - Example 2 - pdf   16:30
The Derivative - Example 3 - pdf   10:57
Differentiability & Continuity - pdf   19:40
13.  1:48:54
The Constant Rule - Introduction
- pdf   2:15
The Constant Rule - Proof
- pdf   2:10
The Constant Rule - Example 1
- pdf   1:42
The Power Rule - Introduction
- pdf   1:21
The Power Rule - Proof
- pdf   6:46
The Power Rule - Examples
- pdf   4:01
The Constant Multiple Rule - Introduction
- pdf   1:23
The Constant Multiple Rule - Proof
- pdf   2:22
The Constant Multiple Rule - Example 1
- pdf   3:10
The Sum/Difference Rule - Introduction
- pdf   1:39
The Sum/Difference Rule - Proof
- pdf   3:22
The Sum/Difference Rule - Example 1
- pdf   2:37
The Product Rule - Introduction
- pdf   1:51
The Product Rule - Extended
- pdf   4:04
The Product Rule - Proof
- pdf   9:09
The Product Rule - Example 1
- pdf   4:18
The Product Rule - Example 2
- pdf   3:55
The Product Rule - Example 3
- pdf   4:33
The Quotient Rule - Introduction
- pdf   1:58
The Quotient Rule - Proof
- pdf   6:11
The Quotient Rule - Example 1
- pdf   2:38
The Quotient Rule - Example 2
- pdf   6:40
The Chain Rule - Introduction
- pdf   2:32
The Chain Rule - Proof
- pdf   3:36
The Chain Rule - Example 1
- pdf   3:12
The Chain Rule - Example 2
- pdf   2:21
The Chain Rule - Example 3
- pdf   1:57
The Chain Rule - Example 4
- pdf   4:09
The Chain Rule - Example 5
- pdf   5:23
The Chain Rule - Example 6
- pdf   7:42

14.  57:40
Implicit Differentiation - Part 1 - pdf   20:36
Implicit Differentiation - Part 2 - pdf   11:28
Implicit Differentiation - Part 3 - pdf   12:16
Implicit Differentiation - Part 4 - pdf   13:20
15.0  37:40
Review - Sin(x) - pdf   11:18
Review - Cos(x) - pdf   9:11
Review - Tan(x) - pdf   4:33
Review - Trigonometric Identities - pdf   5:24
Sine & Cosine of π/4 - pdf   2:59
Since & Cosine of π/3 and π/6 - pdf   4:15
15.  1:09:54
Limit of sin(h)/h as h goes to 0 - pdf   16:11
Limit of (1-cos(h))/h as h goes to 0 - pdf   6:23
sin(A+B) & cos(A+B)
- pdf   15:06
The Derivative of Sin(x) - pdf   7:23
Derivatives of Trig. Functions - pdf   24:51
16.0  45:38
Logarithms - Definition - pdf   3:29
Logarithms - Graph (Part 1) - pdf   6:54
Logarithms - Graph (Part 2) - pdf   5:22
Logarithms - Fundamental Properties - pdf   2:06
Logarithms - Proof of Property 1 - pdf   0:52
Logarithms - Proof of Property 2 - pdf   2:13
Logarithms - Proof of Property 3 - pdf   2:10
Logarithms - Proof of Property 4 - pdf   2:48
Logarithms: Simplification - 1 - pdf   3:01
Logarithms: Simplification - 2 - pdf   4:16
Logarithms: Simplification - 3 - pdf   4:10
Logarithms: Expansion - pdf   8:17
16.  1:07:27
d/dx of Exp. & Log. Functions - Part 1 - pdf   23:39
d/dx of Exp. & Log. Functions - Part 2 - pdf   10:15
d/dx of Exp. & Log. Functions - Part 3 - pdf   12:18
d/dx of Exp. & Log. Functions - Part 4 - pdf   21:15
17.  29:14
Logarithmic Differentiation -
pdf   29:14
18.  1:01:17
d/dx of Inverse Trig. Functions - Part 1 - pdf   23:28
d/dx of Inverse Trig. Functions - Part 2 - pdf   24:43
d/dx of Inverse Trig. Functions - Part 3pdf   13:06  
19-20.  1
:19:19
The Derivative & Other Variables - pdf   15:26
Related Rates - Problem 1 - pdf   13:37
Related Rates - Problem 2 - pdf   15:08
Related Rates - Problem 3 - pdf   16:29
Related Rates - Problem 4 - pdf   18:39
21. 
34:24
Differentials - Definition - pdf   7:10
Differentials - Geometric Meaning
- pdf   6:43
Differentials & Uncertainty - 1
- pdf   3:48
Differentials & Uncertainty - 2.1
- pdf   7:49
Differentials & Uncertainty - 2.2
- pdf   8:54

22. 
26:18
Linear Approximation - Approach 1 - pdf   6:45
Linear Approximation - Approach 2
- pdf   4:39
Linear Approximation - Example 1
- pdf   7:44
Linear Approximation - Example 2
- pdf   7:10
23.  1:39:23
L'H˘pital's Rule - Introduction - pdf   8:29
L'H˘pital's Rule - Heuristic 1
- pdf   5:03
L'H˘pital's Rule - Heuristic 2 - pdf   7:40 (Optional)
L'H˘pital's Rule: Basic Example - 1 - pdf   5:42
L'H˘pital's Rule: Basic Example - 2 - pdf   4:55
L'H˘pital's Rule: Basic Example - 3 - pdf   4:00
L'H˘pital's Rule: Basic Example - 4 - pdf   2:29
L'H˘pital's Rule: Special Case - 1 (Type 1) - pdf   6:06
L'H˘pital's Rule: Special Case - 2 (Type 1) - pdf   5:38
L'H˘pital's Rule: Special Case - 3 (Type 1) - pdf   10:52
L'H˘pital's Rule: Special Case - 1 (Type 2) - pdf   14:49  
L'H˘pital's Rule: Special Case - 2 (Type 2) - pdf   5:56  
L'H˘pital's Rule: Caution - 1 - pdf   7:17
L'H˘pital's Rule: Caution - 2 - pdf   8:22
L'H˘pital's Rule: Caution - 3 - pdf   9:45
24.  33:59
Vertical and Horizontal Asymptotes - pdf   33:59
25.  40:30
Higher Derivatives - Introduction - pdf   7:19
Higher Derivatives - Simplification - pdf   22:15
Higher Derivatives & Implicit Differentiation - pdf   10:56
26.  3:18:48
Curve Sketching - Introduction
- pdf   9:17
The Second Derivative - Concave Up
- pdf   4:27
The Second Derivative - Concave Down
- pdf   3:47
Critical Points
- pdf   5:22
Inflection Points
- pdf   6:22
Classifying Critical Points
- pdf   12:37
Curve Sketching - Example 1
- pdf   17:29
Curve Sketching - Example 2
- pdf   20:50
Curve Sketching - Example 3
- pdf   18:28
Curve Sketching - Example 4
- pdf   35:30
Curve Sketching - Example 5
- pdf   38:42
Curve Sketching - Example 6
- pdf   25:57
27.  51:25
Extrema - Introduction - pdf   18:00
Extrema - Example 1 - pdf   7:30
Extrema - Example 2 - pdf   11:20
Extrema - Example 3 - pdf   14:35
28.  2:28:54
Optimization - Example 1 - pdf   10:44
Optimization - Example 2 - pdf   13:43
Optimization - Example 3 - pdf   22:00
Optimization - Example 4 - pdf   15:55
Optimization - Example 5 - pdf   15:16
Optimization - Example 6 - pdf   16:57
Optimization - Example 7 - pdf   25:02
Optimization - Example 8 - pdf   29:17
29. 
1:00:55
Rolle's Theorem - pdf   15:58
Mean Value Theorem - pdf   21:08
Mean Value Theorem - Example 1 - pdf   5:18
Mean Value Theorem - Example 2 - pdf   5:35
Mean Value Theorem - Example 3 - pdf   3:42
Mean Value Theorem - Example 4 - pdf   4:55
Mean Value Theorem - Example 5 - pdf   4:19

Review
Multiplication Table
Trigonometry
Logarithms
Review Quiz
(without answers)
Review Quiz (with answers)
Review Document


Problem Sheets:
Additional problems are strongly recommended.
1
- Fractions
- additional problems
2- Exponents
- additional problems
3- Factoring
- additional problems
4- Functions & Newton's Quotient
- additional problems
5- Limits Graphically
6- Limit of a Function - Part I
7-  Limit of a Function - Part II
8- Undefined Limits
9- Limits at Infinity
10- Continuity
11- Velocity & Tangent Lines
12- Limits & the Derivative
13- Rules of Differentiation
14- Implicit Differentiation
(Without curves)
       Implicit Differentiation (With Curves)
15.0 - Review of Trigonometry
15- Derivatives of Trigonometric Functions
16.0 - Review of Logarithms
16- Derivatives of Exponential & Logarithmic Functions
17- Logarithmic Differentiation
18- Derivatives of Inverse Trigonometric Functions
19- Related Rates - Part I
20- Related Rates - Part II
(Optional)
21- Differentials
22- Linear Approximation
23-
L'H˘pital's Rule
24-
Asymptotes
25-
Higher Derivatives
26- Curve Sketching
27- Extrema
28- Optimization
29- The Mean Value Theorem


Class Notes (Under construction...)
Limits
Limits - Numerically
Continuity
Velocity
The Derivative
The Derivative - Animation
Rules of Differentiation
Law of Cosines - Proof
Law of Sines - Proof
Derivatives of Trig. Functions
Summary of Differentiation
L'H˘pital's Rule
Curves Sketching - Steps to Follow
Extrema a Function


Maple Help Files (Optional)
Introduction
Limits & Continuity
Derivatives
Loops
If Statements
Procedures