Math 201-103-RE
Differential Calculus

ANNOUNCEMENTS: Test #3 is on Tuesday, November 19.

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


* All documents (videos, transcripts, problem sheets and class notes) can be downloaded directly from any school computer.
   The folder can be found by accessing the public drive. The exact pathway is: P:\Courses\pcamire\Math 103.
   The total size is about 40 GB. 

Tests
Test #1 - Monday, September 16.
Test #2 - Friday, October 11.
Test #3 - Tuesday, November 19.
Final Exam - Summary of Topics




MyYouTube

0.  29:50
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. 
15:52
Undefined Limits - Part 1 - pdf   15:52
Undefined Limits - Part 2 - pdf   12:07 - Optional
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. 
44:20
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 - Optional
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 
40:16
Logarithms - Definition - pdf   3:29
Logarithms - Graph (Part 1) - pdf   6:54
Logarithms - Graph (Part 2) - pdf   5:22 - Optional
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. 
38:53
d/dx of Inverse Trig. Functions - Part 1
- pdf   23:28
d/dx of Inverse Trig. Functions - Part 2
- pdf   24:43 - Watch up to 15:25.
d/dx of Inverse Trig. Functions - Part 3
pdf   13:06 - Optional 
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. 
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
22.
  42:11
Supply & Demand Function - pdf   6:45
Market Equilibrium
- pdf   3:46
Elasticity of Demand - Introduction
- pdf   13:46
Elasticity of Demand - Example
- pdf   6:32
Elasticity of Demand & Marginal Revenue
- pdf   11:22
23. 
30:28
Differentials - Definition - pdf   7:10
Differentials - Geometric Meaning
- pdf   6:43
Differentials & Change in Revenue -
pdf   16:35
Differentials & Uncertainty - 1
- pdf   3:48  - Optional
Differentials & Uncertainty - 2.1
- pdf   7:49 - Optional
Differentials & Uncertainty - 2.2
- pdf   8:54 - Optional
24.  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
(Optional)
L'H˘pital's Rule: Special Case - 1 (Type 2) - pdf   14:49
(Optional)
L'H˘pital's Rule: Special Case - 2 (Type 2) - pdf   5:56
(Optional) 
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
25. 
33:59
Vertical and Horizontal Asymptotes - pdf   33:59
26. 
29:34
Higher Derivatives - Introduction - pdf   7:19
Higher Derivatives - Simplification - pdf   22:15
Higher Derivatives & Implicit Differentiation - pdf   10:56 - Optional
27. 
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
28. 
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
29. 
1:34:35
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 - Optional
Optimization - Example 8 - pdf   29:17 - Optional
30. 
0:00
Rolle's Theorem - pdf   15:58 - Optional
Mean Value Theorem - pdf   21:08 - Optional
Mean Value Theorem - Example 1 - pdf   5:18 - Optional
Mean Value Theorem - Example 2 - pdf   5:35 - Optional
Mean Value Theorem - Example 3 - pdf   3:42 - Optional
Mean Value Theorem - Example 4 - pdf   4:55 - Optional
Mean Value Theorem - Example 5 - pdf   4:19 - Optional










Review
Multiplication Table

Trigonometry
Logarithms
Review Quiz
(without answers)
Review Quiz (with answers)
Review Document
(
Optional)


Problem Sheets: Addional 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- Linear Approximation
22- Applications to Business & Economics
23- Differentials & Marginal Analysis
24- L'H˘pital's Rule
25- Asymptotes
26-
Higher Derivatives
27- Curve Sketching
28- Extrema
29- Optimization
30- The Mean Value Theorem
(Optional)


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


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