Calculus Videos

Video lessons go from why slopes are studied in high school algebra or geometry lessons  to the chain rule and technical discussions of limits.  Some of these videos also appear in area lessons and in volume 3, Why Slopes and More Math, 

1. [Play Video]  80 seconds: Slope Sign Interpretation for Linear Functions. For this and  next few videos, read Chapter 2, Slopes and Ski Trails, in Volume 3., Why Slopes and More Math. See too the appetizers Why Slopes,Excuse the duplication. Some ideas are repeated.
   
2. [Play Video]  2¼ minutes:  Slope Interpretation for a 2D ski hill y = f(x).
   
3. [Play Video]  1¾ minutes: Along a 2D ski trail, How height y = f(x) and slope m = f'(x) both depend on the horizontal coordinate x.
   
4. [Play Video]  2¼ minutes:  Slope Sign Analysis. Example  of how to describe where a 2D hill has increasing height and decreasing height from sign analysis of a linear expression  for the slope (derivative) of a function.

   For this and  next few videos, read Chapters 3 & 4, Slope Sign Analysis and More Sign Analysis, in Volume 3., Why Slopes and More Math.

5. [Play Video]  4¼  minutes: Sign Analysis for  slope given by product of two linear terms, terms that appear here after the factorization of a quadratic.
   
6. [Play Video]  6¾ minutes: Sign Analysis for  slope given by product of three linear terms
   
7. [Play Video]  5 minutes: (coming soon)  Sign Analysis for  slope given by quotient of linear terms
   
8. [Play Video]  5½ minutes: Limits and Error Control for Linear Expressions

   For this and next videos on limits, continuity and derivatives, see chapters 14 to 17 and Appendices E & F  Volume 3., Why Slopes and More Math, 

9. [Play Video]  2¾ minutes: Error Control to N decimal Places, say 5 or 10. see chapter 14 in Volume 3., Why Slopes and More Math.
   
10. [Play Video]  3¼ minutes:  Limits as Error Control for an unlimited number of decimal places.  See chapter 14 in Volume 3., Why Slopes and More Math.
    
11. [Play Video]  4½ minutes: Algebraic View of Limits. Example involving sums and quotients.
    
12. [Play Video]  4½  minutes: Approximating Slope of a tangent line, or taking the approximation to Limit, when possible, to give a definition of the slope of a tangent. Saying how to compute or approximate a number or quantity defines. See chapters 15 & 16 in Volume 3., Why Slopes and More Math.
    
13. [Play Video]  3 minutes:  Common changes of notation in the limits that yield the slope or derivative.
    
14. [Play Video]  2¼  minutes: Derivative as a Limit of a Quotient. First pass at finding the derivative or slope of  f(x) = x². Algebraic View. See Chapter 15 in Volume 3., Why Slopes and More Math. for this first pass and the next two.
    
15. [Play Video]  2¼  minutes: Second pass at finding the derivative or slope of  f(x) = x² .at two values of x. Numerical Examples of Limit Evaluation to suggest a pattern.
    
16. [Play Video]  3¾ minutes:  Third pass at finding the derivative or slope of  f(x) = x². Back to the algebraic view and a conclusion.
    
17. [Play Video]  2½   minutes: Algebraic Properties of Limits I.
    
18. [Play Video] 2¼ minutes: Algebraic Properties of Limits II.
    
19. [Play Video]  2 minutes: Product and Quotient Rules for Differentiation. Statement Only
    
20. [Play Video] 2½  minutes: Product Rule for Differentiation,  indication of proof (why it holds)
    
21. [Play Video] 2½  minutes: Derivative of a Linear Expression cx+d via Limits.
    
22. [Play Video] 2¼ minutes: Derivative of x³ algebraically via Limits.
    
23. [Play Video]  3½ minutes: Three Notations for derivatives, prime, functional or Liebniz y' = y'(x) = ^dy/_dx
    
24. [Play Video]  4¾ minutes:  Why ^d/_dx (xⁿ) = n x^n-1 - Proof by mathematical induction.
    
25. [Play Video]  4¾ minutes:  Derivative of Polynomials, Three Examples.
    
26. [Play Video]  4 minutes:  Using the Quotient Rule, Example with linear expression and quadratic as numerator and denominator.
    
27. [Play Video]  4¼ minutes: Why ^d/_dx (uⁿ) = n u^{n-1 du}/_dx - Proof by mathematical induction. (Chain-Rule for Powers)
    
28. [Play Video] 1 minutes: 1st Example using rule ^d/_dx (uⁿ) = n u^{n-1 du}/_dx -
    
29. [Play Video] 1¾ minutes: 2nd Example using rule ^d/_dx (uⁿ) = n u^{n-1 du}/_dx -
    
30. [Play Video]  1¾ minutes: 3rd Example using rule ^d/_dx (uⁿ) = n u^{n-1 du}/_dx -
    
31. [Play Video]  2½  minutes: Chain Rule for Polynomials as outer function.
    
32. [Play Video] 2½  minutes: (i) Derivatives of ln(x), e^x, cos(x) and sin(x) and (ii) Chain Rule for general outer functions.
    
33. [Play Video] 2½ minutes: Chain Rule Examples with y = sin(3x) and y = ln( x²+1). 
    
34. [Play Video]  2¼ minutes: Derivatives of ln(x), a^x  and 5^x using the formulas  a^x  = e^{x ln(a)}  and the chain rule when a >0  is not a function of x.  Exercise find the derivative of g(x)^f(x) =  e^f(x)ln(g(x)) using the chain rule twice. Assume g(x) > 0 for all x.
    
35. [Play Video]  3½ minutes: More Chain Rule Examples - cases where the chain rule is applied separately to terms in a  sum.
    
36. [Play Video]  7 minutes: Graphing a Cubic y = x³ - 3x² + 2x+1 using values of the  function at the y intercept, and local maximums and local minimums after locating the latter using slope (or derivative) sign analysis or the first derivative  test for maxs and mins. (Example not choosen for easy numerical evaluation of y)
    

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More Calculus
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Calculus Videos
0.   First Calculus Preview
0. Triangle Inequality
0 Inequalities
0. Solving Inequalities
1. Distance+Midpt Formulas
1. Function Domains
1.Polynomial Domain+Range
1. Fn:  Linear Combinations
1. Fn Composition II
1. Fn Composition I
1. Solving y**n = x**m
2 .Real Numbers
2. Limits Numerical View
2. Limits,. Formal Definition
2. Limit Properties Numerically
2. Decimal View of Limits
2. Error Control View
2. Limits & Continuity
2. Limit Vals via Substitution
2. Limits & Composite Fns
2.. Limit Examples
2. One Sided Limits
2. Infinity and Limits
2. Parameters in Limits
3. Derivative Motivation
3.  Derivative Definition I
3. Derivatives Definition II
3. Calculus: Why Radians
3 d/dx of sin(x) & cos(x)  (I)
3 d/dx of sin(x) & cos(x) (II)
3.Sum Rule
3. Product Rule
3. Power Rule
3. Previous Rules Combined
3. d/dx for Polynomials
3. Reciprocal Rule
3. Reciprocal Law: sec & csc
3. Reciprocals & Power Rule
3. Power Law for Integers < 0
3. Quotient Rule
3. Quotient Rule Examples
3. Quotient Rule: tan & cot
3.  Linear Chain Rule
3. Chain Rule for Powers
3. Chain Rule - Polynomials
3. Chain Rule Examples I
3. Chain Rule Examples II
3. Linear Approximation I
3. General Chain Rule
3. Inverse Fns Derivatives
3. Chain Rule: ln(x) & exp(x)
3. Square & Cube Roots
4.  Linear Approximation
4. Second Derivative Test
4. Sketch y = x^3 - 6x^2- 12x
4. Sketch y = x^3 - 3 x^2 - 9x
4. Sketch y = 1 - 1/(1+x^2)
5. Indefinite Integrals A
5. Indefinite Integrals B.
5  Indefinite Integrals C
6. Definite Integral D
6. Area Under Curves
7. Volume of a Sphere

To Learn More, visit Volumes 2 and 3.

Advanced Topics

Limit Properties Algebraically
Pigeon Hole Principle
Bolzano
Constant Difference Thm
Continuous Functions
Rational Functions
Mean Value Theorem
One Side Range Theorem
Range On One Side
From Lipschitz Continuity

To Learn More: Visit Real Analysis.

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