Calculus I CD Contents


Cd List

The table of contents for each CD is listed under the respective link.

#Gen 1

CD #2: Calculus I, #'s 3-7

Cd #3: Calculus I, #'s 8-12

Cd #4: Calculus I, #'s 13-16

Cd #5: Calculus I, #'s 19-21

CD #6: Calculus I, #'s 22-25

CD #7:  Calculus I, #'s 26-29

CD #8:  Calculus I, #'s 30-33

CD #9:  Calculus I, #'s 34-38

CD #10:  Calculus I, #'s 39-41


Gen 1 Calculus Video Clips

Calculus Week 1 Video Clip 01 flow: is depth changing at increasing, decreasing or const rate? What about range?

Calculus Week 1 Video Clip 02 which graph shape (if any) best represents the depth vs. clock time?

Calculus Week 1 Video Clip 03 we observe data in long tube, 90 cm to 0 cm; data is average over class observations, not too reliable

Calculus Week 1 Video Clip 04 graph

Calculus Week 1 Video Clip 05 calculate `dy / `dt values

Calculus Week 1 Video Clip 06 calculate slope, interpret

Calculus Week 1 Video Clip 07 summarize from table to graph, show slopes between successive points

Calculus Week 1 Video Clip 08 Physics says that we can model data with a quadratic model

Calculus Week 1 Video Clip 09 creating model: select three points, obtain system of 3 simul. lin. eq. for parameters

Calculus Week 1 Video Clip 10 solving the equations: reducing system to 2 eq.

Calculus Week 1 Video Clip 11 reducing 2 eq. to 1, solving 1

Calculus Week 1 Video Clip 12 back substitution

Calculus Week 1 Video Clip 13 questions to ask of model

Calculus Week 1 Video Clip 14 answers to questions: graphical

Calculus Week 1 Video Clip 15 when depth is 0

Calculus Week 1 Video Clip 16 what is y when t=30, when is y=42?

Calculus Week 1 Video Clip 17 modeling rate of depth change by function: finding the two points

Calculus Week 1 Video Clip 18 calculating the slope, the ave. rate of change

Calculus Week 1 Video Clip 19 goal: exact rate at t = 10. calculating rate over a shorter time interval

Calculus Week 1 Video Clip 20 symbolizing the shortening of the interval, calculating y in symbols

Calculus Week 1 Video Clip 21 calculating the slope in symbols

Calculus Week 1 Video Clip 22 taking the limit

Calculus Week 1 Video Clip 23 arbitrary point t: finding y(t+`dt); student should complete.

Calculus Week 1 Video Clip 24 another model: finding y(t+`dt) - y(t), cancellation of all of y(t)

Calculus Week 1 Video Clip 25 completing `dy / `dt, taking limit

Calculus Week 1 Video Clip 26 the connection between the original model and the rate function, dy/dt and y'(t) notations.


CD #2: Calculus I, #'s 3-7

Lecture #3:  The Rate of Change of a Quadratic Depth Function:   Differentiation and Integration

Lecture #4:  The Concepts of Differentiation and Integration in the Context of Rate Functions

Lecture #5:  :  Growth of an Exponential Function; Trapezoidal Representation of Approximate Derivatives and Integrals

Lecture #6:  Project #3;   Derivative of y = a x^3; The Differential

Lecture #7:  The Differential; Tangent Line Approximation to Differential


Cd #3: Calculus I, #'s 8-12

#08:  Lecture #08: Text problems; First Introduction to Differential Equations

#09:  Lecture #09:  Text problems; Introduction to Natural Logarithms and Composite Functions; Numerical Solution of Differential Equations

#10:  Lecture #10:  Predictor-corrector methods; Sine and Cosine functions

#11:  Lecture #11:  Trigonometric Functions; Brief Intro. to Polynomials

#12:  Lecture #12:  Rational Functions, Continuity


Cd #4: Calculus I, #'s 13-16

#13:  The Derivative

#14:   The Derivative Function

#15:   Interpretation of the Derivative; the Second Derivative

#16:   Second Derivative


CD #5: Calculus I, #'s 19-21

#19:   Review Notes for Test

#20:   The Fundamental Theorem of Calculus; Derivatives of Polynomials

#21:   The Fundamental Theorem of Calculus; Derivatives of Polynomials


CD #6:  Calculus I, #'s 22-25

#22:   Product and Quotient Rules

#23:   The Chain Rule

#24:   The John Glenn Launch:  A review of proportionality and integration; Trigonometric Functions

#25:   Trigonometric Functions; Applications of Chain Rule; Inverse Functions


CD #7:  Calculus I, #'s 26-29

#26:   Inverse Functions; Chain Rule; Implicit Differentiation

#27:   Implicit Differentiation; Tangent Line Approximation; l'Hopital's Rules

#28:   Implicit Differentiation; Maxima, Minima and Inflection Points

#29:   Local Maxima and Minima; Families of Functions


CD #8:  Calculus I, #'s 30-33

#30:   Families of Functions; Optimization

#31:   Optimization

#32:   Optimization; Completeness Axiom; Limits

#33:   Limits, Differentiability, Review


CD #9:  Calculus I, #'s 34-38

#34:   Test Review (includes practice test)

#35:    Class Review (continued)

#36:   Marginality; Modeling Problems

#37:   Modeling

#38:    Modeling; Introduction to Hyperbolic Functions


CD #10:  Calculus I, #'s 39-41

#39:   Hyperbolic Functions, Continuity  (Lecture 12/07/98)

#40:   Review I, Part I (Lecture 12/09/98)

#40 part II:  Review I, Part II (Lecture 12/09/98)

#41:   Review II (Lecture 12/11/98)