Applied Calculus II CD Contents

CD List

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

Applied Calculus II Chapter 4

Applied Calculus II Introduction to Integration

Calculus II CD #1, #'s 01-09

Calculus II Cd #2 #'s 10-16

Applied Calculus II Chapter 7, Part a (through maxima and minima)

Applied Calculus II Chapter 7, Part b (through maxima and minima)

Applied Calculus II Chapter 4

Exponential Functions:  Compound Interest

Example:   Population Growth

Example:   Radioactive Decay

Exponential Equations

Graphs of Exponential Functions

More Graphing

Analyzing Compound Interest

The number e

Continuous Compounding

The Derivative of e^x

The Chain Rule and the Derivative of an Exponential Function

General Derivative of an Exponential Function

Example:   Maximizing Revenue

Example:   The Normal Curve

The Natural Log Function as the Inverse of the Exponential Function

Example:   Doubling Time

Solving Exponential Equations using Logarithms

The Derivative of the Natural Log Function

The Derivative of a More Complicated Log Function

Analyzing a Graph

Example:   Rate of Memory Change

Derivative of Log to a Different Base

Exponential Growth

Example of Exponential Growth

Example:   RAM loss 

Applied Calculus II Introduction to Integration

See Also Chapter 3; you may request the Chapter 3 CD.

This CD provides an introduction to the concept and practice of integration.  It also points out slight notational differences between your text and the notation used on CD 1

The Depth Function Model

Depth from Rate, Initial Condition

General Rate Function and Quantity Function Releationship

Change in Depth from Rate Function and Initial Condition

Change in Depth from Rate Function Only

Rules of Integration

Family of Depth Functions given Rate Function

Using Rules of Integration

Another Example

Marginal Cost and Cost Function:  Another Rate and Quantity Situation

Generalized Integration Rule for Power Function and the Chain Rule

Generalized Rule for Integral of Exponential Function

Generalized Rule for Integral of Log Function

Integral of Sine and Cosine Functions

Generalized Integrals of Sine and Cosine Functions

Applying Generalized Rules to Sine and Cosine Functions

Integration by Parts (defer until you encounter the section on Integration by Parts)

Calculus II CD #1, #'s 01-09

Class #01:   Overview of Sections 6.1-6.3

Class #02:    Finding Antiderivatives Graphically and Analytically

Class #03:     Integrals and differential equations

Class #04:    2d Fundamental Theorem, integration by substitution  

Class #05:    2d Fundamental Theorem

Class #06:    Uniform acceleration and Differential Equations

Class #07:   Integration by Substitution, Integration by Parts

Class #08:   Integration by Substitution, Integration by Parts

Class #09:    Integration by Parts

Calculus II Cd #2CD #1, #'s 10-16

#10:    Integration Techniques

#11:    Integration by Tables

#12:    Integration by Approximation I:  Left, Right, Midpoint, Trapezoidal Rules

#13: Integration by Approximation II:   Simpson's Rule; Errors of Various Techniques

#14:    Improper Integrals

#15:    Improper Integrals

#16:    Improper Integrals

Applied Calculus II Chapter 7, Part a (through maxima and minima)

Demonstration:   3-dimensional

Distance Formula in 3 dimensions

Equation of a Sphere

Sphere in Space

Traces in Coordinate Planes

Traces in Planes Parallel to Coordinate Planes

Equation of a Plane

Equation of a Plane part 2

Equations of Various Special Planes

Conic Sections:  Review

Quadric Surfaces

A Paraboloid

Representing a Function of 2 variables by a Table

Level Curves

Function of 2 variables defined by an Integral with Variables as Limits

Difference Quotient

Domain of a Function of 2 variables

Another Function, another domain

Happiness-at-a-meeting Model and Partial Derivatives

Partial Derivatives of the Happiness Function

Partial Derivative of a Modified Happiness Function

Geometric Interpretation of Partial Derivatives

Slope of a Surface at a Point

Demonstration of Partial Derivatives on a Christmas Tree Ornament

A Demand Function of Two Variables

Marginal Costs

Contour-line Example of Maxima and Minima

Critical Points of a Function of Two Variables

Maximum or Minimum of a Paraboloid

Trickiness of Saddle Points

Test for Maxima and Minima

Applying the Test for Maxima and Minima 

Applied Calculus II Chapter 7, Part b (through maxima and minima)

Fitting a Straight Line to Data

Finding Squared Error

Minimizing Squared Error

Using the Least-Squares Line

Generalizing the Process

Evaluating a Double Integral

Describing a Region in the Plane

Area of a Region in the Plane

Reversing the Order of Integration

Volume of a Solid, I

Volume of a Solid, II

Double Integral of Population Density

Average Value of a Function of Two Variables

Calculating Average Values