| Calculus and Pre-calculus LabsThere are thirteen calculus and pre-calculus interactive computer
labs with problem sets (a total of 432 problems) that are part of
the Converge software. All these
labs can be accessed from the Options Menu. The labs are organized in the standard Windows
help format. The lab titles are the (help) "books", and the lab sections for a
lab are the "help topics" for a book.
These labs are as follows.
Shifting,
Reflecting, & Stretching a Graph
1. Adding or Subtracting a Constant
2. Replacing X by X + c or X - c
3. Multiplying by -1
4. Replacing X by -X
5. Multiplying by a Constant
6. Replacing X by cX
7. Making Multiple Changes
Problem Set
Curve Fitting
Introduction
1. Scatterplots and Correlation
2. Linear Curve Fitting
3. Non-linear Curve Fitting
Problem Set
The Limit of a Function
Introduction
1. Limit Fundamentals & One-sided Limits
2. Def. of F(x) at a vs. Limit as x Approaches a
3. Using Graphs to Visualize Limits
4. Limits where Y approaches infinity
5. Limits where F(x) is Not Defined on One Side of a
6. A Constant Function
7. An Oscillating Function (optional)
8. Another Oscillating Function (optional)
Problem Set
The Definition of Derivative
1. A Tangent Line
2. Derivatives & Left- and Right-hand Derivatives
3. Applying the Definitions
Problem Set
Differentiability and Continuity
Introduction
1. The Derivative at a Jump Discontinuity
2. The Derivative at another Non-removable Discontinuity
3. The Derivative at a Removable Discontinuity
4. Must a Function be Differentiable where it is Continuous?
5. Another Point where the Function is Continuous
6. A Point where the Graph has a Vertical Tangent
7. A Point where the Graph is Connected and Smooth
Problem Set
Graph of the Derivative
Introduction
1. Graphing a Derivative Function
2. Graphing another Derivative
Problem Set
The Definite Integral
1. Sequences of Riemann Sums
2. The Definite Integral
3. Definite Integrals of some Non-linear Functions
Problem Set
Some sections of the following labs involve some use of Derive
5.
Introduction to Derive
1. Authoring, Highlighting, and Deleting Expressions
2. Graphing, Solving Equations, and Substituting into
Expressions
3. More Substituting
4. Finding Derivatives
Problem Set
Newton's Method
1. Visualizing Newton's Method
2. Getting Very Accurate Estimates
with Newton's Method
Problem Set
Estimating and Calculating Integrals
1. The Trapezoidal Rule
2. Simpson's Rule
3. Comparing Simpson's and Trapezoidal Rule Estimates
4. An Upper Bound for the Error in Using Simpson's Rule
Problem Set
Solutions of First Order
Differential Equations
1. Graphical Solution of a Simple Equation using a Direction
Field
2. Graphical Solution of a More
Complicated Equation
3. Finding Algebraic Solutions
Problem Set
Sequences and Series
Introduction
1. The Convergence of a Sequence
2. Another Sequence
3. One More Sequence
Problems Involving Sequences
4. The Convergence of a Series
5. Another Series
6. Applying Tests for Convergence of Series
Problems Involving Series
Taylor Polynomials
1. Taylor Polynomials for Cos x
2. Taylor Polynomials for ln x
3. The Accuracy of Taylor Polynomials
Problem Set |