Maple Demonstrations for Math 103



Maple Demonstrations for Math 103

Some of the demonstrations here indicate how to use Maple to solve basic calculus problems. Others are examples of more sophisticated use of Maple to solve more involved and 'interesting problems. Still others simply illustrate math concepts and can be used as interactive "visual aids".

In this list, the demonstrations progress from the beginning of Math 103 through the end of Math 114 and 115. There is an indication next to each demo concerning to which courses it applies. Each demo should be loadable with either Maple 6, 7, or 8.

Functions and their properties

(These are mostly useful for Math 103)

• Linear functions / plotting to determine the range of nonlinear functions

• Basic properties of exponential functions

• Power functions / use of solve and evalf

• Calculating inverse functions in Maple / logarithms

• Operations on functions (scaling of independent and dependent variables) / trigonometric functions

Limits and derivatives

(These are mostly useful for Math 103 and the beginning of Math 104)

• Limits - by graphing, numerical approximation, and symbolically

• Idea of the derivative, average rate of change as slope of secants

• Derivative as limit of average rate of change

• Definition of the derivative

• Maple's diff command, finding equations of tangent lines, graphical interpretations of derivatives

• Derivatives and linear approximations / second derivatives

• Bitangents (lines tangent to a curve at two different points) - connects to a sequence of problems in the Lab Manual

• Review of basic Maple (plot, solve, diff); illustrations of the chain rule and implicit differentiation

• Newton's method

• Using the derivative to solve max and mm problems

Integrals

(Useful for Math 103 and Math 104)

• Illustration of integrals as limits of Riemann sums

• More on integrals and Riemann sums - graphics and evaluation of integrals as limits

• Fundamental theorem of calculus illustrations, area between two curves

• Solids of revolution -- illustration via tubeplot and volume via integration (see also the first demo in the differential equations section below)

• Symbolic integration - definite and indefinite

Exponentials and logarithms

(Useful for Math 103 and Math 104)

• Exponential functions -- finding the exponential function through two points, exponential growth, derivatives of exponential functions, exponential models from differential equations

• Logarithms - use to solve exponential equations, calculus of logarithms

• More exponential function -- compound interest

• Exponential (radioactive) decay

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