MATH 1712 Survey of Calculus:
Maple Explorations

Here you will find a collection of Maple worksheets designed to help you in your studies. The following online resourses were written with this course in mind.

• Since Maple is very powerful and very popular in studying Calculus, you definitely should learn how to take advantage of it.
  There are some excellent sites you can find tutorials on Maple. Certainly the most famous site is the Maple's inventor MapleSoft (external link). In the School of Mathematics, Georgia Tech, Professor Cain worksheet to help you get started. Also, extensive Maple worksheets and other resources can be found in Doug Meade Doug Meade at South Carolina.
• Polynomials and Rational Expressions: We learn how to use Maple commands to factor polynomials, expand products of rational expressions, and simplify sums or quotients of products of rational expressions, and simplify sums or quotients of rational functions.
• Plotting Graphs: One of the primary uses of the computer will be to give visualization. This worksheet gives syntax for plotting graphs. The worksheet does not use the calculus. Rather, it is an introduction to techniques for plotting graphs with Maple.
• Interpreting Graphs: The goal of this worksheet is to understand the graph of the following function:
  > h:=x->(x^3+3*x-5)/(x^2+2);
  Although you can just plot it in Maple, we want to do this systematically to get a better idea what to look for when looking at the graph. Read each question, and try to see if you could have guessed this by looking at the graph of the function.
• Limits: This worksheet introduces the Maple commands for finding one- and two-sided limits of functions. In this worksheet, the reader also learns how to examine the graphs of functions to find the limit graphically.
• Slopes, Tangent Lines, and Derivatives: This worksheet gives animated visualization for the computation and role of a tangent line. The worksheet is appropriate at an early stage in a study of differential calculus.
• Solving Equations: This worksheet is about continuity, the intermediate value property of continuous functions, etc. Equations are solved using "bisection", regula falsi, and Newton's method. This assignment help you understand the Maple procedures.
• Solving f(a) = b: The Method of Bisection: The Method of Bisection for finding roots of an equation is not conceptually hard. It has two especially good features: first, it is easily understood, and second, it can provide initial guesses for methods which might converge faster --such as Newton's Method. We illustrate the method and provide an example to show that a little care must be taken.
• Reflections on Differentiation: This worksheet is designed to introduce how to differentiate both functions and expressions. The problem of finding extreme values of simple functions is illustrated by using Fermat's Principle to find the path of reflected light. Some fancier plotting capabilities and also the equation solving ability of Maple are also introduced.
• Implicit Differentiation: This Maple worksheet uses Maple's ability to do implicit plots to give you a visual understanding of implicit differentiation problems.
• Curve Sketching: This worksheet takes the reader through all the steps of the curve sketching process using Maple commands.
• The Year of the Fastest Growth for the US Population: The U. S. Constitution requires a census every ten years. We provide a "Logistic Fit" for that data and graph the fit superimposed with the data. This worksheet then asks the following question: In what year does this logistic fit suggest the fastest growth in the U. S. census data?
• Finding Absolute Extrema: This worksheet introduces all the Maple commands necessary to find the absolute maximum or minimum of a continuous function on a closed interval.
• Maximum Heart-Rate for a Runner: The heart's pulse-rate for a well-trained runner will increase at the beginning of a run, and then decrease as the runner experiences experiences a "second wind". There after, the pulse-rate will gradually increase as the runner switches from metabolizing glycogen to converting fat into an energy source. This toy model mimics this phenomena. It asks when the maximum heart rate will occur. The answer is obtained with the standard tool: set the derivative equal to zero and solve. It may be that the "solving" is the most interesting part from the perspective of computing in this worksheet.
• Important geometric relationships exist between the graphs of function f, the derivative of f and the integral of f. This worksheet compares their graphs and asks the user to identify which is which in an overlay of the three graphs.
• Growth, Decay, and Exponential Functions: The real reason we learn about the exponential function in this course is that it has a lot of important applications. In this worksheet we discuss some of their applications to archaeology (carbon dating), atmospheric radiation, and predictions of populations.
• Area by Chance: The Riemann integral is usually defined as the limit of a collection of approximating sums. There after, the fundamental theorem of integral calculus provides methods for evaluating integrals without computing limits of sums. As an alternative idea, this worksheet introduces a random number generator and what is usually called "Monte-Carlo Techniques" to evaluate integrals. "Area by Chance" is a good worksheet to examine early in the introduction of the integral.
• Finding Area: This worksheet simply illustrates how to use Maple to find the area between two curves. You should already read two previous worksheets: Plotting Graph and Interpreting Graphs.
• Techniques of Integration: Substitution and Integration by Parts: It used to be that a calculus class would study the techniques of integration so well that the student could work out how to integrate functions such as x arcsin(x). The computer can be used to help with the calculus when methods such as substitution or integration-by-parts are correct choices for integration techniques.
• Three Dimensional Graphics: Maple can be used to help visualize the shapes of surfaces, as well as for the computation of algorithms. Some tools are suggested in these two worksheets. The first one illustrates the commands with straightforward examples, while the second one develops some graphics tools in a specific context.
• Local Extrema in 3-D: This worksheet introduces the Maple commands and procedures necessary to finding relative extrema for functions of two variables.
• Lagrange Multipliers and Constrained Optimization: This Maple Worksheet illustrates how to solve the constrained optimization problems using Maple.
• Evaluating Double Integrals: This worksheet introduces the commands for computing double integrals using Maple. An example dealing with average value is also presented.
• A worksheet on using Maple to solve differential equations.

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Last Modified: . School of Mathematics, Georgia Institute of Technology.