Maple

Maple is a symbolic mathematics program. It is a delightful tool for experimenting with mathematics and it will solve many, if not all, of the problems in our undergraduate courses. Of course, you do have to learn how to pose the problems! I encourage you to learn Maple, and to play with it.

You may wish to use Maple to check your homework answers. If you do then keep in mind that Maple sometimes gives the wrong answer, usually because you asked incorrectly, or because of niceties of analytic continuation. You may even be bitten by an occasional Maple bug, though that has become fairly unlikely. Even with as powerful a tool as Maple you will still have to devise your own checks and you will still have to think.

Mth 254: Maple does have built-in support for double and triple integrals. That support is part of the student package (which comes standard with Maple) - you have to execute


>  with(student);

to make it available. Maple returns double (and triple) integrals as unevaluated, so you have to apply


>  value(%);

(or similar, or specify a numerical evaluation) in order to evaluate the integrals. Maple also provides a facility for doing some simple change of variables in double and triple integrals.

Mth 256: Maple is capable of solving many standard differential equations symbolically. In addition Maple has built-in numeric solvers. Some differential equations can not be solved explicitly or have symbolic solutions that are inconveniently complicated. In such cases Maple's numeric solvers may be used. By symbolic and numeric solutions may be graphed in a number of ways.

Mth 351: I use Maple quite a bit in Mth 351. Mth 351 is not a programming course but some programming experience is assumed. Your experience need not be with Maple however.

Mth 355 (399): This course deals with discrete mathematics and programming in Maple and Matlab. In practice I emphasize Maple, sometimes to the exclusion of Matlab.

Maple is available in many campus computer labs. In particular, it is available in the lab in the MLC (Kidder 108). There is also a student version which you may purchase in the OSU bookstore. (I believe the student version runs on PCs, Mac's and under Linux. You may want to check before making a purchase.)

Maple Documents

There are many Maple worksheets and instructions in the following document areas: Mth 232, Mth 254, Mth 256, Mth 341, Mth 351, Mth 355, and elsewhere. Some, but not all, of them are listed below.

2003 Winter Mth 355 (399) Assignment 1. Set Theory and Maple Programming
MWS, 34 KB, 3 problems, Maple Worksheet
PDF, 53 KB, 14 pages: Introduction. Getting started. Assignment and ditto operators. Execution time. Set, intersection, union, difference. Functions. Symmetric difference of sets. Cardinality of a set. Elements of a set. Lists. Subsets of a set. Maple procedures. Cartesian product of sets. Problems.

2003 Winter Mth 355 (399) Assignment 2. More Maple commands. Some combinatorics
MWS, 32 KB, 3 problems, Maple Worksheet
PDF, 248 KB, 18 pages: Digits. Functions and expressions. Derivatives. Integration. Plotting. Stirling numbers of the second kind, S(r,n). Bell numbers. Number of factorizations of a square-free natural number. Construction of all partitions. r-permutations. Multinomial and binomial coefficients. r-cobinations. Problems.

2003 Winter Mth 355 (399) Assignment 3. Maple Topics: Differential Equations. Prime Numbers
MWS, 28 KB, 4 problems, Maple Worksheet
PDF, 119 KB, 17 pages: Introduction. Equations. Functions and differentiation. Plotting multiple functions. Ordinary differential equations (symbolic). Ordinary Differential Equations (Numeric). Prime numbers. Problems.

2003 Winter Mth 355 (399) Assignment 4. Linear Recurrence Equations in Maple
MWS, 18 KB, 6 problems, Maple Worksheet
PDF, 89 KB, 14 pages: Linear recurrence equations - examples. Linear homogeneous recurrence equations of finite order. Linear inhomogeneous recurrence equations of finite order. Problems.

2003 Winter Mth 355 (399) Assignment 5. Linear Recurrence Generating Function. Graphs, Adjacency Matrix
MWS, 22 KB, 6 problems, Maple Worksheet
PDF, 97 KB, 15 pages: Linear recurrence equations - generating functions. Graphs, adjacency matrix, number of paths of a given length.

2003 Winter Mth 355 (399) Assignment 6. Partial Fractions. Least Squares. Limits
MWS, 27 KB, 3 problems, Maple Worksheet
PDF, 88 KB, 17 pages: Partial fractions. Full partial fractions. Trigonometric expressions. Least squares fit (stats). Least squares fit (linalg). Limits. Problems.

2003 Winter Mth 355 (399) Assignment 7. Interpolation. Planar Graphs. Numeric Derivatives
MWS, 16 KB, 5 problems, Maple Worksheet
PDF, 167 KB, 14 pages: More Maple commands: Interpolation polynomials. Interpolation splines. Planar graphs. Constructing numeric derivative estimates by the method of undetermined coefficients.

2003 Winter Mth 355 (399) Assignment 8. Linear Algebra - the Maple linalg package
MWS, 24 KB, 2 problems, Maple Worksheet: We look at a few commands from the linalg package.

2003 Winter Mth 355 (399) Assignment 9. Pedagogical stuff - the Maple student package
MWS, 27 KB, 2 problems, Maple Worksheet: The student package provides double and triple integrals, change of variables in integrals, trapezoidal and Simpson's numeric quadrature rules, and some other goodies. Some things are not fully implemented - for example if we change variables in a multiple integral we have to compute the limits of integration separately. As another example, in the trapezoid rule and in Simpson's rule we can not specify the number of subintervals except in the most primitive way. Maple explains these short-comings by stating, "The student package is a collection of routines designed to carry out step-by-step solutions to problems. " In other words, the purpose of the student package is pedagogical.

2002 Fall Mth 351 Elementary Numerical Analysis MLC Lab Visit
MWS, 36 KB, Maple Worksheet
PDF, 307 KB, 26 pages

2002 Fall Mth 351 Newton's Iterative Method for Systems of Nonlinear Equations
MWS, 31 KB, Maple Worksheet: This worksheet illustrates Newton's root iteration for a system of two nonlinear equations.

2002 Fall Mth 351 Assignment 3 - Maple's linalgpackage
MWS, 64 KB, 6 problems, Maple Worksheet
PDF, 117 KB, 30 pages: Problems on LU factorization, Cholesky factorization, symbolic row reduction, cubic interpolation polynomial, roundoff in calculating the matrix inverse, Vandermonde determinant.

2002 Summer Mth 351 Introduction to Maple - MLC Lab Visit
MWS, 78 KB, Maple Worksheet
PDF, 420 KB, 49 pages: Introduction. Login. Logout. Getting started. The worksheet. Assignment and ditto operators. Constants. Digits. Functions and expressions. Derivatives. Integration. Some plots. More plots. Taylor series and Taylor polynomials. Interpolation polynomials. Interpolation splines. Trapezoidal and Simpson's rules. Sums and products. Number theory. Solving equations. Linear algebra (linalg package). Limits. Recursion and remember. Set theory.

2001 Fall Mth 355 (399) Assignment 2 Maple Programming
MWS, 13 KB, 5 problems, Maple Worksheet
PDF, 43 KB

2001 Fall Mth 351 Introduction to Maple - MLC Lab Visit
MWS, 58 KB, Maple Worksheet
PDF, 378 KB, 36 pages

2001 Spring Mth 351 Visit to the MLC Computer Lab
MWS, 31 KB, Maple Worksheet
PDF, 164 KB, 20 pages: This Maple 6 worksheet (it should work in Maple 5 too) presents an introduction to Maple in the MLC Computer Lab. Some examples relevant to Mth 351 are also given: interpolation polynomials, natural cubic splines, trapezoidal and Simpson's rules, etc. Some simple but useful interactive techniques are described (but there is no discussion of programming). The PDF file contains all of the Maple output including the plots. The worksheet does not include any Maple output. You have to create the output by executing the commands in the worksheet. Anyone content simply to execute the worksheet the way it is lacks courage or is missing the point! Change things! Experiment! You can always download a fresh copy if you get in trouble.

2001 Winter Mth 256 Laplace Transform in Maple
PDF, 52 KB, 4 pages
MWS, 11 KB, Maple Worksheet: This Worksheet illustrates how to solve (linear) initial value problems by using the Laplace transform. Maple is useful here by eliminating the large amounts of (simple, but overwhelming) algebra needed when doing transform problems by hand.

2001 Winter Mth 256 Differential Equations with Maple
PDF, 211 KB, 10 pages
MWS, 46 KB, Maple Worksheet: This worksheet illustrates how to solve differential equations in Maple, how to extract pieces of the data structure that Maple returns and a bit of plotting. It is just a short introduction!

2000 Fall Mth 256 Linear differential equations with Dirac-delta and Heaviside terms: Examples
PDF, 84 KB, 6 pages
MWS, 29 KB, Maple Worksheet

2000 Fall Mth 256 Newton's Law of Cooling - examples
PDF, 110 KB, 3 pages
MWS, 17 KB, Maple Worksheet: We solve two problems illustrating Newton's law of cooling. We note the system temperature tracks the ambient, but with a time delay and with reduced amplitude of fluctuation.

2000 Spring Mth 341 Linear Algebra - First Lab Visit
MWS, 19 KB, Maple Worksheet
PDF, 37 KB, 19 pages
TXT, 25 KB, ASCII text: This worksheet is an introduction to using Maple in linear algebra (with the linalg package). At this point only row reduction and the solution of systems of linear equations are considered. More advanced topics will be considered later in the term. I have added a few comments and examples to illustrate that while Maple is very powerful it is no substitute for understanding. The worksheet is intended to be used in the Lab, but a text and a PDF version are provided for perusal on any PC, even one without Maple.

2000 Spring Mth 341 A Short Introduction to Maple in the MLC Lab
MWS, 28 KB, Maple Worksheet
PDF, 35 KB, 17 pages
TXT, 21 KB, ASCII text: The MLC lab contains 20 PC's running Windows NT. These workstations are equipped with some popular mathematical software. This note has a few comments on using the lab, some general comments on using Maple, and then a few examples pertaining to linear algebra (with linalg package) . The ASCII file should be viewable in any browser. The PDF file will, of course, require the Acrobat plug-in.

2000 Winter Convex hull, Lucas theorem, Aziz's theorem and the Sendov-Ilyeff conjecture
PDF, 551 KB, 15 pages worksheet
MWS, 39 KB, Maple Worksheet: In this worksheet I implement the Jarvis walk for calculating the convex hull of a finite set in the plane. This code is then used to illustrate Lucas' theorem that the set Z(P') of roots of the derivative P'(z) of a complex polynomial P(z) lies in the convex hull of the set of roots Z(P) of P(z). Some random polynomials are generated for this purpose. In all cases the convex hull of Z(P') and the convex hull of Z(P) are much more similar than one might at first expect. I then point out the (trivial) fact that a theorem of Aziz and the conjecture of Sendov and Ilyeff really say something about the Hausdorff distance between Z(P) and Z(P'). Finally I invite you to think about the Sendov-Ilyeff conjecture. All of this is for fun really - and to celebrate Feb 29, 2000, a rare leap day!

2000 Winter Introduction to Maple, Part 1
PDF, 43 KB, 8 pages: This introductory note introduces Digits, unassign(), subs(), eval(), D(), diff(), int(), Int(), evalf() and showtime, in a cursory way, and provides simple examples and a bit of discussion.

1999 Summer Mth 351 Simpson's Rule and Cubics
MWS, 16 KB, Maple Worksheet
PDF, 22 KB, 4 pages: Simpson's quadrature rule is exact for cubics. The reason is that for any three points on a cubic, with equispaced abscissas, the area under the graph of the cubic from the first to the last point is the same as the area under the graph of the unique interpolating quadratic through the three points. There is an analogous property for the case of polynomials of degree 2n+1 and 2n. This worksheet illustrates this property by computing the integrals symbolically (through degree 7).

1999 Summer Mth 351 Newton-Cotes Quadrature
MWS, 19 KB, Maple Worksheet
PDF, 24 KB, 7 pages: We develop a Maple routine to do Newton-Cotes quadrature of any degree and any order. We note the weights are not positive in degree 8 and some higher degrees, though they are positive in degree 9 and in degrees 1 through 7. We note Boole's rule is no more difficult to use than Simpson's rule but may be much more accurate for smooth functions.

1999 Summer Mth 351 Romberg Quadrature
MWS, 25 KB, Maple Worksheet
PDF, 26 KB, 9 pages: We develop a simple Maple procedure to do Romberg quadrature and experiment with its behavior.

1999 Summer Mth 351 Gauss Quadrature
MWS, 14 KB, Maple Worksheet
PDF, 19 KB, 4 pages: This worksheet introduces some Maple procedures that allow one to experiment with Gauss quadrature. The required Gauss nodes and Gauss weights are computed by a simple Maple procedure. A comparison with Simpson's rule for a few examples, is given.

1998 Spring Mth 252 Computing partial fractions in Maple
PDF, 18 KB, 6 pages: This Maple V5 worksheet illustrates that Maple's convert command, with the options parfrac and fullparfrac, provides a convenient way to expand rational functions in partial fractions. This worksheet just consists of a few simple examples.

1995 Summer Mth 341 Maple and Linear Algebra
PDF, 110 KB, 15 pages: Fifteen pages of instructions on how to use some of the features of Maple's linalg package to solve problems in linear algebra

| HOME | TOP |