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Maple Student Video Tutorials New to Maple? Need a quick tutorial on how to use Maple to solve a particular math problem? Check out the following video tutorials that are specially tailored and student oriented to demonstrate Clickable Math techniques for solving the most common math problems arising in high school, college, or university math courses. Select a category below: Differential Calculus   Optimization A tutorial that solves an optimization problem using Maple's Optimization Assistant. The Assistant that calculates the maximum and minimum values of a function with constraints. A graphical analysis is also provided. Integral Calculus   Antiderivatives Maple's Antiderivatives Tutor graphs a function and its family of antiderivatives. Analytic representations of the antiderivatives are also provided. Riemann Sums: Approximating Area Under Curve Students approximate the area under a curve using Maple's Riemann Sums Tutor. The Tutor also animates the relation between increasing partitions and the area under the curve. Definite Integrals Familiarizes the student with the concept of definite integrals via clickable methods. Students will learn how to set up and solve (in a syntax-free way) problems in which area under a curve is to be calculated. Indefinite Integrals Demonstrates Maple's clickable tools that make it easier for students to write and evaluate indefinite integrals. Area Between Curves Helps students determine the intersection between two curves and calculate the area between them using Maple's Integration Methods Tutor. Finding Partial Fractions The Partial Fractions Finder is a powerful and unique tool. With just a few clicks, this highly interactive tool shows you the major steps in determining partial fractions just like how a teacher would show you on a blackboard. Volume by Revolution For a solid generated by revolving a curve about a horizontal axis, the Volume of Revolution Tutor determines the volume by the method of disks. The Tutor sets up the appropriate integral, displays calculations, and shows the discretization as a stack of disks. To improve students' intuition, an animation shows a representative disk sweeping through the solid. Volume by Cylindrical Shells For a solid generated by revolving a curve about a vertical axis, the Volume of Revolution Tutor determines the volume by the method of cylindrical shells. The Tutor sets up the appropriate integral, displays calculations, and shows the discretization by concentric cylinders. To improve students' intuition, an animation shows a representative shell sweeping through the solid. Arc Length Maple's Arc Length Tutor graphs the function and its arc length as a function of the endpoint, and displays the calculations of the definite integral. Differential Equations: Initial Value Problems A tutorial that solves an initial value problem for an ordinary differential equation. It uses Maple's ODE Assistant, which provides analytic or numeric solutions, and graphs of the solution, its derivatives, or orbits in the phase plane. Linear Algebra   Orthogonal/Orthonormal Bases Using the Gram-Schmidt process and Maple's ability to compute the dot product, the following tutorial goes through the steps for creating an orthogonal or orthonormal basis for a set of vectors. Diagonalizing Matrices Using two methods, this tutorial shows you how to determine whether or not a matrix is diagonalizable. Also, using Maple’s Context Menu to compute the eigenvectors of a matrix, the tutorial displays the steps for how to diagonalize a matrix. Least Squares The following tutorial applies Maple's Curve Fitting Assistant to a set of data points to find the equation of the best (least-squares) fit of both a linear and a quadratic function. The Curve Fitting Assistant also displays a graphical representation of the line or curve of best fit. In addition, the tutorial articulates how to pass from an overdetermined set of equations to the matrix form of the least-squares problem, and how to use matrix computations to find the least-squares solution and the least-squares error. Quadratic Forms This tutorial takes advantage of Maple's ability to form a Hessian matrix, normalize vectors and compute eigenvectors. It displays the steps for manipulating the quadratic form, obtaining its matrix, and diagonalizing it, that is, transforming it into a new form with no cross-product terms. Change of Basis The following tutorial describes two methods for using given bases to find the change-of-coordinate matrices and coordinate vectors. The first method uses matrix manipulations, whereas the second method writes and solves systems of equations for the coefficients of linear combinations relating the two sets of basis vectors. Solving Linear Systems The following video tutorial shows you how to determine the solution set for a given linear system. The tutorial considers three examples of linear systems that have solution sets containing 1 point, infinitely many points, or no points. Using Maple's Linear System Plot Tutor the tutorial displays a graphical representation of the equations in each linear system and how they intersect. Geometric Applications of Determinants The area of a triangle or parallelogram, and the volume of a tetrahedron or parallelepiped can be computed by evaluating a determinant containing the coordinates of vertices. This video tutorial shows how to use the Context Menu to implement these calculations. The same determinantal device allows one to obtain the equation of a plane through three points, and to determine if three points are collinear, or four points are coplanar. Where applicable, the Plot Builder is used to provide visual representations. RSA Algorithm This tutorial takes you through two exercises that use the encryption and decryption algorithm that Rivest, Shamir, and Adleman described. The exercises use a cipher code to morph a message into a numerical value. Using public and private keys, the exercises use tools to show how you can both encrypt and decrypt a cipher message. Eigenvalues, Eigenvectors, and Eigenspaces This tutorial articulates three methods in which you can use Maple to find eigenvalues, eigenvectors, and eigenspaces of a given matrix. With Maple's Context Menu you can immediately obtain the eigenvalues, eigenvalues, and characteristic polynomial of a matrix. Using Maple's Eigenvalues and Eigenvectors Tutor you can see the step-by-step computation of the eigenpairs. This tutorial also contains a solution that illustrates how to find the eigenpairs using a stepwise solution similar to the one you would use if you were doing the calculations by hand. QR Decomposition Using Maple's Context Menu, this tutorial shows you how to obtain the QR Decomposition of a matrix. Also, this tutorial implements a stepwise solution for finding the QR decomposition using the Gram-Schmidt process. As well, the tutorial displays the steps for using the QR decomposition to find the least-squares solution of an overdetermined system of equations. Multivariable Calculus   Limits and Continuity of Multivariable Functions A clickable tool that produces a 3D graph and a table of values that helps students analyze a function’s continuity and behavior near the origin. Level Curves and Cross Sections Students can greatly benefit from the interactive Cross Sections Tutor. It displays level curves, cross sections, and even intersections between curved surfaces and planes at an angle. Tangent Planes and Linear Approximations Select a point on the surface and Maple will plot the plane tangent to the surface and will give the equation of the plane as well. Students can better understand the connection between tangent planes and linear approximations. Directional Derivatives and the Gradient Vector Students can benefit from this video tutorial which shows everything from calculating the unit vector, directional derivative, and gradient through the Directional Derivatives Tutor, Gradient Tutor and first principles. Minimums and Maximums of Two Variable Functions Two powerful techniques to locate minimums and maximums are demonstrated. In cases of multiple minimums or maximums, Maple’s Optimization Assistant graphs the function. From the graph, you can guess the approximate location of minimum or maximum and the Optimization Assistant will determine the exact location of the closest minimum or maximum. Lagrange Multipliers The Method of Lagrange Multipliers Task Template is a unique clickable tool. Simply enter the objective function and the constraint. All quantities including the Lagrange Multipliers are calculated and displayed. Iterated Double Integrals A tutorial that evaluates iterated double integrals using 4 different Maple tools. The Approximate Integration Tutor evaluates the iterated double integral while providing a 3-dimensional representation. The Integration Task Template sets up the double integral and shows the steps for evaluating it. A clickable tool and the Expression palette allow you to evaluate the double integral using first principles. Double Integrals over General Regions Learn how to evaluate double integrals over regions that are not rectangles. Using Maple's Plot Builder to graph the region's bounding functions, the tutorial articulates two techniques for forming and evaluating an iterated double integral. Back to Adoption Student Center