Tim Howard's Maple Worksheets

• College Algebra
1. Solving equations algebraically and graphically
2. Compound interest. Select from investment plans in which interest is compounded by different schemes. Graphs of total earnings over time are used in the comparison.
• Calculus
1. Polynomial interpolation
2. Approximating by interpolation. Find a quadratic approximation for a given function by choosing three points on the graph, and then interpolating.
3. Second degree Taylor polynomials. Find quadratic approximations by matching a given function's value, first, and second derivatives at a specified point. Maple is used to solve the associated equations and draw graphs.
4. Exploring Simpson's Rule.  Walk through the derivation of Simpson's Rule for approximating a definite integral.  This assignment involves determining the associated quadratic approximations which are then integrated.  We also use the error formula and the graph of the fourth derivative to determine how many subintervals are necessary.
5. Optimal shipping plan. Select the average driving speed for a fleet of trucks given data about fuel performance. This involves a trade-off between truckers' wages and fuel costs. Mathematically, this assignments involves data fitting and minimizing functions over a closed interval.
6. Approximations using moments. Determine quadratic approximation for a function by matching the given function's zeroth, first, and second moments.
7. Finite Fourier series. Approximate functions using truncated Fourier series. Compare graphs in Maple.
• Differential Equations
1. "The Worms are Coming!" involves a model for a spruce budworm population.  Mathematically, this assignment involves the use of Maple to obtain solution curves and slope fields for a first-order differential equation.
2. "Eating Worms" revisits the spruce budworm model, adding a modification to account for birds which eat the worms.  This assignment introduces the notion of a bifurcation.
3. "Equilibria for nonlinear systems". Use the linearization to determine the stability of an equilibrium point and the geometry of nearby solutions.
4. I have written an illustration of Euler's method in Maple.