Maple via Calculus : A Tutorial Approach Tables of Contents 1 Basic Plotting 2 Parametric Equations 3 Optimization Problems 4 Interpolation 5 Conic Through Five Points 6 An Implicit Function 7 Inverse Functions 8 Partial Fraction Decomposition 9 Derivatives by Definition 10 Implicit Differentiation 11 Taylor Polynomials 12 Teaching the Definite Integral 13 Deriving Simpson’s Rule 14 Numerical Integration 15 Improper Integrals 16 Integration by Trig Substitution 17 Integration by Parts 18 Integration by Parts Twice 19 Surface Area of a Solid of Revolution 20 A Separable Differential Equation 21 Newton’s Law of Cooling 22 Logistic Growth 23 L’Hôpital’s Rule 24 Lines and Planes 25 Curvature from Every Angle 26 The Lagrange Multiplier Part One 27 The Lagrange Multiplier Part Two 28 The Lagrange Multiplier Part Three 29 Iterated Integration. Modern software tools like Maple have the potential to alter radically the way mathematics is taught learned and done. Bringing such tools into the classroom during lectures assignments and examinations means that new ways oflooking at mathematics can becomepermanent fixtures ofthe curriculum. It is universal access that will make a software based approach to mathematics become the norm. In 1988 with NSF funding under an III grant I had the opportunity to bring Maple into the calculus classroom at Rose Hulman Institute of Technology. Since then a new curriculum based on the availability ofcomputer algebra systems has evolved at RHIT and in my own courses. This volume contains a record of some of the insights gained into pedagogy using Maple in calculus. The activities and ideas captured in these Maple worksheets reflect concepts in calculus imple­ mented in Maple. There is an overt message to the reader that carries with it a side effect. However it is possible that for one reader the side effect is the message and the message is the side effect! I had intended to put before my audience examples extracted from my Maple based curriculum to entice a wider acceptance ofthe benefits of making a computer algebra system become the basis of a revised calculus syllabus. By examples I had hoped to demonstrate the rightness of using software tools for teaching and learning calculus.