Maple Via Calculus : A Tutorial Approach

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. Front Matter....Pages i-xiii Basic Plotting....Pages 1-6 Parametric Equations....Pages 7-14 Optimization Problems....Pages 15-18 Interpolation....Pages 19-22 Conic Through Five Points....Pages 23-25 An Implicit Function....Pages 26-29 Inverse Functions....Pages 30-33 Partial Fraction Decomposition....Pages 34-37 Derivatives By Definition....Pages 38-42 Implicit Differentiation....Pages 43-43 Taylor Polynomials....Pages 44-48 Teaching the Definite Integral....Pages 49-54 Deriving Simpson’s Rule....Pages 55-56 Numerical Integration....Pages 57-61 Improper Integrals....Pages 62-67 Integration by Trigonometric Substitution....Pages 68-70 Integration by Parts....Pages 71-72 Integration by Parts Twice....Pages 73-75 Surface Area of a Solid of Revolution....Pages 76-79 A Separable Differential Equation....Pages 80-82 Newton’s Law of Cooling....Pages 83-84 Logistic Growth....Pages 85-87 L’Hôpital’s Rule....Pages 88-90 Lines and Planes....Pages 91-96 Curvature from Every Angle....Pages 97-132 The Lagrange Multiplier, Part One....Pages 133-139 The Lagrange Multiplier, Part Two....Pages 140-159 The Lagrange Multiplier, Part Three....Pages 160-162 Iterated Integration....Pages 163-166 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.- 2