"Modern software tools like Maple have the potential to alter radically the way mathematics is taught, learned, and done." With this principle firmly in mind, the author of Maple via Calculus brings to teachers and students a fresh look at the standard calculus curriculum, colored by the existence of technology like Maple - a tool that can be used in class during lectures and exams and at home while working assignments, a tool whose universal access will eventually make a software-based approach to mathematics the norm.
Whether one uses this book primarily to learn Maple or to learn calculus, the student who works through the exercises will learn a great deal about both. Drill exercises and rote manipulation are replaced here with conceptual learning activities and an exploratory interaction with mathematics not seen in traditional courses. A surprising feature is that fewer than 90 Maple commands are necessary to do all the calculus activities in the book, thus making it an ideal text for learning Maple basics. By implementing this powerful computer algebra system in their courses, teachers can clearly delineate the fundamental ideas of calculus while demonstrating the efficient use of Maple.
The techniques illustrated in this text have passed the test of student acceptance. The author has used them with great success in his own courses and demonstrated them in workshops and presentations in many locations in North America and Europe. Everyone interested in bringing the computer into the calculus classroom will find the book a valuable resource.
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
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