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Title

Calculus I - IV Mathematica Labs
Authors

Marcia Birken
Organization: Rochester Institute of Technology
Department: Department of Mathematics & Statistics
Patricia Clark
Organization: Rochester Institute of Technology
Department: Department of Mathematics & Statistics
Education level

College
Objectives

Calculus I - IV is a four quarter sequence of calculus courses covering the standard topics in single and multivariable calculus. These courses meet four hours per week for ten weeks. Professors Marcia Birken and Patricia Clark teach these courses using one class period per week in a teaching computer laboratory where they utilize Mathematica labs which they have authored. The remaining three classes per week are taught in a more traditional lecture format. Other faculty can use our labs as out of class assignments for their students. The purpose of the RIT Department of Mathematics & Statistics Virtual Library (where these labs are catalogued and accessible for download) is to provide a location for sharing teaching resources. Professors Birken and Clark created the Virtual Library under a small internal grant from the College of Science at Rochester Institute of Technology.
Materials

Calculus, 4th edition by Stewart, Brooks Cole (ITP)
Description

The laboratories found in the RIT Department of Mathematics & Statistics Virtual Library cover topics from each of the four calculus courses. They follow the order of materials in Stewart's 4th edition of Calculus, the text for the course.

These labs can be used in a variety of ways - to introduce a topic, to reinforce material presented in a lecture or as an outside assignment for students to use as a learning device. Students are most enthusiastic about the labs.

Topics:
Calculus I Derivative Calculus
  • Introduction to Mathematica
  • Graphing
  • Limits
  • Derivatives
  • Implicit Differentiation
  • Related Rates
  • Newton's Method
  • First Derivative & Graphing
  • Graphing - The Big Picture
  • Optimization
Calculus II Integral Calculus
  • Introduction to Mathematica
  • Area
  • Directionfields
  • Fundamental Theorem of Calculus
  • Method of Substitution
  • Volumes of Solids of Revolution
  • Calculation of Work
  • Inverse Functions
  • Exponentials & Logarithms
  • Trigonometric Functions & Inverses
  • Integration by Parts
Calculus III Infinite Series, Polar & Parametric Equations
  • Introduction to Mathematica
  • Advanced Integration Techniques
  • Approximation of Definite Integrals
  • Convergence of Integrals & Sequences (3 labs)
  • Geometric Series
  • Integral Test
  • More Series Testing
  • Taylor Series
  • Parametric & Polar Equations
  • Arc Length & Area
Calculus IV - Multivariable Calculus
  • Introduction to Mathematica
  • Vectors, Lines & Planes
  • Vector Vlued Functions & Space Curves (2 labs)
  • Graphing & Partial Derivatives
  • Maxima & Minima
  • Double Integrals
  • Triple Integrals
Subjects

*Applied Mathematics > Optimization
*Mathematics > Calculus and Analysis > Calculus
URL

http://www.rit.edu/~mkbsma/mathematica/