Course ePortfolio

Calculus 101

These are resources that can be used for a college calculus course. The subject in this first course is differential calculus. Beginning with functions and limits, this course includes techniques and applications of differentiation, indefinite and definite integrals and applications of integration. Topics include functions, limits, continuity, differentiation of algebraic and trigonometric functions, mean value theorem, and applications of derivatives. A suggested textbook would be "Calculus" by Howard Anton, Sixth Edition, Vol. 1, Wiley
Course: Beginning Calculus
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Math placement exam; completion of high school algebra and trigonometry

Pedagogical Approach

None

Learning Outcomes

1 To master algebraic topics introduced in precalculus and trigonometry. 2. To understand limits and investigate some of their basic properties. 3. To understand the basic relationship between tangent lines, rates of change, and the derivative. 4. To master the techniques of differentiation. 5. To become familiar with the standard applications of the derivative in physics, engineering, biology, chemistry, and economics. 6. To become familiar with parts of the theoretical framework that are appropriate at this level. 7. To understand the integral and its relation to the derivative. 8. To master techniques of integration for simple integrals. 9. To learn how to use a graphing calculator.

Assessment

Problem completion

Other Information

None

Course Resources

  • Numerical Integration Rules
    Limited functionality, but very clear depiction of integration and the error involved with different integration... More
  • Numerical integration simulation
    This applet provides a visual representation of various techniques of numerical integration including right rectangle,... More
  • Riemann Sums
    Riemann Sums (Simulation)
    Numerical integration methods include left rectangle, right rectangle, midpoint, Simpsons, and trapezoidal. The user has... More
  • Mathematical Visualization Toolkit
    This site consists of a collection of plotting and solving applets featuring a uniform user interface. This site was... More
  • Numerical Integration Applet
    This applet provides a visual representation of various techniques of numerical integration including left rectangle,... More
  • Gallery of Volume Visualizations
    This is an extensive gallery of colorful visualizations for disk, washer, shell and cross-section methods of finding... More
  • Partial Derivative Geometrically Gallery
    This is a great collection of animations of partial derivatives and the slope of the tangent lines. A series of... More
  • Volumes
    Volumes (Tutorial)
    This is a collection of tutorials (Flash and Java) on various applications of integration including area between two... More
  • Visual Calculus: Applications of Integration
    This site is a collection of tutorials (Flash and Java) on various applications of integration including area between... More
  • Visual Calculus: Applications of Integration-Work
    This site is a collection of tutorials (Flash and Java) on the concept of Work including Hooke's Law, pumping liquids... More