MAT 126 -- Calculus I
Course Description
Professor: D.
Bradley (http://www.umemat.maine.edu/faculty/bradley/index.html)
Text: James Stewart, "Calculus: Concepts and Contexts,"
Brooks/Cole, Boston, 1998. Chapters 1-5.
References:
- How to Ace Calculus, by Colin Adams, Abigail Thompson and Joel Hass, W. H. Freeman and Company, New York, 1998.
-
Michael Spivak, Calculus, (3rd ed.) Publish or Perish Inc.,
Houston, 1994.
-
R. L. Jeffery, Calculus, University of Toronto Press, 1955.
Syllabus:
-
Functions
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Parametric Curves
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Exponential Functions
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Inverse Functions and Logarithms
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Limits and Derviatives
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The Tangent Problem
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The Limit of a Function
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Continuity
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Rates of Change
- Derivatives
- Linear Approximations
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Differentiation Rules
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Derivatives of Polynomials and Exponential Functions
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The Product and Quotient Rules
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Derivatives of Trigonometric Functions
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The Chain Rule
- Implicit Differentiation
- Derivatives of Logarithmic Functions
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Applications of Differentiation
- Related Rates
- Maximum and Minimum Values
- Graphing
- Indeterminate Forms and L'Hopital's Rule
- Optimization Problems
- Newton's Method
- Antiderivatives
- Integrals
- Areas and Distances
- The Definite Integral
- Evaluating Definite Integrals
- The Fundamental Theorem of Calculus
- The Substitution Rule
- Integration by Parts
- Numerical Integration
- Improper Integrals