MATH120 - Differential Calculus for Measurement

This is the second in a series of courses that cover the equivalent of a one-year college course in calculus. These courses are

• MATH119 - Functions, Limits, and Continuity
• MATH120 - Differential Calculus for Measurement
• MATH121 - Sequences, Limits, and Series
• MATH122 - Integral Calculus for Measurement
• MATH123 - Series, Approximation, and Sensitivity

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This course will cover the topic of differential calculus with applications to measurement. This course will cover the following:

• Introduction
• Definition of the derivative
• Left and Right Hand Derivatives
• Notation
• Theorems involving derivatives - Part I
  • Derivative of a constant a
  • Derivative of aƒ(x)
  • Derivative of x
  • Derivative of xƒ(x)
  • Derivative of xⁿ
  • Derivative of ƒ(x)+g(x)
  • Derivative of a Polynomial
• Physical motivation for the Derivative
  • Motion in one dimension, position, speed, acceleration, jerk
  • Slope of the a tangent line
  • Maxima, Minima, and Points of Inflection
  • Approximation
  • Forces, Equilibrium, and Stability
  • Sensitivity
• Theorems involving derivatives - Part II
  • Derivative of ƒ(x)g(x) - Product Rule
  • Derivative of ƒ(g(x)) - Chain Rule
  • Derivative of ƒ(x)/g(x) - Quotient Rule
  • L'Hopital's Rule
• Implicit Differentiation
• Examples of derivatives
  • Trigonometric Functions
  • Exponential Functions
  • Hyperbolic Functions
  • Logarithmic Functions
  • Inverse Trigonometric Functions
  • Inverse Hyperbolic Functions
  • Derivative of x^r, r real
• Summary

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