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

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

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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