Engineering Lecture 4: Disturbances & Sensitivity - Functions & Differentiation, Exercises of Automatic Controls

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4 Lecture 4: Disturbances and Sensitivity

4.1 Math Topics

• Functions
• Differentiation
• Partial Differentiation

4.2 Functions

Required Skills

• Understand the concept of an independent and dependent variable (argu- ment of a function)

The functions you will encounter for this lecture are G(s) and T (s), both in the Laplace domain.

Resources

For a review of functions and a list of resources, see the notes for lecture #2.

4.3 Differentiation

Required Skills

• Be able to take the derivative of a function.

For a review of basic differentiation definitions please refer to the following resource.

• http://www-math.mit.edu/∼djk/18 01/chapter02/contents.html

MIT OCW Resources

• 18.01 Lecture Notes
• 18.013A Readings: Kleitman, Calculus with Applications, Chapter 8: Cal- culation of Derivatives by Rule

Readings

• Simmons, Calculus with Analytic Geometry, Chapters 2-4: The Derivative of a Function, The Computation of Derivatives, Applications of Deriva- tives

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Other Resources

• Strang, Calculus, Chapter 2: Derivatives (PDF)
• Strang, Calculus, Chapter 3: Linear Functions (PDF)
• Strang, Calculus, Chapter 4: The Chain Rule (PDF)

4.4 Partial Differentiation

Required Skills

• Be able to take the partial derivative of a multivariate function.

For a review of partial differentiation please refer to the following resources.

Readings

• Simmons, Calculus with Analytic Geometry, Chapter 19: Partial Deriva- tives

Other Resources

• Strang, Calculus, Chapter 13: Partial Derivatives (PDF)

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