Shop Essentials (Applied Mathematics)

Concepts of Calculus 310

This class covers the basic concepts of calculus.

  • Difficulty Advanced

  • Format Online

  • Number of Lessons 14

  • Language English


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Course Outline
  • Objectives
  • What is Calculus?
  • Functions
  • Graphing Functions
  • Lines
  • Graphing a Line
  • Finding the Slope of a Line
  • Limits
  • Evaluating Limits
  • The Difference Quotient
  • Differentiation
  • Integration
  • The Role of Calculus in Manufacturing
  • Summary
  • Define calculus.
  • Describe functions.
  • Describe how to represent functions on graphs.
  • Define a line.
  • Describe how to graph a line.
  • Describe the process for finding the slope of a line.
  • Define limits.
  • Describe how to evaluate limits.
  • Define the difference quotient.
  • Define differentiation.
  • Define integration.
  • Describe the role of calculus in closed-loop control systems.
Vocabulary Term


A branch of math that uses known quantities to find unknown quantities. Algebra can be used for functions involving regular shapes and straight lines.


A type of mathematics that measures changes in one quantity in relation to another. Calculus is used for functions involving curves.

closed-loop system

A type of control system that automatically changes the output based on the difference between the feedback signal to the input signal.

continuous function

A function that can be compared to a bridge that connects a road on both sides. Just as a bridge allows you to drive along the road with no interruptions, obstacles, or detours, a continuous function allows you to draw a line or a curve without lifting your pencil.


A number that indicates a location in 2- or 3-dimensional space. Two-dimensional graphs use x- and y-coordinates.


A mathematical operator used to indicate a change in a value. It is represented by the Greek letter Δ.

dependent variable

A value that is typically the output of a function.


The rate of change.

difference quotient

The ratio of the change in y-values over the change in x-values. The difference quotient is simply a more complex variation of the formula for slope.


The process of determining the rate of change of a curve.

discontinuous function

A function that has a break, hole, or jump in the graph.


The difference between the setpoint and the process variable. When errors are detected, the controller sends instructions to the control system to adjust the output to compensate.


A relationship between two things in which the value of one thing depends on the value of the other. Functions can be represented by graphs.


A two-dimensional representation of a function on an x- and y-axis.

independent variable

A value that is typically used as input for a function.


The value or independent variable entered into a function.


A small part of a larger whole.


The process of summing up small areas under a curve to determine the total area.


A value that you would expect the function to go to, or a value that gets extremely close to the value you want to reach.


A set of two or more points that extend endlessly in two directions. A line is the quickest way to get from one point to another.

linear equation

An equation of the form y = ax + b, where a and b can be any real number. Linear equations are a way to represent lines.

negative slope

When a line goes down and to the right.


The end result or dependent variable of a function.

PID control

One of the most common types of process control. Proportional, integral, derivative control adjusts system outputs when there is a difference between the setpoint and process variable.


A dot that indicates a definite position or location. A point has no width, depth, or length.

positive slope

When a line goes up and to the right

process variable

The actual value detected by a sensor as a process is taking place.


The vertical movement of a line.


The horizontal movement of a line.

secant line

A line that intersects the graph at two points.


A preset value such as a specific temperature, speed, or flow rate that the control system is supposed to reach.


A measure of the slant or steepness of a line.

substitution method

The simplest method for evaluating limits. In the substitution method, you replace x with another value.

summing junction

The part of a PID control system in which the SP and PV are compared to each other. The difference between the SP and PV is called error.

tangent line

A line that touches the graph only once.