Calculus

Before you can dive into engineering you first need to have an understanding of mathematical concepts Calculus, Trigonometry/Geometry, and Algebra.

The basis of Calculus is the idea of determining the "derivative" or rate of change of a function with respect to another variable.

Simply put "the rate of A in relation to B"

Common Angles and Radians Conversion

Shapes and Equations

Ln Functions

Common Angles and Radians Conversion

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Concepts to Remember

Study Guide and Cheat Sheet:

Derivative of Trig Functions
Power Rule
Product Rule
Quotient Rule
Ln Rules
Eulers Constant Rules
Series and Sequences
Trig Expansion and Taylor Series Expansions
Arc Length and Surface Area

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Taking a Derivative

The problems to the right showcase examples of taking a derivative from the various functions but not real-life scenarios.

Related Rates

The problems to the right showcase related rates or scenarios in which calculus can be used to determine an unknown rate in a system in which some variables are given.

For example, if you witnessed something moving but wanted to know how fast in relation to another moving part in the same system how would you determine that?

Flying Kite

A kite is flying horizontally at an altitude of 300ft at 20ft/s. How fast is the string being let out when it is 500ft long? How fast is the angle theta changing?

Falling Ladder Scenario

A 5-meter-long ladder begins to slide down the wall. When the bottom of the ladder is 4 meters from the wall it is moving at 2 meters a second. How fast is the top of the ladder moving at that point?

Conical Réservoir

A conical reservoir that is 8 feet in diameter and 10 meters tall is being fill with water at 2 cubic feet a second. How fast is the water level rising when it is 5 feet deep?

Flying Kite

A kite is flying horizontally at an altitude of 300ft at 20ft/s. How fast is the string being let out when it is 500ft long? How fast is the angle theta changing?

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Maximize and Minimize

The problems to the left showcase scenarios in which you are tasked with maximizing the area with given dimensions and parameters.

For example, if you were an engineer and you were given "x" amount of rope to work with how would you maximize the area?

Maximize a line on a curve

Maximize the function P = x*y^2 on the ellipse Y^2 + 2x^2 = 8

Maximize Usable Area

300 feet of rope is supposed to be used to make a rectangular area. The rope is to be used only on 3 sides because it is being built against a wall. Find the dimensions to maximize the area.

Maximize the Area of the Box

A rectangualar box with a square base and no top must contain 256 cubic inches of stuff. Find the dimensions that maximize the area of the box.

Maximize a line on a curve

Maximize the function P = x*y^2 on the ellipse Y^2 + 2x^2 = 8

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Finding Slope of Tangent Line

The problem to the right showcases how you would find the slope and equation of a tangent line.

For example, if you were a material science engineer and you were given a stress-strain plot for a material but wanted to know the rate of plastic deformation occurring at a specific point.