Applied Math Problems – Real World Math Examples will cover many real life uses of Math from Algebra to advanced Calculus and Differential Equations.

Please keep in mind, the purpose of this article and most of the applied math problems is not to directly teach you Math.

If you use this as a reference please be sure to properly cite us and link to the original. Thank you 🙂

## Why is Kinvert Making Applied Math Examples?

Though I have a Mechanical Engineering Degree and an Aerospace Engineering Degree, I wasn’t always good at Math.

As with most things in my life, I struggle with things I don’t see the point of.

Sure, I could find that x + 5 = 10, sure, x = 5. Who cares?

But when I was trying to solve a real world problem I independently invented Newton’s Method, Numerical Integration, etc.

I learn when I know the WHY of what I’m learning.

That’s what this article on applied Math examples is all about. I’m not here to directly teach you Math, at least in these articles. This all exists to help show you the reason and uses for Math in the real world.

If you know a real world use of a Math concept, please let me know in the comments below!

## We Will Be Updating These Applied Math Problems and Real World Math Examples

This is a living list that will be updated with time. Some of these topics might end up with so many example’s we’ll have to link to a separate article for it. For example, if we list every example where we use a Function, which is a topic of Algebra, that list in and of itself would contain just about every real world math example we’ll make.

We divided these applied math problems and real world math examples in to mathematical disciplines.

## Applied Algebra Examples

See that robot? Our students made it. Without applying Algebra it would not have been possible.

- Statics, Dynamics, a ton of stuff
- Intro
- Real Numbers
- These are used all the time for just about everything

- Synthetic Division
- Division is used all the time. If you are stranded on a desert island and want to make a helicopter from coconuts, you might need Synthetic Division

- Real Numbers
- Graphs
- Distance Between Two Points
- Building a Bridge in Minecraft –
**https://youtu.be/P2vd-8ilNs0** - Navigation

- Building a Bridge in Minecraft –
- Midpoint Between Two Points
- Actual Use in Minecraft –
**https://youtu.be/0hjUqseXf0w**Factoring- RSA Encryption (cyber security)

- Actual Use in Minecraft –
- Circles
- Computer Graphics

- Distance Between Two Points
- Linear Equations
- Calibrating a Joystick –
**https://youtu.be/Vb_GaXuB15c** - Building a Bridge in Minecraft –
**https://youtu.be/P2vd-8ilNs0**

- Calibrating a Joystick –
- Polynomials
- Degree of Polynomial
- Quadratic Equations
**Applied Math Example – Double Definite Integral – Finding Lift on Race Car Wing**- Applied Math Example – Definite Integral – F1 Race Car Telemetry Data Braking

- Higher Order Polynomials

- Complex Numbers
- Electrical Engineering
- Kirchhoff’s Current Law
- Kirchhoff’s Voltage Law

- Electromagnetism

- Electrical Engineering
- Functions
- Almost Everything
- Intro to some uses –
**https://youtu.be/r0xLvCLoBOA**

- Composite Functions
- Find Kinetic Energy as Function of Time –
**https://youtu.be/eeGOUeX2keo** - Temperature Changing Function of Time – Convert to Rankine From Celcius

- Find Kinetic Energy as Function of Time –
- Exponential Functions
- Exponential Growth
- Exponential Decay
- Economics

- Logarithmic Functions
- Interest
- Compounding
- Decibels
- Graphing
- Richter Scale

- Conics
- Orbital Mechanics

- Ellipse
- Orbital Mechanics

- Parabola
- Orbital Mechanics

- Hyperbola
- Orbital Mechanics

- Systems of Linear Equations – Substitution and Elimination
- Applied Math Example – Elimination – Equilibrium of Rigid Bodies
- Applied Math Example – Elimination – Force on F1 Nose Cone
- Equilibrium of a Rigid Body
- Applied Math Example – Cude Home Value Estimation –
**https://youtu.be/VHxOWbF1VLM** - Building a Bridge in Minecraft –
**https://youtu.be/P2vd-8ilNs0** - Estimating Car Price / Value –
**https://youtu.be/mbGPkzwjY1o** - 3D Printer Pre Heating –
**https://youtu.be/us8YRqdNEbA**

- Matrices
- Computer Graphics

- Determinants
- Finding the Moment or Torque on a Wrench

- Matrix Alebra
- See Linear Algebra below – Applied Linear Algebra Examples

- Partial Fraction Decomposition
- Systems of Non Linear Equations
- Sequences

## Applied Linear Algebra Examples

- Dot Product – Scalar Product
- Applied Math Example – Dot Product – Finding the Angle Between Two Vectors
- Many More Uses

- Vector Product- Cross Product
- Finding the Moment or Torque on a Wrench
- Magnetic Fields

- Elimination
- Applied Math Example – Elimination – Equilibrium of Rigid Bodies
- Applied Math Example – Elimination – Force on F1 Nose Cone

- Basis
- Computer Graphics

- Projections
- Computer Graphics

- Least Squares
- Fitting Equations to Data
- Machine Learning

- Determinants
- Finding the Moment or Torque on a Wrench

- Eigenvalues
- Eigenvectors
- MDOF Vibration

- Positive Difference
- Singular Value Decomposition
- Linear Transformation
- Computer Graphics

## Applied Calculus Examples

- Limits
- Differentiation
- Rates of Change
- Velocity and Acceleration

- Indefinite Integrals
- Definite Integrals
- Distance Traveled by F1 Car Under Braking
- Applied Math Example – Definite Integral – F1 Race Car Telemetry Data Braking
- Mass Flow Through 2D Constant Area Profile
- Distributed Loads
- Centroids
- Area Moment of Inertia
- Work
- Linear Impulse and Momentum

- Series
- Approximating Functions

- Fourier Series
- SDOF Periodic Forced Vibration
- Spectrograms

- Parametric Equations
- Partial Derivative
- Differentials
- Double Integrals
- Conservation of Mass
- Conservation of Linear Momentum
**Applied Math Example – Double Definite Integral – Finding Lift on Race Car Wing**- Applied Math Example – Double Integral Polar Coordinates – Flow in F1 Airbox Inlet
- Applied Math Exmaple – Double Integral – Flow in F1 Sidepod Inlet

- Triple Integrals
- Conservation of Mass
- Conservation of Linear Momentum

- Change of Variables
- Vector Fields
- Curl
- Fluid Dynamics – Vorticity and Irrotationality

- General
- Magnetic Fields
- Fluid Dynamics
- Maxwell’s Equations

- Curl
- Line Integrals
- Circulation
- Ampere’s Law
- Faraday’s Law
- Maxwell’s Equations
- Mass of a Wire
- Work Done by Vector Field

- Green’s Theorem
- Planimeter – Finding Area

- Surface Integrals
- Electric Flux
- Electric Charge on a Surface
- Electric Fields
- Gauss’s Law
- Capacitance
- Force of Pressure on an Area
- Mass Flow

- Divergence
- Bernoulli

- Stoke’s Theorem

## Applied Differential Equations Examples

In college I struggled with Differential Equations at first because the only use I really saw was certain circuits and harmonic motion.

So I set out to find a use, and I ended up simulating the heat transfer through brake rotors. I personally learn Math best when I see actual uses. Let’s look at real life uses of Differential Equations.

If I am missing any, please let me know in the comment section below.

- First Order
- Separable Variables
- Suspension Bridge

- Linear Equations
- Newton’s Law of Cooling
- Terminal Velocity
- Air Resistance
- Inclined Slope Sliding

- Exact Equations
- Solutions by Substitutions
- Non Linear
- Air Resistance

- Brief Numerical

- Separable Variables
- Second Order Linear
- Simple Harmonic Motion

- Higher Order
- Linear
- Cantilevered Beam Deflection
- Simply Supported Beam Deflection
- Free Vibration
- Rotational Imbalance
- Column Buckling
- Applied Math Example – 2nd Order Initial Value Differential Equation – F1 Front Wing Bending

- Initial Value
- Cantilevered Beam Deflection
- Applied Math Example – 2nd Order Initial Value Differential Equation – F1 Front Wing Bending

- Boundary Value
- Simply Supported Beam Deflection

- Homogeneous
- Free Vibration

- Non Homogeneous
- Forced Vibration
- Rotational Imbalance

- Reduction of Order
- Homogeneous Linear with Constant Coefficients
- Undetermined Coefficients
- Variation of Parameters
- Couchy Euler
- Elimination
- Projectile Motion

- Non Linear
- Rocket Motion
- Motion in Force Field
- Non Linear Springs

- Linear
- Series
- Power Series

- Laplace Transform
- Car Over a Bump
- Springs and Mass
- Beam Deflection

- Systems of Differential Equations
- Beam Fixed on Both Ends

- Partial Differential Equations
- Navier Stokes
- Couette Flow

## Applied Numerical Examples

- Newton’s Method
- Applied Math Example – Newton’s Method – Finding the Area Ratio for Rocket Nozzles

- Riemann Sums
- Shooting Method
- Beam Deflection

- Interpolation
- Trapezoidal Rule
- Simpson’s Rule
- Taylor Series
- Precise Approximation in CS

- Runge Kutta
- BVP
- Elliptic
- Parabolic
- Hyperbolic

## We Welcome Your Suggestions!

If you know of a real world use for a certain Math concept please let us know in the comments below.

Also, please remember this is a work in progress. With time we will be adding more real world Math examples to this applied Math list.

## Suggested Math Textbooks

Calculus – In College I primarily used Calculus Early Transcendental Functions by Larson et all – **Check price on Amazon** – **https://amzn.to/2LuiI3K**

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