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 🙂

Applied Math Problems Outline

Here is what we’ll be going over in this article about the Sphero RVR SDK.

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 and PreCalculus Examples

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

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

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 5the 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

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

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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