Perform any Aerodynamic computations using the AERODYNAMICS MADE EASY with your powerful TiNspire CX at https://www.tinspireapps.com/?a=ADME . Compute Thrust, Lift, Drag, Pressure, Bernoulli Equation, Gas Laws, Mach Number, Mass Flow Rates, Continuity Equation and much more. Read the App’s extensive functionality below.

Use the free trial at https://www.tinspireapps.com/trials

• Mach Number
• Mass Flow Rate
• Wind Tunnel Analysis
• Drag
• Drag Coefficient
• Wing Analysis: Pressure, Velocity, Density
• Pressure Solver
• Pressure under Water Surface
• Thrust Equation Solver
• Lift Equation Solver
• Bernoulli Equation Solver
• Continuity Equation Solver
• Combined Gas Law
• Ideal Gas Law
• Read: The Big 5 Equations
• Average Speed=Distance/Time : v=d/t
• Linear Motion: vf^2=vo^2+2*a*d
• Linear Motion: v=vo+a*t
• Linear Motion: d=(vo^2+vf^2)/2 * t
• Linear Motion: lambdax=v0t + 1/2at^2
• Linear Motion: v=v(2*g*h)
• Rotational Kinetic Energy K=1/2*I*lambda^2
• Harmonic Motion: T=2p/lambda
• Harmonic Motion: E=1/2*k*A^2
• Harmonic Motion: T=2p*v(l/g)
• Harmonic Motion: f=1/T
• Harmonic Motion: T=2*p*v(m/k)
• Harmonic Motion: T=2*p*v(I/mgd)
• Harmonic Motion: x=A*cos(lambdat+F)
• Harmonic Motion: v=v(A^2-x^2)
• Harmonic Motion: Max Velocity
• Harmonic Motion: Max Acceleration
• Period of Spring T=2*pv(mass/spring constant)
• Spring F=k*x
• PotentialEnergy of Spring Us=1/2*k*x^2
• Spring Time T=2*p*v(l/g)
• Time Frequency T=1/f
• Wave Length lambda=v/f
• Time T=2*p*v(m/k)
• Waves+Vibrations: v=v(T*(m/L))
• Waves+Vibrations: k=2*p/lambda
• Waves+Vibrations: lambda=2pf
• Sound: Doppler Effect
• Sound: l_b-l_a=1/2*lambda
• Sound: beta=10*log(I1/I2)
• Sound: lambda=v/f
• Sound: f1=f/(1 plus/minus s/c)
• Sound: v=v(B/lambda)
• Sound: lambdaP=rho*v*omega*s_max
• Sound: I=lambdaP_max^2/(2*rho*v)
• Sound: I=P/(4*p*r^2)
• Fluids: lambda=m/V
• Fluids: P=F/A
• Fluids: F2=F1*A2/A1
• Fluids: Fb=Fa*r_b^2/r_a^2
• Fluids: P=Po+p*h*g
• Fluids: F=lambda*V*g
• Fluids: p+(1/2)*lambda*v^2+lambda*g*h=a
• Fluids: Ds/Di=h_sub/h_s
• Fluids: Q=p*r^4*(P1-P2)/8*mu*L
• Fluids: T=F/L
• Fluids: lambda1*A1*v1=lambda2*A2*v2
• Kinetic: Translational
• Kinetic: Rotational
• E_pot=E_kin : lambda*x^2=m/k*v^2
• Potential Energy
• Potential: Spring (Us)
• Potential: Universal Gravitat. (UG)
• Heat: Q=m*c*deltaT
• Heat: Q=m*L
• Heat: W=deltaP*d*lambdaV
• Heat: deltaE=Q-W
• Heat: Conduction
• Heat: Convection
• Heat: w=-n*r*t*ln(vf/vi)
• Miscellaneous: Heat (H)
• Miscellaneous: W=F*s*cos(?)
• Miscellaneous: W=F*s*sin(?)
• Miscellaneous: Power=W/t
• Miscellaneous: E=mu*dx
• Work Energy Theorem
• Photon Energy: E=h*c/lambda
• Volume of Gas
• Boyle’s Gas Law
• Charles’ Gas Law
• GayLussac Gas Law
• Combined Gas Law
• Ideal Gas Law
• Adiabatic Expansion of Ideal Gas Law
• Gas Sum / Dalton Law
• Graham’s Gas Law
• Circle Solvers
• Angle Finder
• Linear <-> Angular Speed Converter
• Periodic Table of Elements: Symbol
• Periodic Table of Elements: Element Name
• Find Absolute Error and % Error
• Convert: Normal to Scientific Notation & back
• Density=Mass/Volume Solver
• Moles & Representative Particles
• Atoms to Moles Conversion
• Relativity: Time-Dilation
• Relativity: Mass-Dilation
• Water
• Ice
• Steam
• Methyl Alcohol
• Benzene
• Wood
• Soil
• Air
• Aluminum
• Marble
• Glass
• Iron/Steel
• Copper
• Silver
• Mercury
• Gold

## TiNspire CX : Real Estate APP available now

Great News: Real Estate agents/students using a TiNspire CX can now use the Ti Nspire Calculator to perform any type of Real Estate related computation using the REAL ESTATE MADE EASY app at https://www.tinspireapps.com/?a=REME . It is by far the most comprehensive calculator APP for Real Estate including Step by Step Computations to Capitalization Rate, Feet, Acre, Yards, .. Conversions, Gross Rent Multiplier, Operating Expense Ratio, Cash on Cash Return, Time Value Computations. Witness this for yourself below.

Try the free trial at https://www.tinspireapps.com/trials/

Functionality included:

• Capitalization Rate
• Cash on Cash Return
• Gross Rent Multiplier
• Loan to Value Ratio
• Debt Service Coverage Ratio
• Operating Expense Ratio
• Lengths
• Areas
• Volumes
• Times
• Currencies
• and many more
• Portfolio: Expected Return
• Portfolio: Expected Return given \$ Amounts
• Portfolio: 2 Assets Risk
• Portfolio: 2 Assets Risk with Weights
• Portfolio: 3 Assets Risk
• Find Portfolio Beta
• Find Correlation of 2 Assets
• Find Covariance of 2 Assets
• All in One 2 Asset Explorer
• Stock: Expected Return
• Stock: Expected Return using Weighted Mean
• Find Stock Beta
• Find Stock Alpha
• Find Stock Risk
• CAPM
• CAPM : Find Risk Premium
• Expected Return using Risk Premium
• Value of Preferred Stock V = D / i
• Gordon Growth Model V = D / (k-g)
• Moving Average
• Simple Interest A=p*i*n
• Future Value fv=pv*(1+r)^t
• Present Value fv=pv*(1+r)^t
• Compounded Interest fv=p*e^(r*t)
• Future Value fv=pv*e^(r*t)
• Present Value fv=pv*e^(r*t)
• Future Value of Annuity
• Present Value of Annuity
• Net Present Value : Even Cash Flow
• Net Present Value : Uneven Cash Flow
• Internal Rate of Return (IRR)
• Modified Internal Rate of Return (MIRR)
• PE Ratio
• Current Ratio = CA / CL
• Quick Ratio = (CA-INV) / CL
• Average Collection Period = AR / CS
• AR Turnover = Sales / AR
• Inventory Turnover = Cogs / Inventory
• Total Asset Turnover = Sales / Total Assets
• Fixed Asset Turnover = Sales / Fixed Assets
• OI-ROI = OI / Assets
• Debt Ratio = Total Debt / Total Assets
• Return on Assets = Net Income / Total Assets
• Return on Equity = Net Income / Equity
• Operating Margin
• Times Interest Earned = EBIT / Interest Expense
• Net Margin Ratio
• Gross Margin Ratio
• Leverage Multiplier
• 3 Step Dupond Return on Equity
• Weighted Cost of Capital
• Capital Asset Pricing Model
• Gordon Growth Model V = D / (k-g)
• Build Up Method
• After Tax Cost of Debt = k*(1-t)
• Tax Effect = (MV-BV)*Tax Rate
• Book Value = Cost – Accum. Depreciation
• Read: Value a Company (Replacement Cost)
• Read: Value a Company (Discounted Cash Flow)
• Straight Line Depreciation
• Payback Period
• Discounted Payback Period
• Dividend Payout Ratio = DIV / NI
• Retention Ratio = 1- DIV / NI
• Sustainable Growth Rate = ROE * (1-b)
• Read: Percent of Sales Method
• Effective Interest Rate (Yield)
• Real Interest Rate
• Inflation Rate
• Present Value of Perpetuity
• Amortized Loan Payment R=Pi/(1-(1+i)^-n
• Loan Solver
• Current Yield Y = C / P
• Yield to Maturity (YTM) Zero-Coupon
• Approximate Yield to Maturity
• Bond Duration – Macaulay Method
• Marginal Profit
• Marginal Revenue
• Break Even Point R=C
• Continuous Income Stream
• Consumer Surplus
• Producer Surplus
• Cobb-Douglas Prod.
• Gini Coefficient
• Differentials
• Logistic Differential Equation
• Simplex Algorithm
• Average Tax Rate
• Marginal Tax Rate
• Price Index
• Real GDP – Expenditure Approach
• Real GDP – Income Approach
• GDP Deflator: Nominal GDP -> Real GDP
• Compute any Rate [%] : Labor
• Nominal & Real Interest Rate
• Unemployment Rate
• Moving Average
• Simple Exponential Smoothing
• Exponential Smoothing/Forecasting (Seed)
• Portfolio Return
• Portfolio Risk

## Ti Nspire CX: Integration of Single and Multivariable Functions – Step by Step

Fortunately, TI Nspire CX users can do Step by Step Integration using Calculus Made Easy at www.TiNspireApps.com . Just enter a function of one or more variables and get the solution immediately. Watch this brief video showing Step by Step Integration:

Just enter a function of one or more variables to find single or multiple integrals – step by step. That involves Integration by parts, U-Substitution, Integration by Partial Fractions, Double and Triple Integrals and Polar Coordinates.

## TiNspire CX: Change the Order of Integration

Changing or Reversing the Order of Integration using the TiNspire CX can be achieved using Calculus Made Easy at www.TiNSpireApps.com as shown below :

First enter the x and y bounds and watch the answer appear at the bottom screen:

## TiNspire : Solve Complex Numbers and Complex Functions

TiNspire users can solve Complex Numbers and Complex Functions – Step by Step – using the Complex Analysis Made Easy app at www.TiNspireApps.com :

The App is comprehensive and capabilities can be viewed below, the free trial can be downloaded at www.TinspireApps.com/trials

Capabilities:

• Step by Step Complex Numbers
• Step by Step Analytic and Harmonic Functions
• Step by Step Cauchy-Riemann Conditions
• Step by Step Solve Contour Integrals
• Step by Step Poles and their Order
• Step by Step Residues and their Sums
• Step by Step Solve Complex Equations
• Step by Step Solve Quadratic Equations
• Step by Step Differentiation and Integration
• Solve any Equation or Inequality
• One Complex Number: All-in-one-Explorer
• Two Complex Numbers: All-in-one-Explorer
• De Moivre Theorem : (a+bi)^n
• De Moivre Theorem : r*(cos(x)+sin(x)*i)^n
• Roots of Unity : z^n=1
• Remainder Theorem
• Find Partial Fractions
• Factor
• Expand/Distribute
• Evaluate f(z)
• Find Poles of f(z)
• Find the Order of Poles of f(z)
• Pole-Zero Plot
• Find Residues of f(z) and their Sum
• Find Limits: lim z->c f(z)
• Compute Discriminant
• Complete the Square
• Complete the Square to find Zeros
• Complete the Square to find Vertex
• Is Complex f Analytic?
• Check Cauchy-Riemann Conditions
• Is f Harmonic?
• Find the Harmonic Conjugate Function
• Find f'(z) and f”(z)
• Evaluate f'(z) and f”(z)
• Step by Step Differentation
• Find Laurent Series at Poles
• Find Integral f(z)dz
• Find Definite Integral (z)dz over [z1,z2]
• Find Contour Integral Integral f(z)dz
• Find Curve Integral Integral f(z)dz
• Find Antiderivative & Constant of Integration: Integral f(x)dx + C
• Step by Step Integration: Integral f(x)dx
• Laplace Transforms
• Solve 2. order Diff Eq using Laplace Transforms
• Solve 3. order Diff Eq using Laplace Transforms
• Table of Laplace Transforms
• Inverse Laplace Transform
• Fourier Transform of Piecewise Def Function
• Fourier Transform of f(t)
• Inverse Fourier Transform
• Table of Fourier Transforms
• Table of Z-Transforms
• Solve any 1. order Differential Equation
• M(x,y)dx+N(x,y)dy=0
• Linear in y Differential Equation
• Newtons Law of Cooling / Heating
• Euler Method given n=Number of Pts.
• Solve any 2. order D.E.
• Homogeneous Differential Equation
• Non-Homogeneous Differential Equation
• All in one Vector Explorer
• Find Norm
• All in one 2-Vectors Explorer
• Find Angle between 2 Vectors
• Find Cross Product
• Laplacian of Scalar Field
• Divergence of a 3D Vector Field
• Curl of a 3D Vector Field
• Line Integral Integral(f1dx+f2dy) over Curve C
• Area under Param. Curve using Line Integral
• Line Integral given Function & Parametrization
• Line Integral given Function & 2 Points
• Line Integral given Vector Field & Parametriz.
• Greens Theorem Integral(Pdx+Qdy)
• Greens Theorem Integral(Pdy+Qdx)
• Surface Integral: Function
• Surface Integral: Function & t-u-Parametrization
• Surface Integral: Vector Field

## TiNspire : Complex Analytic and Harmonic Functions

In Complex Analysis you will be asked to check if a complex function is analytic which requires checking the 2 Cauchy Riemann Conditions. Fortunately, the TiNspire has the ability to deal with those and we can go ahead and solve those problems using the Complex Analysis Made Easy app at www.TinspireApps.com to solve those problems step by step.

Say we are given a complex valued function in the format u+i*v such as x^2-y^2+i*2*x*y as shown below. Out comes the solution with steps showing that this function is indeed analytic. Insiders realize that this is actually the function f(z)=z^2

When entering z^2 in the top box we will get naturally the same answer. See below

Next Question: Is a given Complex Function Harmonic? And if so what is its harmonic conjugate ?

Lets select that option in the menu as shown below:

Lets answer the first question first : Is e^(-3x)*cos(3y) harmonic ? Well, let’s just enter it as shown below:

Voila! It is Harmonic. And we understand why 😉

Lastly, let’s find the harmonic conjugate function to x^2-y^2 , entered as shown below:

Beautiful, good thing we have our handy dandy TiNspire to provide those answers.

## Z-Transforms using the TiNspire CX CAS

We again listened to your request and added Z – Transforms and Inverse Z-Transforms to the Differential Equation Made Easy APP at www.TiNspireApps.com .

Lets take a look at the menu to see the lengthy listing of the forward Z Transforms.

Here is an example of the Z-Transform of an exponential function:

Below find the menu options for the Inverse Z-Transform:

Options A and B offer a Table of Z Transforms and Partial Fraction Decomposition which are useful tools when doing Z Transforms.

## TiNspire: CoFactors , Determinant , A as Product of Elementary Matrices

To Find a Determinant given CoFactors in a Row use Linear Algebra Made Easy at www.TiNspireApps.com and enter your quadratic Matrix and selected Row as follows:

When selecting Row2 we get the following CoFactors and of course the same determinant:

To Express a quadratic Matrix as a Product of Elementary Matrices we simply keep track of the RREF Operations when finding its Inverse Matrix. See below:

and finally

Voila !