# ExceLabTM 3.0Excel Calculus Powerhouse Add-in

## Solve complex calculus problems with simple formulas

• Solvers just like Built-In Math functions

• No coding. No learning curve. Just basic Excel skills

• Fast 20-sec installation and you are up and running

## What our users say

".. the ability to share models and results in a highly familiar platform..with near-zero learning-curve in using the program, have compelled me to break from the past and put in the effort to move our models to ExceLab."
"It is easy to learn and support provided by the admin staff is very nice. If anyone working on multi PDEs equation problems, just try this one you will love this solver"
What can you solve with ExceLab

Integrals

Derivatives

Interpolation

Algebraic Systems

ODEs

PDEs

Dyn. Optimization

Optimal Control

## Compute numerical integrals

• Formulas, VBA functions, and (x,y) data points

• Multiple integrals of any order by direct nesting

• Finite and infinite limits

• Singular integrands

 A 1 #NUM! 2 -4

## Compute numerical derivatives

• Formulas, VBA functions, and (x,y) data points

• Mixed partial derivatives of any order by direct nesting

• First and higher-order derivatives

$f\left(x\right)=xsin\left({x}^{2}\right)+1$
 A 1 =X1*SIN(X1^2)+1 2 =DERIVF(A1,X1,PI())
 A 1 1 2 -18.248596

## Interpolate 2D and 3D data points

• Map your scattered (x,y) and (x,y,z) onto a uniform grid and plot the surface in Excel

• Best known Natural Neighbour Algorithm

 A B C 1 x y z 2 0.124162 0.011109 0.124162 3 0.468730 0.229740 0.747031 .. ↓ 51 0.222274 0.049164 0.635259
 E F G .. P 1 0 0.1 → 1 2 0 =INTERPXYZ(A2:B51, z, grid_x, grid_y) 3 0.1 .. ↓ 12 1

## Find exact or best solution

• Non-linear coupled equations

• Systems with inequalities constraints

• Roots of non-linear equations

• Proven Levenberg-Marquardt Algorithm

${10}^{4}{x}_{1}{x}_{2}-1=0$ ${e}^{-{x}_{1}}+{e}^{-{x}_{2}}-1.0001=0$
 A X 1 =10^4*X1*X2-1 1 2 =EXP(-X1)+EXP(-X2)-1.0001 1
 A B 4 =NLSOLVE(A1:A2,X1:X2) 5
 A B 4 X1 9.10614674 5 X2 1.09816E-05

## Solve ordinary differential algebraic equations

• Initial value problems

• Boundary value problems

• Highly-staple highly-accurate fully-implicit adaptive algorithms

• Formatted output ready for plotting in Excel

$\frac{dv}{dt}=-2\zeta \omega v-{\omega }^{2}x$ 
 A B C D 2 t w 1 3 x 1 zeta 0.25 4 v 0 6 dx/dt =v 7 dv/dt =-2*zeta*w*v-w^2*x
 I J K 1 =IVSOLVE(B6:B7,(t,x,v),{0,12}) .. 32

## Solve partial differential algebraic equations

• Robust Method of Lines with adaptive time step

• Multiple regions with discontinuous properties

• General boundary conditions

• Flexible output formats for plotting transient and snapshot views

 Left Bc Right Bc A B C D 1 t k 1 2 x 3 u =IF(x=0,100,0) 4 ux 5 uxx 6 du/dt =k*uxx =u-100 =ux
 A B C D 8 =PDSOLVE(B6,B1:B5,C6,D6,{0,1},{0,1}) .. 30

## Solve dynamical optimization and parameter estimation problems

• Seamless integration with Excel Solver or ExceLab Solver

• Optimize your model parameters for best fit with experimental data

#### Applications

• Estimate differential system parameters

• Compute integrals limits

• Maximize a constrained dynamic objective with Excel Solver

• Dynamic curve fitting

• Numerous possibilities

$f\left(x,a,b\right)=\underset{a}{\overset{b}{\int }}1-{x}^{2}+b\cdot dx$

Find $a,b$ such that

$f\left(x,a,b\right)=8.333333$
 A B 1 a 0 2 b 1 3 integrand =1-x1^2+b 4 integral =QUADF(B3,X1,a,b) 5 constraint =B4-8.333333
 A B 7 =NLSOLVE(B5,(a,b)) 8
 A B 7 a -2 8 b 3

## Solve optimal control problems

#### Maximize (or Minimize)

$J=H\left(\mathbit{x}\left(T\right),T\right)+\underset{0}{\overset{T}{\int }}G\left(\mathbit{x}\left(t\right),\mathbit{u}\left(t\right),t\right)dt$

#### Subject to

$M\frac{d\mathbit{x}}{dt}=f\left(\mathbit{x}\left(t\right),\mathbit{u}\left(t\right),t\right)$ $\mathbit{x}\left(0\right)={\mathbit{x}}_{0}$ $\mathbit{x}\left(T\right)={\mathbit{x}}_{T}$ $\left|\mathbit{u}\left(t\right)\right|\le {\mathbit{u}}_{max}$
• Obtain rapid solutions with minimal effort and simple formulas. No programming.

• Structured direct solution procedure combining ExceLab calculus functions with Excel Solver.

• Remarkable convergence and performance illustrated by several worked examples.

• Consistent and sometime better results than complex methods See Publications.

Why should you work with us

• ### Evaluate freely to see the value and experience the difference for yourself.

• We stand behind our product which stands on its own merits.

• We help you with fast and effective support from expert staff.

• We deliver timely fixes to your issues.

• We listen to your needs. Get involved in shaping the next release with features that matter to you.

• Featherlight efficient library with one click installation and you are up and running.

• State of the art proven algorithms that work. Best default settings yet you have full control with optional arguments.

• Get rapid solutions with simple formulas in familiar Excel. Leave tedious coding and expensive complex tools behind.

• Share your results workbook with any one who has Excel. Who doesn't !

• Flexible licensing plans that suit your needs.

• Excel is virtually on every computer. Very easy to learn the basics and use.

• Help your students spend their time solving problems, not figuring out how to use complex tools.

• Intutive yet powerful differential equations solvers and integrated optimization.

• Simplified effective approach to optimal control problems for Engineering and Social Studies.