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Comprehensive Mathematical Software Tool for Engineers

TK Solver™ release 6 is the latest version of a product that has been in the international market since 1982. It does mathematical modeling and equation solving using a very unique declarative programming method while also providing procedural programming capabilities available in other languages like Python, Visual Basic, FORTRAN, C, C++, Pascal, etc. It is also great for modeling thermodynamic systems, and very useful for rapidly developing and deploying Excel applications.

Learn more about TK Solver

Since 1982 many thousands of very satisfied customers have been using TK Solver in a wide range of industries such as:

Aerospace
Chemical and petrochemical
Automotive, agricultural and construction equipment manufacturing
Defence
R&D
Engineering colleges and universities – faculty, researchers and students

Companies that trust TK Solver

TK Solver Capabilities

Data Analysis

Explore, model and analyze data

Graphics

Visualize and explore data

Programming

Create scripts, functions, and classes

App Building

Create desktop and web apps

External Language Interfaces

Use TK Solver with Python, C/C++, Fortran, and other languages

TK Solver in the Cloud

Run TK Solver models in cloud environment using UTS CalcEdge™ platform and share your models online

Powerful technology at an affordable price. That’s TK Solver

Powerful versatile easy to use and significant time saving

Algebraic linear or nonlinear equations as well as differential equations can be easily handled in TK Solver. It also provides significant time savings by a factor of 10 to 100 in setting up problems compared to other methods used for the same tasks. TK Solver can be readily used for a wide range or problems from a single formula to many thousands of equations. TK Solver also has a very easy to use and powerful way to work with units - a very important aspect in solving engineering and scientific problems. This is much easier to do in TK than in matrix-oriented products like Matlab or Excel spreadsheets which lack facilities for handling units. TK has excellent facilities for working with engineering data such as table look ups data from graphs of relationships etc.

Rule-based problem solving

The unique rule-based declarative method for setting up problems gives TK Solver the power and major time saving capability. Other programming and analysis environments use a procedural approach that requires precise sequencing of instructions and formulas where the known and unknown variables are sorted out ahead of time. Not so with TK Solver. You don’t need to decide what variables will be inputs and which ones will be outputs when creating a mathematical model. This unique capability completely eliminates tedious “busy work” allowing you to accomplish more in less time.

Multi-Directional

Additionally, TK Solver gives you the ability to “backsolve” making it the ideal tool for testing “what if”, or “how can I get a specific answer” scenarios. Imagine being able to solve for anything, in any direction and reverse engineer a solution without having to rewrite the equations. TK Solver also has a built-in iterative solver. Just give TK Solver your best guess and it will use the iterative solver to find the answer.

Seamless integration with Microsoft Excel

Use TK Solver to rapidly develop Excel applications. Much easier and faster than using VBA dramatically reducing application development time. Set up the formulas in TK Solver and let it work in the background while you work in Excel, if that is what you like to do.

Other handy facilities in TK Solver

Instant MathLook As you enter the rules see them in a two dimensional rendering as if written by hand making it easy to check if what you just entered is correct. Change fonts and colors just like you do in Excel. Solution Tracer tracks and documents every detail of a solution for unprecedented control. Dynamic Plot Annotations displays highly detailed and customizable data analysis and visualization. Report Wizard delivers on-demand custom reports that can be saved as PDF files. Tutorials interactive and convenient online guides to help you get the most out of TK Solver. Many videos are also available in YouTube.

Convert legacy programs to a modern platform

If you have old code written in other programming languages, the fastest and most cost effective way to convert them into a modern and easy to use environment is to use TK Solver. It is the perfect answer! The UTS team can show you how to do this or do it for you as a service.

Sharing on the go

TK Solver math models can be shared with others via the CalcEdge web site. CalcEdge apps can be accessed with a browser or smart phone. The author of a CalcEdge app can choose exactly what they want to share. The algorithms are protected. The CalcEdge app interfaces can be customized in TK’s versatile MathLook Window. MathLook lets authors copy paste and position TK objects (variables, lists, plots, etc.) exactly where they want them. And MathLook allows you to include links to related web sites and videos.

TK Solver is also ideal for building enterprise applications and the good news is you don't have to be an expert to use it.

TK Solver readily integrates with standard databases as well as 3D CAD systems. There is no limit to what TK Solver can do!

TK Solver allows you to concentrate on the principles of the subject instead of the algebraic manipulations or the syntax of the programming code.

BOTTOM LINE: TK SOLVER FOCUSES THE MATH, SO YOU CAN FOCUS ON YOUR BUSINESS. IMAGINE POWER AND PRODUCTIVITY !

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+ How does TK Solver work?

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TK Solver: Case Studies

Case Study: Interest Calculations

The TK Solver Library includes a collection of functions useful for calculations involving interest. The factors that affect the equivalence are the amount of the cash flow, the timing of the cash flow, and the interest rate

Case Study: Iterative Solutions of Spiral Torsion Spring Equations

The nonlinear equations involved in designing spiral torsion springs can produce some surprising results. The simultaneous nonlinear equations must be solved iteratively for some scenarios.

Systems of Linear Equations, Math Languages and TK Solver

Solve a system of linear equations as part of a TK model, it may be best to simply type the equations as is and let the iterative solver do the work

LRC Circuits and Differential Equations

Kirchoff’s laws and the current-voltage relation for each circuit element provide a system of algebraic and differential equations from which the voltage and current throughout the circuit can be determined as a function of time

Converting a chart to a function

To computerize a plot with 4 curves to allow a user to solve for points not necessarily along those lines.

Pharmacokinetics

This case study shows how TK Solver can be used to solve a set of pharmacokinetic equations in order to model the distribution of methotrexate (MTX), a drug used mainly to treat cancer. The content for this example was provided by Professor Prasad Dhurjati of the University of Delaware.

Solving Complex Equations

A customer presented us with the following problem, along with a note suggesting that they were having difficulty solving the equations. The problem involved some geometry calculations. Specifically, the solution to the problem represented the point at which two surfaces blended together. The equations forced the slopes to be equal at the solution point.

Simplifying can make things less complex

Since (k-1)/k = 1 – 1/k, we have...

Order of Equations / Choice of Guess Variables

There are four equations and four unknowns. All the equations have two or more unknowns, so TK’s Direct Solver can make no progress and an initial guess is required. The purpose of this case study is to learn why TK responds to different guess variables as it does.

Interpolating Plots with One or More Log Scales

Application developers frequently need to convert tables and plots into continuous functions so that users of the program are not required to manually look up values. TK’s list function capability is perfect for handling functions of one argument, y = f(x).

List Solving vs. Procedure Function

Learn method about list solving and procedure function.

Handling Complex models

A customer sent me a TK5 model which wasn’t loading into TK6 properly. I was getting “Incomplete Load” errors in TK6. I looked at the rule sheet in TK5 and saw that an old TK Library function named Simpson was being used to do numerical integration. The topic of the model was beam deflection using the “Generalized Castigliano Theorem”

Case Study: Adding Calculus Functions to Excel

Excel is a good tool for organizing and summarizing data. Programs such as TK Solver are better suited for solving more sophisticated problems. Fortunately, it is easy to use these two programs together. This case study shows how TK Solver can be used to do numerical integration and the results passed to Excel.

Case Study: Adding Constraints to Equation Solving

TK’s iterative solver does not allow users to constrain the solution to be within a certain range. However the new optimizer in TK5 solves that problem.

Case Study: Finding the Best-Fitting Circle

Given a set of coordinates, determine the center and radius of the circle that fits the points most closely.

Case Study: Bivariate Normal Probabilities in Engineering

An extensive study was made of shear strength (x2) and weld diameter (x1) in an attempt to substitute a less expensive, nondestructive testing procedure for a destructive test.

Case Study: LRC Circuits and Differential Equations

The theory of electric circuits consisting of inductances, resistors, and capacitors, is based on Kirchoff’s laws: (1) The net flow of current through each node or junction is zero, (2) the net voltage drop around each loop is zero.

Case Study: Rapid Conversion of a Technical Paper to a Mathematical Model

A technical paper, in PDF form, containing an algorithm with over sixty linear, nonlinear and integral equations is converted to a mathematical model in TK Solver and subsequently linked to Excel and a web application.

Case Study: Converting Excel Formulas

Many customers are interested in converting their existing spreadsheet files to TK Solver files. One reason is that TK files can be run with RuleMaster, effectively distributing those models worldwide from a single server.

Case Study: Statistics and Curve-Fitting

Excel is loaded with statistical tools but TK Solver provides a handy collection of its own and can be used as a supplement in several areas. Data can be copied from Excel into TK lists or tables.

Case Study: Division By Zero

A customer sent in the following problem involving a five-member truss and reported that he was getting an unexpected error message - “Division by zero” - during iterative solution.

Case Study: Equation Solving

Case Study: Mathematical Modeling of Families of Charts

TK Solver is used to computerize stress calculations involving spherical shells with radial loads on nozzle connections. Bulletin 107 from the Welding Research Council is the source for the calculations.

Case Study: Fitting a Normal Distribution to a List of Values

The TK Library includes a family of routines for fitting data to probability distributions. This example shows a normal (Gaussian) distribution.

Case Study: Fortranvs TK

Here is an excellent comparison of TK and FORTRAN. The example is obtained from the following textbook: Introduction to Computing by James, Smith and Wolford; Harper-Collins.

Case Study: Optimization

The following problem is taken from “Basic Programs for Production and Operation Management” by Pantumsinchai, Hassan, and Gupta (Prentice-Hall, 1983).

Case Study: Heat Transfer on TK

(Based on Fundamentals of Heat and Mass Transfer by Incropera and DeWitt) Here is a listing of the topics covered by the collection of TK Solver math models.

Case Study: Himmelblau’s function.

We will investigate an equation known as Himmelblau’s function.This equation is used in the Graphics Utilities section TK Library as an example for creating contour plots.

Case Study: Items of Interest for OR/MS Today Readers

TK Solver as a math modeling tool - Easy-to-use equation solver - Solves problems forward, backward, for any combinations of inputs

Case Study: Douglas Knowledge Management System

Douglas Machine designs and manufactures high speed packaging machinery for clients in the United States and abroad. These machines are primarily for the food and beverage industries.

Case Study: Frustum of a Cone

The popular cone model is too simple to illustrate the “laws of TK”. The model of a frustum of a cone may do a better job. It has been derived by considering two cones: a cut-off upper cone (variables with suffix 1) and a complete cone (variables with suffix 2).

Case Study: Automating Linkage Plots

This paper describes the process in building a TK Solver model to solve linkage equations for both a single position and repeatedly through a range of motion.

Case Study: Interpolating Plots with One or More Log Scales

Application developers frequently need to convert tables and plots into continuous functions so that users of the program are not required to manually look up values.

Case Study: Matrix Function Examples

TK5 includes many new functions for calculations involving matrices. Although, many of these functions were previously available through the TK Library, the performance will now be much better.

Case Study: Numerical Integration and Differentiation

A manufacturer has the capability of transforming thin, flat sheets of metal into uniformly corrugated sheets of various pre-determined thicknesses.

Case Study: TK Solver Optimization

A certain corporation is planning to produce and market three different products. Let x1, x2, and x3 denote the number of units of the three respective products to be produced.

Optimization Case Study: Manufacturing Engineering

This example is taken from Engineering Optimization, Methods and Applications by G.V. Reklaitis, A Ravindran, and K. M. Ragsdell, published in 1983 by John Wiley & Sons.

Optimization Case Study: Pipeline Transmission System

This example is taken from Engineering Optimization, Methods and Applications by G.V. Reklaitis, A Ravindran, and K. M. Ragsdell, published in 1983 by John Wiley & Sons.

Optimization Case Study: Welded Beam Design

This example is taken from Engineering Optimization, Methods and Applications by G.V. Reklaitis, A Ravindran, and K. M. Ragsdell, published in 1983 by John Wiley & Sons.

Optimizer Case Study: Working with Differential Equations

TK Solver includes several built-in functions for solving differential equations numerically. They are all used similarly. For this example, we use the ODE_RK4 function.

Case Study: Optimizing Quality

A company produces rubber used for tires by combining three ingredients: rubber, oil, and carbon black. The cost of rubber is 0.04 per pound. The cost of oil is 0.01 per pound. The cost of carbon black is 0.07 per pound.

Case Study: Performance Issues

This article presents several issues concerning minimizing solution times. For comparison purposes, our test computer was running at 450 MHz.

Case Study: Pharmacokinetics

The content for this example was provided by Professor Prasad Dhurjati of the University of Delaware. It is used there in the class Applied Mathematics for Chemical Engineers (MATH 305).

Case Study: Random Numbers and Simulation

To develop an understanding of the set of possible outcomes for a particular scenario, we can set up and observe the actual events of interest or we can use a computer to model or simulate the events.

TK Solver Case Study: Applying Families of Functions in Product Selection Applications

Math models created for product selection or sizing frequently require the creation of families of performance functions. Given inputs defining the required performance, the model then repeatedly loops through the functions until the best product is found.

Case Study: Simplifying

Simplifying can make things complex Consider the equation

TK Solver Case Study: Creating Summary Tables

The TK Solver variable sheet provides a concise summary of the inputs and outputs of a mathematical model. However, if several different scenarios are run, the variable sheet can only store one at a time.

TK/Excel Link Case Study: Table Solutions

TK Solver’s versatile List Solver lets you generate tables and plots of variables within systems of equations. Once TK models are linked to Excel, you can still use the List Solver but you can also use Excel’s functionality to generate tables of solutions based on the linked variables.

Time-Step Solutions: Tank Draining

This example is taken from an excellent book by Johannes Gessler of Colorado State University, entitled TK Solver -- A Tutorial, published by McGraw-Hill. The book features many enlightening exercises and we encourage anyone wishing to hone their TK skills to purchase a copy.

TK Solver – A Tool Kit of Many Solvers!

TK’s Direct Solver performs inverse mathematical operations and inverts functions in an equation to solve for a single unknown. Then it applies what it learns to subsequent equations, making additional passes through the rules to solve previously bypassed equations and checking for inconsistencies.

Advanced Math -- Uncertainty Analysis

Uncertainty analysis is a technique for determining an estimate for the interval about a reported result within which the true result is expected to lie with a certain degree of confidence.

Case Study: Uncertainty Analysis

Uncertainty analysis is a technique for determining an estimate for the interval about a reported result within which the true result is expected to lie with a certain degree of confidence.

TK Solver 6.0 Limited Period Offer

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$199

Less than $17 /month for one user (paid yearly)

Network (per user)

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$599

Less than $50 /month per floating license (paid yearly)

Site (unlimited user)

Best for large teams

$4500

$375 /month pays for all user located at one physical location (paid yearly)

TK Solver 6.0 Special Offer for Academics

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