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Worksheets marked with use PTC Mathcad premium features, otherwise they are Express compatible. All worksheets created in PTC Mathcad Prime 2.0 except where indicated.

Worksheet name | Category | Description |
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Analyzing Process Capabilities | Mechanical Engineering | This worksheet using PTC Mathcad takes a normal distribution to represent the amount of products lying outside the tolerance limits. |

Applying the Momentum Equation to Determine Water Depth between Bridge Piers | Civil Engineering | This worksheet shows the application of the momentum equation to determine the water depth between bridge piers. For this problem, the pier width, upstream depth of the river and velocity, and the drag coefficient of the piers are given. |

Balancing the pH Balance and Composition of Two Chemical Solutions | Chemical Engineering | This worksheet first lists the equations necessary including the mass balance on Na and the charge balance. Next the worksheet identifies the proton condition and lists the terms of the given and unknown elements. |

Bearing Capacity and Maximum Load of a Pier | Mechanical Engineering | This worksheet shows you how to calculate the bearing capacity factor for a specific pier, and then uses this calculation to find the maximum load of the pier. |

Building Structural Design | Civil Engineering | These worksheets solve typical problems encountered in the structural design of buildings. |

Calculating Fault Current Magnitude in Mathcad | Electrical Engineering | This worksheet shows you how to compute bus faults on power systems.Most faults in power systems occur at points on the line some distance away from the substation bus. |

Calculating Force on a Truss Connection Joint | Mechanical Engineering | This worksheet using PTC Mathcad helps you to calculate the force and pressure on a connection joint within the specified dimensions of the joint for a particular material, and under particular trusses and weld lengths. |

Calculating the Tensile Stress and Tensile Forces in the Bolts of a Flange Pipe | Civil Engineering | This worksheet using PTC Mathcad looks at a problem where a portion of a pipe containing two discharges is bolted to the remainder at the flange and is interested in solving for the tensile forces in the bolts at the flange required to hold the pipe in place. |

Calculating Volume of a Pressure Vessel | Algebra & Geometry | This worksheet teaches you how to calculate the total volume of a chamber given the various geometries. An Excel component object allows you to specify the diameters/heights of the chamber at various points. |

Calculating Water Amount for Borehole Drilling | Chemical Engineering | This worksheet finds the particular amount of water in the air on an air drilling operation from thermodynamics, to be injected. |

Choosing a Cam-Type Clutch to Drive a Centrifugal Pump | Mechanical Engineering | This worksheet using PTC Mathcad shows you how to properly choose a cam-type clutch to drive a centrifugal pump. |

Comparing Air Pressure and Elevation for Air Volume Calculations | Civil Engineering | This worksheet shows you how to compare the air pressure versus elevation when calculating the air volume in an air and aerated mud drilling. |

Complex Numbers in PTC Mathcad | Algebra & Geometry | This worksheet using PTC Mathcad shows you how to work with complex numbers when using PTC Mathcad software. |

Converting Nonlinear Systems to Linear Ones | Statistics & Data Analysis | This worksheet using PTC Mathcad teaches you how to change nonlinear problems into linear problems. You are able to make this change when a problem is mostly linear, and the nonlinear part appears in the same style throughout the worksheet. |

Cubic Spline Interpolation | Algebra & Geometry | This worksheet helps to differentiate between regression and interpolation. Regression is a mathematical process that attempts to find a best-fit curve through a set of data. |

Determining Suction Lift Pump Height Using Solve Blocks | Mechanical Engineering | This worksheet using PTC Mathcad helps you to determine the maximum height that a pump can be placed under a reservoir, and maintain the operating conditions set by a pump manufacturer. |

Developing IDF Curves from Rainfall Data | Statistics & Data Analysis | This worksheet using PTC Mathcad provides you with the data for twenty years of annual maximum rainfall depths for specified durations. |

Differential Algebraic Equations in PTC Mathcad | Statistics & Data Analysis | This worksheet using PTC Mathcad shows you how to solve an ordinary differential equation whose solution has additional equality constraints beyond initial or boundary conditions. |

Eigenvalues and Eigenvectors in PTC Mathcad | Algebra & Geometry | This worksheet using PTC Mathcad shows you how to use the PTC Mathcad functions "eigenvals" and "eigenvecs" to find the eigenvalues and eigenvectors of a matrix. |

Ergodicity in a Harmonic Oscillator | Statistics & Data Analysis | This worksheet models a classical particle described by a Hamiltonian and is an example of how one can conduct experiments involving mathematics and physics in practical, realistic scenarios. |

Example of Solving a Set of Coupled, Non-linear Equations with Units | Civil Engineering | This worksheet illustrates PTC Mathcad's ability to solve a set of nonlinear coupled equations for several unknowns, where the unknowns each have different units. |

Example of Using Laplace Transforms to Solve an ODE | Mechanical Engineering | Illustrates PTC Mathcad's ability to symbolically solve an ordinary differential equation using Laplace transforms. In this example, from dynamics, the worksheet demonstrates how to find the motion of a mass m attached to a spring and dashpot due to a known applied force. |

Example of Using Symbolic Math to Solve an ODE | Statistics & Data Analysis | This worksheet illustrates PTC Mathcad's ability to symbolically solve an ordinary differential equation. In this example the worksheet shows you how to find the solution to a linear equation of first order in the canonical (standard) form using the integrating factor method. |

Statistics & Data Analysis | This worksheet employs assumptions about the distribution of risk to simulate expected rates of default for the purposes of financial planning. | |

Finding Channel Height, Channel Width, and Velocity of Water | Civil Engineering | This worksheet using PTC Mathcad models the low water crossing geometry as a trapezoid to find the height, width, and velocity of the water in a channel. |

Finding the Actual Force and Break Capacity of a Long-Shoe Internal Drum Brake | Mechanical Engineering | This worksheet using PTC Mathcad shows you how to determine the actuating force and the brake capacity of a long-shoe internal brake. |

Finding the Shear Force and Bending Moment Along a Beam | Mechanical Engineering | This worksheet provides you with an example of how the shear force and the bending moment along a simply supported beam can be determined as a function of the distance from one end. |

Finite vs. Infinite Life and Fatigue Failure for a Steel Object | Mechanical Engineering | This worksheet using PTC Mathcad provides an example of how to calculate for the fatigue failure of a rotating beam specimen made of ductile steel. |

Fitting Hyperbolic Data | Statistics & Data Analysis | This worksheet using PTC Mathcad helps you to fit a hyperbolic function to collected data. This worksheet shows you how you can use the "minimize" solver function to fit a simple hyperbolic function to some data. |

Gauss- Newton Nonlinear Regression | Statistics & Data Analysis | This worksheet uses the Gauss-Newton regression method, applied in PTC Mathcad Prime, in order to display curve-fitting non-linear models. |

Gaussian Probability Distribution in Mathcad | Statistics & Data Analysis | This PTC Mathcad worksheet walks you through an example of two random variables with joint density. It then visualizes the density function via surface and contour plots, and calculates the probability of an event. |

Generating Polar Histograms in PTC Mathcad | Statistics & Data Analysis | This worksheet teaches you how to plot a polar histogram using PTC Mathcad software. |

Inventory Control Example in PTC Mathcad | Statistics & Data Analysis | This worksheet using PTC Mathcad shows you how to solve a classical inventory control problem commonly found in operational research. |

Linear and Angular Momentum of Three Small Balls | Mechanical Engineering | This worksheet looks at three small spheres of equal mass that are connected to a small ring by three inextensible, inelastic cods of equal length and equal space. |

Load Flow Calculations | Electrical Engineering | This worksheet using PTC Mathcad shows you how to describe the network for a five-bus power system, using a matrix containing the transmitting and receiving bus numbers, the series impedance, and shunt admittance. |

Logistic Map and Ideal Random Number Generator | Statistics & Data Analysis | This worksheet using PTC Mathcad software describes the search for an ideal uniform random number generator, ultimately proving that the logistic random number generator simulates the behavior of the ideal uniform random number generator. |

Manufacturing Performance Curves in Mathcad | Statistics & Data Analysis | This worksheet discusses how the output of a manufacturing process can be sampled to control the quality of the items shipped and how this sampling can be performed by plotting three performance curves. |

Measuring Traffic Flow and EAL for Vehicles | Civil Engineering | This worksheet using PTC Mathcad performs calculations to measure the traffic flow and evaluation assurance level for normal trucks and construction vehicles. |

Modeling of SAW Delay Lines | Electrical Engineering | Shows how you can model SAW sensors in aerospace vehicles. The lack of support for transcendentals within the Differential Algebraic Equation framework prevents the use of the frequency domain analysis in analog extended Hardware Description Languages. |

Monte Carlo Simulation of the Streeter Phelps Equation | Statistics & Data Analysis | This worksheet using PTC Mathcad provides you with the basic Streeter Phelps equation which allows for the calculation of the dissolved oxygen deficit in a stream or river as a function of the distance downstream. |

Numeric and Symbolic Variables in PTC Mathcad - Undefining a variable | Statistics & Data Analysis | This worksheet explains the elements of variables and their role in PTC Mathcad software. Specifically, this worksheet teaches you how to undefine a variable using two simple methods. |

Numeric vs. Symbolic Representations in PTC Mathcad | Statistics & Data Analysis | This worksheet using PTC Mathcad Prime 2.0 shows you how to use an in-place evaluation of numeric definitions and a symbolic evaluation of results in functions. |

Performing a Weighted Fit in PTC Mathcad | Statistics & Data Analysis | This worksheet using PTC Mathcad shows you how to fit a set of sample data by using the Least Squares Error (LSE) method to minimize the sum of squares error function normalized by a weighting function. |

Planar Regression in Mathcad | Statistics & Data Analysis | This worksheet using software provides you with a sample data set that then shows you how to create a matrix containing the x and y coordinates of the data set using the augment function. It also shows you how to perform a regression on the data using the "regress" functions. |

Plotting Frequency Distribution Data in PTC Mathcad | Statistics & Data Analysis | This worksheet shows you how to use PTC Mathcad to calculate a frequency distribution for values in a vector that fall in a specified number of bins within the range of the data, and how to plot the resulting histogram. |

Preparing Time Series for Data Analysis | Statistics & Data Analysis | This worksheet shows how you can import a data file consisting of time series data into PTC Mathcad. |

Preventing System Failures with Reliability Testing for Pump Systems | Mechanical Engineering | This worksheet shows you how to determine the minimum number of pumps needed so that the probability of not having a system failure (system reliability) during a three year period is more than .95. |

Random Triangles in the Unit Square | Statistics & Data Analysis | This worksheet using PTC Mathcad supposed that three points are independently and uniformly chose in a unit square to determine a unique triangle. |

Random Walks in PTC Mathcad | Statistics & Data Analysis | This worksheet using PTC Mathcad shows you how to simulate a random walk and visualize it through the use of graphs and charts. |

Response Surface Modeling in PTC Mathcad | Statistics & Data Analysis | This worksheet using PTC Mathcad provides you with an example of a box-behnken experiment with three parameters at three levels. |

Risk Probability and Flood Proofing a Bridge Over a River | Civil Engineering | This worksheet using PTC Mathcad provides you with a scenario of a bridge that is built over a river. |

RLC Circuit Analysis | Electrical Engineering | This worksheet includes an example of an engineer designing a hi-fi speaker that must meet a certain frequency response. The horizontal trend must be over the whole spectrum of the audible range with a tolerance of +/- 1dB. |

Seeded Iteration in Mathcad | Algebra & Geometry | This worksheet using PTC Mathcad shows you how to iterate through a variable based on an initial seed value. |

Solving Coupled ODEs in PTC Mathcad | Statistics & Data Analysis | This worksheet sets up a set of coupled ordinary differential equations. A matrix of the functions for the x/y positions and velocities is defined. It's then passed to the RKadapt function. The x/y positions are plotted with a 3D plot of the sinusoidal humps. |

Solving Systems of Equations in Mathcad Using the Find Function | Statistics & Data Analysis | This worksheet shows you how to use the Find Function in PTC Mathcad software. The Find Function can be used to solve linear and nonlinear systems. |

The Weibull Distribution Function in Reliability Statistics | Mechanical Engineering | This worksheet using PTC Mathcad shows you how to define a 2-parameter Weibull distribution and shows you how the distribution can be influenced by scale and shape parameters. |

Theory of the Capacitor revised | Electrical Engineering | This worksheet will solve a common 2-circuit physics problem to determine charges and energy, keeping in mind the Reciprocal System Theory and the conventional theory. |

Three Phase Power System in PTC Mathcad | Electrical Engineering | This worksheet discusses how to find the power distribution and parameters for power lines. Unbalanced power systems require analysis by the method of symmetrical components. |

Tracking the Development of a Storm Using 30 Minute Interval Convolution | Statistics & Data Analysis | This worksheet shows you how to use a 15 minute UH hydrograph to estimate the runoff from a rainfall hyetograph, also called convolution. |

Using Cubic Splines to Determine Characteristics and Efficiency of a Pump | Civil Engineering | This worksheet provides you with an example of a problem where you need to determine a pipe operation point in terms of head and discharge, operation efficiency, suitability of the pump chosen, and input horsepower to the pump. |

Using Henry's Law and Solve Blocks in Chemistry and Environmental Engineering | Chemical Engineering | This worksheet is used to solve 6 equations 100 times and then plot each species as a function of the overlying partial pressure of H₂S, and determine how the H₂S partitions between the liquid and gas phases. |

Using the Finite Element Method on Truss Structures | Civil Engineering | This worksheet shows how to design a warehouse based on a steel beam structure. Truss design is commonly taught in engineering courses, but based on a hand calculations approach. Instead, this worksheet uses a robust and error-checking method that can be performed automatically and repeatedly. |

Modelling the Ocean | Oil & Gas | This worksheet is created in PTC Mathcad Prime 3.0 and modelles the ocean as a sum of simple sinusodial waves with different heights, lengths and directions. |

Visualisation of Typical Wellbore Survey Data | Oil & Gas | This worksheet is created in PTC Mathcad Prime 3.0 and converts real world coordinates to cartesian form to visualise a well bore drill path. |