College of Engineering

MTH Course Information*


Prof. Lee Townsend

UH Links

Fall 2015

Calculator Info

Course Handouts





UH Links


Math and Technical Communications


University Main Page

Math/Physics Links

UH Academic Calendar

Fall 2015 Final Exam Schedule

Prof. Lee Townsend (go back to my main page)


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Fall 2015


MTH 122 Syllabus Spring 2015 (pdf)

MTH 241 Syllabus Spring 2015 (pdf)

MTH 112 Syllabus Fall 2015 (pdf)

MTH 232 Syllabus Fall 2015 (pdf)

My weekly schedule Fall 2015 (pdf)

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Nspire CAS, and other CAS


TI-Nspire CX CAS overview (YouTube)

Some examples of how to use the TI-89 - a tutorial I wrote several years ago.

Tables of contents for EE-PRO, ME-PRO and EE-200 software

I know where it is on the TI-89 so where is it on the TI-Nspire CX CAS?

A great TI-89 tutorial site also found at Prenhall's TI-89 tutorial site

See the Hassen and Schiffman link for more great TI-89 information.

Graphing integrals and derivatives on the TI-89.

Implicit Differentiation using a CAS calculator (from Batesville HS physics site) and from TI

Got a TI-Nspire CX CAS? I just bought one. Check out the links below for a great set of video tutorials. Be sure to put a screen protector on the device as mine got scratched easily.
Handheld device
Computer software emulator (it comes with the hardware.)

iOS calculators:

iPhone Symbolic Calculator ($1.99)
iPad Symbolic CalculatorHD ($1.99)
Graphing Calculator Pro - Free
Graphing Calculator Pro ($1.99)

You can find an online calculator for which there is also an iOS app, both free and paid ($1.99).

I have no financial or other non-academic interest in these calculators. I just found that SymCalc performed almost all the TI-89 functions needed in my classes except graph analysis. GraphCalcPro finds intersections, intercepts, and max/min. It also finds the first and second derivatives at a point.



A great site for understanding math



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Course Handouts



Differential equations


Summer Bridge

Final Grade Ranges and Cheating Policy

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MTH 112

MTH 112 Exam 1 Practice (Multiple Choice)

MTH 112 Exam 2 Sample - Fall 2012

MTH 112 Exam 2 Sample - Solutions - Fall 2012

MTH 112 Exam 2 Review - Fall 2013

MTH 112 Exam 2 Practice Problems - Fall 2013

MTH 112 Exam 2 Practice Problems Solutions- Fall 2013

MTH 112 Exam 3 Practice (Multiple Choice)

MTH 112 Exam 3 Summary Review

Solving 2x2 and 3x3 simultaneous equations using both the TI-89 and traditional analytical techniques

Quadratics and Parabolas

Trig in Four Quadrants

Demystifying the Natural Logarithm (ln)

An Intuitive Guide To Exponential Functions & e

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MTH 122

Solving oblique triangles

A Visual, Intuitive Guide to Imaginary Numbers

Trig graphs

Trig Graphs spreadsheet

MTH 122 Exam 1 Sample

MTH 122 Exam 1 Sample - Solutions

MTH 122 Exam 2 Sample exam

MTH 122 Exam 2 Sample exam - solutions

Chapter 20 Trig Identities

MTH 122 Exam 3 Sample

MTH 122 Exam 3 Sample Solutions

Adding polar to rectangular representations and vice versa of a 2D vector in the iOS app Symbolic Calculator


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MTH I-IV Formulas Wallet Card revised 02/2014

MTH 232 - Derivatives and Conic Sections

Chapter 23 Derivative Rules

Derivative rules for Chapter 23

Derivative Table


Step by step - Taking derivatives

Chapter 24 (Applications of the derivative) Study Guide (2012)



Some notes for the Chapter 24 exam (Exam 2)


Conic Sections-Fall 2013


Ellipses-Fall 2013-Revised

Graphing conics (YouTube)

Sample Exams

MTH 232 Exam 1 Sample

MTH 232 Exam 1 Sample - Solutions

Previous MTH 232 Exam 1 Sample

Previous MTH 232 Exam 1 Sample - Solutions

Fall 2010 MTH 232 Exam 2 - Makeup with answers

Fall 2006 MTH 232 Exam 2 - Makeup with answers

Solution to both MTH 232 Exam 2 Makeups

MTH 232 Review Fall 2013

MTH 232 Exam 3 sample

Solutions for MTH 232 Exam 3 sample

MTH 232 Exam 3 review sheet

External links:

How To Understand Derivatives: The Product, Power & Chain Rules

How To Understand Derivatives: The Quotient Rule, Exponents, and Logarithms

MTH 241 - Integrals

Some notes for Chapter 25 - basic integrals

Wikipedia shows that the area under a curve is the definite integral. It is one aspect of the Fundamental Theorem of Calculus which relates differentiation and integration. The short version (an extract) just shows the geometrical argument.

A great site that has animated disk, shell, and washer methods for integration. Also check out the sine wave animation as well as lots of other trig animations. Here is the main TOC for their animations library. Sometimes you will need to be patient as the animation does not start immeidately.

Fourier Transforms

Fourier Series Integrals

Fourier slides from class

Short-time Fourier transform (Wikipdiea) - For the audio students: "The short-time Fourier transform (STFT), or alternatively short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time."

An Interactive Guide To The Fourier Transform

Sample Exams

MTH 241 - Problem 9 page 747 - Numerical Integration

MTH 241 Exam 1 Sample

MTH 241 Exam 1 Sample Solutions

MTH 241 Exam 2 Sample

MTH 241 Exam 2 Sample Solutions

MTH 241 Exam 3 Sample

MTH 241 Exam 3 Sample Solutions - Revised


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Differential equations

Rewrite Acos(wt)+Bsin(wt) as Csin(wt+phi)

Solving second order nonhomogeneous equations

Nonhomogeneous Differential Equations and Resonance

Variation of Parameters for solutions of nonhomogeneous differential equations.



Formulas from calculus and precalculus that are handy for D.E.

Second order equations for a driven and damped spring

An example of an overdamped spring driven by an exponential decaying force

Series and parallel RL, RC, and RLC circuit analysis from a D.E. perspective

A short table of Laplace Transforms from Derrick and Grossman, Elementary Differential Equations

Notes on the forward Laplace Transform

Analysis of real-world RLC circuits using Laplace Transforms

Time constants for RL series circuits, RC series circuits, and terminal velocity

Newton's Law of Cooling

Analyzing Damped Oscillation Graphs

The Logistic Equation as model refinement

Completing the Square TI-89 program: (Text Version)

For direction fields for second order equations on the TI-89 as well as other wonderful information about differential equations on the TI-89 get the following document:

Hassen and Schiffman also have nice documents on linear algebra and :and an introduction to the TI-89. All three documents can be found on Hassen's web site:

Previous Exams:

Fall 2009 Exam 1 (censored a bit)

Fall 2009 Exam 1 (censored a bit) with solutions.

Fall 2009 Exam 2 (censored a bit)

Fall 2009 Exam 2 (censored a bit) with solutions.

Fall 2009 Exam 3 (censored a bit)

Fall 2009 Exam 3 (censored a bit) with solutions.

Fall 2004 Final with solutions

Solving differential equations using the iOS app Symbolic Calculator - detailed instructions and
pdf emailed from the app.


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Occasionally my students ask for help on physics problems. Here are some examples I have used.

The paper discusses an approach to basic kinematics, conservation of energy, and conservation of momentum.

The solution of Newton's Second Law problems can be difficult. This example problem, finding the acceleration for an inclined plane with friction, breaks it down into small steps with suggestions on how to set up coordinate systems for this type of problem.


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Summer Bridge

August 2014

This summer I had the great pleasure of working with sixteen incoming freshmen, Kelly Turner, Sara Gambacorta, and Patricia Mellodge in the CETA Summer Bridge program. It was an ideal teaching environment. Patricia would work with the students on Boe-Bots in the morning class and I would teach them the math and computer skills they needed for Patricia's class the following morning. The students could immediately see the application of the theory to experiment.

Below are links to my handouts from the week.

Class Notes:



Boe-Bot BASIC_Stamp_Manual_3 from Parallax, Inc. - the source of the following three handouts.

Boe-Bot Manual - chapter 4












Boe-Bot software from Parallax Inc.

Boe-Bot's BASIC Stamp Editor Software for both Mac and PC

BASIC Stamp Syntax and Reference Manual - v2.2


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Most, but not all, of my pdfs have an associated .doc or .docx file. Feel free to download them so you can personalize them. If you do more than use it for personal use, please give me credit for the original work. Thanks.

The equation writer I use is MathType from



Final Grade Ranges

Grade scaling, if any, will occur on the final course grade only. Historically the typical grade ranges started at

Final Grade Ranges

These are approximate values and are subject to minor changes.

Cheating on Exams - Policy

1) Don't cheat.
2) Problems with clear evidence of copying receive a grade of zero for the copied problem(s) on both exams.
3) You are ineligible for all makeup exams starting with the exam in question.
4) You my not sit near each other in future exams.
5) If I find further evidence of solution copying, you will receive a grade of F in the course.
6) If you feel unjustly accused, you may appeal to Dean Alnajjar.
7) Just don't cheat.

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The University of Hartford (the "University") wishes to thank Prof. Lee Townsend for preparing this web page on behalf of the University, which provides any information included or referenced within this web page "AS IS" for the sole purpose of illustrating Microsoft® Excel® spreadsheet application techniques. Despite any contrary indication, the University provides no warranty of any kind concerning this web page, either express or implied including, without limitation: any implied warranty of merchantability, fitness for a particular purpose or non-infringement. The University further does not warrant that any aspect of this web page will meet any party's requirements or that the operation of any aspect of this web page will be error free. The University accepts no responsibility or liability for the accuracy, copyright compliance, legality or decency of any material contained in or referenced through this web page.

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 Last Updated 11/25/15