Department of Mathematics, Engineering, and
ENGR 104 Engineering Graphics & CAD Applications 3 Cr
An introduction to modern computer drafting and engineering design using
a CAD (computer aided design) software system. Fundamental concepts
of technical drawing in two and three dimensions including orthographic
projections, isometric projections, three-dimensional and solids modeling,
and rendering. Spring semester.
ENGR 105 Introduction to Engineering 1 Cr
A broad-brush overview of the various aspects of engineering with emphasis on civil engineering and other areas of engineering. After a brief
exposure to licensing, ethics and engineering societies, we will jump into the
design and construction of bridges made entirely of manila folder material.
There will be several guest speakers to introduce students to other areas
of engineering like mechanical and chemical. Students will be led through
a reverse engineering activity by determining how a simple coffee maker
works and the physical processes involved. One or two field trips will take
students to various locations in and near Helena to look at engineering in
action. Then students will learn about surveying, its role in engineering,
and conduct field exercises with a level survey and a resource-grade GPS
(global positioning system) unit. Students will learn to work in teams to
reach a common goal. Fall semester.
ENGR/PHYS 155 Robotics and Experimental Physics 3 Cr
Learn how to build and control simple robotic devices, and along the way
you will learn the fundamentals of logic and control common to all computer
programming languages. We will perform numerous discovery exercises in
the laboratory, to introduce and practice experimental methods and mathematical modeling useful for physics. Two 2 hour laboratories per week.
Prerequisites: Mathematics at the level of high-school pre-calculus (i.e.,
algebra, trigonometry, and elementary functions) will be used throughout
this course, but calculus is not a prerequisite; high-school physics is recommended but not required. Fulfills the CORE requirement for a laboratory
course in the natural sciences. Fall semester.
ENGR 202 Water Distribution Systems 1 Cr
An introduction to water distribution theory and design practice. A project-oriented course that includes water supply, storage, distribution, and
computer analysis of water distribution networks. Spring semester.
ENGR 205 Civil Engineering Materials and Testing 2 Cr
The purpose of this course is for students to learn the properties and behaviors of various construction materials that are commonly used in civil
engineering projects. Steel, concrete, wood, soil, asphalt, geo-synthetics,
pipes, and other materials are studied and tested. In addition, students
learn some of the standardized testing procedures for these construction
materials. Fall semester.
ENGR 300 Field Experience 1 Cr
Pending curriculum committee approval
ENGR 302 Engineering Mechanics I: Statics 3 Cr
Equilibrium of bodies under the action of forces. Force systems and resultants; equilibrium of mechanical systems; trusses, frames, and machines;
centroids and centers of mass; shear and moments in beams; hydrostatics;
friction; and virtual work. Introduction to mechanics of solids and computer
analysis of structures, as time permits. Emphasis on solving practical engineering problems in complete, documented style. Prerequisite: Grade of
“C” or better in PHYS 205 or MA 233. Spring semester.
ENGR 303 Engineering Mechanics II: Solids 3 Cr
An introduction to the mechanics of deformable solids. Topics covered
include stress, strain, rotation-of-axes transformations, constitutive relations, equilibrium, compatibility requirements, stability, and deformation
of structural elements. Uni-axial, torsion, bending, and shear loads on and
deformations of prismatic bars are also studied together with Euler buckling
of slender columns. Three credits of lecture. Prerequisites: Grades of “C” or
better in ENGR 302, MA 131, and either MA 232 or MA 141. Fall semester.
ENGR 304 Engineering Mechanics III: Dynamics 3 Cr
Motions of bodies under the action of forces; kinematics and kinetics of particles, systems of particles, and rigid bodies; work-energy and impulse-momentum; area and mass moments of inertia. Emphasis on solving practical
engineering problems in complete, documented style. Prerequisites: Grade
of “C” or better in ENGR 302. Fall semester.
ENGR/PHYS 305 Electronics and Circuit Analysis I 4 Cr
An introductory survey of the behavior of electrical circuits. Review of
current, voltage, and passive circuit elements (resistors, capacitors, and
inductors). Kirchhoff’s Laws, network theorems, and basic network analysis. General characteristics of amplifiers and electronic instrumentation.
308 Course Descriptions—ENGR: Engineering
Introduction to operational amplifiers and active elements (transistors).
Laplace transform analysis of transient (switching) response, and complex
phasor analysis of sinusoidal steady-state response. Three hours lecture
and one 2-hour laboratory per week, in which students build and test
circuits and learn how to use typical circuit simulation software (PSPICE).
Prerequisites: Grades of “C” or better in PHYS 206, MA 131, MA 233, and
either MA 232 or MA 141. Fall semester.
ENGR /PHYS 306 Electronics and Circuit Analysis II 4 Cr
A continuation of ENGR/PHYS 305. Systematic node-voltage and
mesh-current methods of circuit analysis. Network transfer functions and
frequency spectra. Mutual inductance and transformers. Diode circuits and
the behavior of single-transistor amplifiers using field-effect or bipolar-junction transistors. Analysis and design of digital logic circuits. Principles of
operation and interfacing of typical laboratory instruments. Three hours
lecture and one 2-hour laboratory per week. Prerequisite: Grade of “C”
or better in ENGR/PHYS 305. Offered spring semesters if warranted by
ENGR 307 Fluid Mechanics 3 Cr
A first course in fluid mechanics for engineering majors. Topics covered
include fluid properties, fluid statics, fluid motion, pressure variations in fluid
flows, momentum principles, energy principles, dimensional analysis and
similitude, surface resistance, flow in conduits, flow measurements, drag,
and lift. Two and one-half credits of lecture and one-half credit of laboratory.
Prerequisites: Grades of “C” or better in ENGR 302, MA 131 and either
MA 232 or MA 141. Fulfills Writing Intensive requirement. Fall semester.
ENGR 308 Thermodynamics 3 Cr
A practical introduction to thermodynamics for engineering students.
Fundamental state variables are defined (e.g., temperature, pressure,
energy, enthalpy, entropy, etc.), and the three laws of thermodynamics are
extensively discussed and illustrated. Applications include power systems,
gas turbines, and refrigerators. Three hours lecture per week. Prerequisites:
Grades of “C” or better in PHYS 205-206, MA 131, MA 233, and either MA
232 or MA 141. Spring semester.
ENGR 309 Geotechnical Engineering 3.5 Cr
An introduction to geotechnical engineering. Topics covered include an
introduction to geology and the classifications of soils, and rocks, and geologic structures. Soil exploration, testing, and classifications are introduced,
and soil characteristics and mechanical properties such as compressibility
and compaction, permeability and seepage, and stresses in soil structures are also studied. Three credits of lecture and one half credit of lab.
Prerequisites: Grades of “C” or better in ENGR 303 and ENGR 307. Spring
Course Descriptions—ENGR: Engineering 309
ENGR 310 Structures I 3 Cr
This is the first in a series of 3 courses in structural analysis and design. The
primary objective of this course is to introduce the principles and methods
of analysis for trusses, beams, and frames so that students develop the
understanding and the skills necessary to analyze and design statically
determinate as well as statically indeterminate structures. While emphasis
is on modern computer methods of analysis, elementary methods are also
studied so students gain an understanding and “feel” for the behavior
of structures. Prerequisites: Grade of “C” or better in ENGR 303. Spring
ENGR 311 Matrix Methods for Structures 1 Cr
This course introduces students to matrix methods for analyzing determinate and indeterminate plane truss and plane frame structures, and
how these methods are implemented on a computer. The programming
architecture used in modern structural analysis programs is presented. This
includes: 1) Input of the geometry of the structure, material properties of
members, and loads; 2) assembly of the system equations to be solved; 3)
solving the system equations for basic unknowns; 4) recovering values of
interest from the values for the basic unknowns; and 5) generating output
of the results. Students work with the instructor to develop programs to
analyze a resistive electrical circuit network, a plane truss, and a plane
frame. The programs are tested using problems that have solutions available to test the programs. Prerequisite: A grade of “C” or better in ENGR
303. Spring semester.
ENGR 313 Hydrology 3 Cr
This course focuses primarily on the basic principles of the hydrologic cycle such as precipitation, hydrologic abstractions, catchment properties,
groundwater flow, and the relationships between precipitation, abstractions,
and runoff. A brief portion of the course deals with the measurement of
various components of the hydrologic cycle. The engineering applications
of basic hydrologic principles are studied. The purpose of this course is to
introduce the fundamentals of hydrologic science, which are used to solve
typical engineering problems. Prerequisites: Grades of “C” or better in MA
131 or MA 121-122, or permission of instructor. Fall semester.
ENGR 315 Transportation Engineering I 2 Cr
This course covers vehicle characteristics, geometric design of highways,
earthwork calculations, pavement design, networks, and statistical applications in transportation. Two class hours per week. Prerequisite: Proficiency
in high school algebra and trigonometry. Fall semester
310 Course Descriptions—ENGR: Engineering
ENGR 323 Water Quality 2 Cr
This course teaches sampling methods, analytical techniques, and principles associated with environmental engineering applications. Topics
include designing a sampling, groundwater and surface water sampling,
field methods, carbonate equilibrium, isotope applications, pathogens in
public water, and groundwater and surface-water contamination issues.
Students will be guided through these topics with homework problems,
field excursions, assigned readings, handouts, guest speakers, and exams.
Prerequisites: Grades of “C” or better in CH 111, BI 102, and either MA
131 or MA 121-122. Fall semester every other year at the discretion of the
ENGR 324 Air Quality 2 Cr
This course will provide engineering graduates with sufficient background
and tools to understand the principle issues associated with air quality. They
will gain an understanding of the science of air pollution and the pollutants
of concern, including greenhouse gases, and their chemistry. Students will
understand the structure and why laws were formed and needed to regulate
the air industry. Students will have experience with air-quality monitoring
and the equipment used. Students interested in air quality will be able to be
trainable in air quality methods and evaluations. Prerequisites: MA 131, and
either MA 232 or MA 141, and junior or higher standing. Spring semester.
ENGR 325 Hydrogeology 3 Cr
This course is a basic junior-level hydrogeology course with fundamentals
as the primary focus. Students taking the course will be prepared to work
in industry and solve problems associated with groundwater resources,
environmental clean-up, restoration, and protection of water rights. An
emphasis is placed on applications. For this reason the course is ideally
suited to professionals who work in the Helena area, such as personnel at
DEQ, DNRC, and other state agencies. Topics include groundwater flow
and hydraulic head, aquifer tests and analysis, including slug testing. Waterquality applications are emphasized. Class activities include weekly homework problems, lectures, applied problems, exams, and a design project.
Prerequisites: Junior standing or consent of the instructor. Fall semester.
ENGR 326 Energy and the Environment 3 Cr
This course will look at the role that energy plays in our modern world.
We will learn about the physics of energy so that students can calculate
the energy content of a variety of systems, such as: gasoline, other fossil
fuels, nuclear, solar, wind, bio mass and so on. Applications of the energy
schemes in our lives will then be explored. We will discuss the global use
and needs of energy and the environmental problems that have resulted
from energy development and how we can improve our community and the
world. Pre-requisites: MA 121-122 or MA 131 and sophomore standing.
Spring semester. Fulfills Global Diversity requirement.
Course Descriptions—ENGR: Engineering 311
ENGR 327 Land and Stream Restoration 3 Cr
This course strives to provide a knowledge and understanding of the current
land and stream restoration practices. To achieve this objective, students
participate in filed excursions, study earth moving methods and equipment,
analyze soil erosion processes, design hydrologic control structures, and
study revegetation and stream restoration methods. Prerequisites: Junior
or higher standing or consent of the instructor. Fall semester every other
year at the discretion of the department.
ENGR/HS 329 Public Health and the Environment 3 Cr
This course provides student with an introduction to an overview of the key
areas and principles of environmental health. Students will gain an understanding of 1) the interaction between Individuals, communities, and the
environment, 2) the impacts of various environmental agents on the health
of the public, and 3) specific applications of environmental health and environmental engineering. Topics to be covered include environmental policy
and regulation, agents of environmental disease, and practices for water
quality, air quality, food safety and waste disposal. Prerequisite: Sophomore
or higher standing or consent of instructor. Fall semester.
ENGR 395 Spanning the Ages: The European 3 Cr
History of Structures from Mycenaean Greece
through the Industrial Revolution
This a 16 day study abroad to trace the history of structural design in Europe
from the time of the Mycenaean civilization in Greece (~1600 BC) through
the Industrial Revolution (~1850 AD) to include the Golden Age of Greece,
the Roman Empire, the Middle Ages, and the Renaissance. The course
will also study the civilizations and cultures that persisted during each era
of structural advancement through the period of study. Art, government
structures, social structures, and the economics of Western European
civilizations and their interconnections with advancement of structural
designs are also studied, together with the rise and fall of several empires
and cultures in Western Europe. During the study abroad trip, students
visit four major European cities (Athens, Rome, Paris, and London), as well
as less urban areas in Italy (Florence) and in the United Kingdom (Wales).
Students will see Western Europe in its modern contexts of art, culture, and
social structures. The importance of various structures in the contexts of
the history and modern circumstances in Europe are also studied. Students
will also be guided in developing their international travel skills. The course
will consist of 4 pre-trip preparation classes in April, the study abroad trip,
and the follow-up submission of a travel and study journal together with an
exploration and discovery paper. There are no prerequisites for this course
other than good academic standing. The course is for 3 credits. Course
to be offered pending sufficient demand. Prerequisite: Good academic
standing and consent of the instructor.
312 Course Descriptions—ENGR: Engineering
ENGR 401 Hydraulics 3 Cr
Hydraulic engineering is the application of fluid mechanic principles to
deal with collection, storage, conveyance, distribution, control, regulation,
measurement, and use of water. This course will focus primarily on analysis and design of pipelines, pumps, and open channel flow systems. The
course will also have a design project to provide an opportunity to apply
the information in a real engineering situation. Three class hours per week.
Prerequisite: Grade of “C” or better in ENGR 307. Fall semester.
ENGR 402 Environmental Engineering 3 Cr
This course focuses on environmental problems, including their causes, the
scientific background needed to understand them, and the methods used
to solve them. The fundamental principles of environmental engineering,
including sources of water and air pollution, water and wastewater treatment, solid and hazardous waste management, and regulatory issues are
presented. Three class hours per week. Prerequisites: Grades of “C” or better in CH 111, BI 102, and either MA 131 or MA 121-122. Spring semester.
ENGR 403 Structures II Steel Design 3 Cr
The purpose of this course is to learn the philosophies and methods of
AISC Load and Resistance Factor Design (LRFD) and AISC Allowable Stress
Design (ASD) of steel structures. Emphasis is on the determination of loads
and load distribution, and the design of structural components (i.e., tension
members, compression members, beams, and beam-columns) and their
connections, in accordance with the AISC Design Specification and the
AISC Manual of Steel Construction. The function and behavior of simple
frame structures is also introduced and each student works on a team to
complete a design project. Three hours of class per week. Prerequisite:
Grade of “C” or better in ENGR 303. Fall semester.
ENGR 405 Water and Wastewater 4 Cr
This course focuses on the fundamental principles for analysis and design
of water processing, water distribution, wastewater collection, wastewater
treatment, and sludge processing systems. Three class hours and 2 lab
hours per week. Prerequisites: Grades of “C” or better in ENGR 313 and
ENGR 401. Spring semester.
ENGR 406 Structures III 2 Cr
Reinforced Concrete Design
The purpose of this course is to learn the philosophy and methods of ACI
strength design of reinforced concrete structures. Emphasis is the design
of concrete structural elements including beams, one-way slabs, and columns. The student works on a team to complete a simple design project.
There are two class hours per week. Prerequisite: Grade of “C” or better in
ENGR 303. Spring semester.
Course Descriptions—ENGR: Engineering 313
ENGR 409 Transportation Engineering II 3 Cr
This course covers the basics of traffic engineering, traffic control, human
characteristics as they relate to transportation, engineering transportation
standards, planning, public policy, and contemporary and future transportation issues. Three class hours per week. Prerequisite: Grade of “C” or
better in ENGR 315 or permission of instructor. Fall semester.
ENGR 411 Senior Design Project I 2 Cr
This course requires the students, working in teams, to take an actual
engineering project from the initial proposal stage through the preliminary
design phase. Students will conduct the necessary activities and prepare
the various documents needed to complete the preliminary design. One
class hour per week. Prerequisite: Senior standing or consent of instructor.
ENGR 412 Senior Design Project II 2 Cr
A continuation of ENGR 411, the design process will continue from the preliminary phase to the completion of a conceptual design of the project. The
students, working in teams, will prepare design criteria, calculations, and
representative engineering drawings of the project’s major components. A
list and general description of the many details and other miscellaneous activities required to complete the project will also be prepared. Finally, general
cost estimates will be computed. Two class hours per week. Prerequisite:
Grade of “C” or better in ENGR 411. Spring semester.
ENGR 424 Groundwater Flow Modeling 3 Cr
This course provides a hands-on experience in converting hydrogeologic
data, using GIS-like tools, into a simulated groundwater-flow system, using
state-of-the-art software. This course presents sufficient theory and allows
practical application in the lab to correctly conceptualize, construct, and
calibrate groundwater-flow models. This start-to-finish experience will allow
the participant to perform applications in industry. Prerequisites: ENGR 325
or consent of the instructor. Spring semester.
ENGR 444 Computational Methods for 4 Cr
This course gives a general introduction to numerical solution techniques for
ordinary and partial differential equations. Most examples are applications
in structural mechanics; however, the techniques are generally applicable
to all areas of engineering. The first part of the course is devoted to solving
ordinary differential equations by approximate methods including finite
differences, direct variational methods, weighted residuals, and energy
based approximations both global and local (finite element) approximating
functions. In the second part of the course, the preceding techniques are
extended to obtain approximate solutions for partial differential equations
314 Course Descriptions—ENLE: English Language, Criticism, & Education
for mixed boundary and initial boundary value problems. Prerequisite: A
grade of “C” or better in MA 342. Spring semester.