V. Curriculum Structure: RoseHulman Institute of Technology Sophomore Engineering Curriculum
At RoseHulman the engineering science material usually covered in Dynamics, Thermodynamics I, Circuits I and Fluid Mechanics has been repackaged into a new sequence of courses called the Sophomore Engineering Curriculum (SEC) where the concepts of conservation and accounting permeate the courses and are used to tie the subjects together. This curriculum has its pedagogical roots in a sophomore curriculum at Texas A&M University [4] and there is at least one textbook that utilizes this methodology [5]. This curriculum is required for all mechanical and electrical engineering students.
A comparison between the old and new curriculum at RoseHulman is illustrated in Figure 1. Parallel to the engineering science course are three math courses Applied Math I (linear algebra and some linear ordinary differential equations), Applied Math II (statistics) and Applied Math II (systems of differential equations). In Fig. 1, the dashed lines are intended to illustrate a weak coupling between courses and a solid line is a strong coupling between courses.
One purpose of the Sophomore Engineering Curriculum is to enhance the students' abilities in solving problems in engineering analysis. We believe that the incoming students have some misconceptions about the problem solving process that need to be corrected before they can progress to the more difficult problems that they will face later in their undergraduate careers. These misconceptions include the ideas that, "solving problems means finding a formula to evaluate," and "I can demonstrate my cleverness by solving problems while showing as little of the actual work as possible." To cause the students to change some of their notions of problem solving, we require a far more formalized and complete approach to problem solving than they have yet experienced.
In the first course, ES201 Conservation and Accounting Principles, students are taught a problem solving methodology and format that is used in all subsequent courses. Next, students take three courses that build on the first course. These courses are and ES202 Fluid and Thermal Systems ES203 Electrical Systems, ES204 Mechanical Systems. In these courses more detailed applications of the conservation principles within more specialized problem areas are discussed as well as some of the additional topics required to solve problems such as Kirchhoffs voltage law and active devices in Electrical Systems, properties in Fluid and Thermal Systems, and kinematics in Mechanical Systems. Finally, the material is brought back into a single course ES205 Analysis and Design of Engineering Systems where multidisciplinary problems are tackled.
Brief Descriptions of the courses
ES201 Conservation and Accounting  In ES201, students are introduced to the elements of the conservation and accounting framework that was describe above and to the problemsolving approach based on the framework. In this class, students develop models for systems by accounting for extensive properties that are conserved such as mass, charge, linear momentum, angular momentum and energy and also entropy. Initially, students work on problems that focus their attention on one extensive problem, but as the course progresses students may need to consider more than one extensive property. For example, a problem may require conservation of mass, conservation of energy, and conservation of linear momentum.
ES202 Fluid and Thermal Systems  Students in ES202 apply the conservation and accounting framework to the specific area of fluid and thermal systems. They both refine the framework to focus on assumptions and extensive properties common to these disciplines. They apply conservation of energy, conservation of momentum, and entropy accounting to thermal and fluid systems. In addition, they work with constituent properties related to fluid and thermal systems, such as fluid and thermodynamic properties of pure substances. Students work with both open and closed systems. They consider special cases such as fluid statics, fluid dynamics, mechanical energy balance and pipe flow, and lift and drag.
ES203 Electrical Systems  Students in ES203 apply the conservation and accounting framework to the specific area of electrical systems. They explore the assumptions necessary to obtain Kirchoff's Laws from the conservation and accounting framework [11] Starting with Kirchoff's Laws, students work with basic circuit elements: sources, resistors, inductors, capacitors, and operational amplifiers. They study traditional circuit topics such as voltage and current dividers. They study transient behavior, especially the cases of first and second order circuits. Finally, they student sinusoidal steadystate behavior, AC circuits and power.
ES204 Mechanical Systems  In the Mechanical Systems course (ES204) taken in the winter quarter, students learn the kinematics necessary to apply the conservation principles to more difficult problems. A traditional dynamics textbook is used in the course and the relationship between how the principles are presented in the dynamics book and how they were introduced the previous quarter is shown. Maple is used extensively in the course and the dynamic simulation program Working Model is used as a visualization tool [6]. The students also perform three labs as a part of this course. The first lab involves using Working Model, the second, angular momentum and the third general plane motion.
In dynamics the primary kinetics principles used to solve problems are usually presented as 1) direct application of Newtons Second Law, 2) workenergy methods, and 3) impulsemomentum methods. In this curriculum these are presented as conservation of linear and angular momentum (rate and finite time forms) and conservation of energy (finite time form). A comparison of the terminology is shown in Figure 2 that is given to the students at the beginning of the course to help them relate the material in the text to the material learned in the previous course.
Principle

ES201 Name

Dynamics Name

Comments

_{}
_{}

Rate form for conservation of linear and angular momentum for a closed system.

Direct application of Newtons Laws

When to use:
 want to find forces and/or accelerations
 want to find velocities and/or distance traveled (which can be found by separating variables and integrating the basic kinematical relationships)
Other:
 Be careful! These are vector equations.
 The book uses H_{0} for angular momentum instead of L_{0}.

_{} , _{}
or if there are impulsive loads acting on the system
_{} ,
_{}
where F_{i} and M_{i} are the external impulsive forces and moments acting on the system.

Finite time form of conservation of linear and angular momentum for a closed system.

Impulsemomentum methods

When to use:
 have an impact or impulsive forces
 the system consists of several objects
 given a force as a function of time
 want to find velocities, times, or forces (especially impulsive forces)
Other:
 Be careful! These are vector equations.
 The book uses H_{0} for angular momentum instead of L_{0}.

_{}

Finite time form of conservation of energy for an adiabatic closed system.

Workenergy methods.

When to use:
 have two locations in space
 given a force as a function of position
 want to find velocities, distances, or forces (sometimes)
Other:
 This is a scalar equation

Figure 2 A comparison between the nomenclature used in Dynamics and the one used in Mechanical Systems
One advantage of this approach is that as the kinematics is taught, it can immediately be applied to kinetics problems thereby motivating the kinematics and reinforcing the kinetics. For example, when normal and tangential coordinates are introduced for particles, problems involving kinetics can be solved. These problems may involve conservation of energy and/or direct application of Newtons Second Law, that is, the rate form of conservation of linear momentum in our framework.
Another advantage of this approach is that students are required to apply the principles outofcontext. Typically in dynamics students know what principle to apply based on the topic currently being discussed in class. With this arrangement of the material, students need to decide which conservation principle is most applicable. Similarly, after the kinematics associated with fixed axis rotation is introduced, it is natural to extend the range of problems to include those involving energy, as well as linear and angular momentum for rigid bodies.
ES205 Analysis and Design of Engineering Systems  The material covered in the spring course, Analysis and Design of Engineering Systems (ES205) is similar to that covered in a traditional systems class. Equations of motion are obtained for mechanical systems, electrical, electromechanical, thermal, fluid, and hydraulic systems. For single degree of freedom systems, topics of free response, step response and response due to harmonic excitation and general periodic forcing, frequency response plots (Bode plots), transfer functions, and Fourier Series are discussed. The concepts of natural frequency and damping ratio are discussed for mechanical as well as electrical and thermal problems. Associated with this course is a threehour lab devoted primarily to the writing of product design specifications, although there are two more traditional labs. One of the labs is focused on system identification for a draining tank and the other involves modeling a DC motor/generator system with a flexible shaft in Simulink.
