Operations Research Analysts

• Utilize quantitative methods to analyze linear and non-linear systems of differential equations
• Utilize qualitative methods to analyze linear and non-linear systems of differential equations
• Illustrate changes in the solution structure via a bifurcations diagram
• Perform linear stability analysis

• use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.
• set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.
• identify separable and linear first-order differential equations and solve those differential equations using separation of variables and the integrating factor, respectively.

• Evaluate systems for stability, causality, and linearity in discrete time
• Analyze circuits in time domain and frequency domain using Z-trasform, DTFT, and DFT in discrete time.

• Use mathematical software to approximate solutions of biological models
• Construct model equations from a description of a biological system
• Classify stability of fixed points and contextualize within the framework of the system

• Apply classical solution techniques to differential equation models of physical systems
• Construct partial differential equation models for physical systems
• Contextualize partial differential equation models of physical systems
• Visualize models graphically

• Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)
• Demonstrate the ability to use a matrix factorization to solve a linear system;
• Recognize the role of the condition number of a matrix as a measure of the sensitivity of the solution to the related linear system of equations;

• Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.
• Describe each of the following system categories: Linear, nonlinear, time-invariant, time-varying, causal, noncausal, memoryless, continuous-time, discrete-time etc.
• Analyze a linear time-invariant system both in the time and frequency domains.
• Explain the relation between the time and frequency domains, and apply techniques for converting from one domain to another.

Analyze discrete system with difference equations.

• Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
• Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

• Independently research mathematical concepts
• Synthesize pertinent mathematical background material

Demonstrate a knowledge of vector valued functions

• Demonstrate knowledge of relationships between exponents and logarithms and their derivatives
• Compute volumes using a variety of methods
• Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions

Implement a program that uses an array to solve a problem.

Work with the applications of geometric transformations in the sciences

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

• Explain the relationship between matroids and different algorithms for solving problems
• Identify the complexity class of a problem

Apply group theoretic concepts to solve mathematical problems

CLO 1: Apply physical rate laws for simple systems

Apply iterative methods for solving systems of equations of at least two non-linear equations

Apply basic linear algebra to economic problems.

• Model linear dynamical systems with state-space methods.
• Model both open and closed-loop systems using both time and frequency domain methods.
• Determine gain and phase margin for a closed-loop system.

Program a memory management simulation.

CLO 1: Determine the value of thermodynamic function to physical situations

• Interpret output from statistical software correctly
• Perform reductions and simplifications of linear models

Write rigorous correctness proofs for algorithms.

Apply the techniques of multiple integration and partial derivatives to applied problems

Analyze a communication system and measure a performance in terms of probability of

• Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
• Construct finite-difference schemes in order to approximate solutions to differential equations and analyze their order of approximation
• Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

• use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.
• set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.

• Apply classical solution techniques to differential equation models of physical systems
• Construct partial differential equation models for physical systems
• Contextualize partial differential equation models of physical systems
• Explain the role of different boundary equations

• Independently research mathematical concepts
• Synthesize pertinent mathematical background material

• Construct model equations from a description of a biological system
• Use mathematical software to approximate solutions of biological models
• Classify stability of fixed points and contextualize within the framework of the system

• Utilize qualitative methods to analyze linear and non-linear systems of differential equations
• Utilize quantitative methods to analyze linear and non-linear systems of differential equations
• Illustrate changes in the solution structure via a bifurcations diagram

• Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.
• Describe each of the following system categories: Linear, nonlinear, time-invariant, time-varying, causal, noncausal, memoryless, continuous-time, discrete-time etc.

• Solve simple differential equations focusing on topics in economics.
• Apply basic linear algebra to economic problems.

Apply group theoretic concepts to solve mathematical problems

Apply the techniques of multiple integration and partial derivatives to applied problems

• Explain the relationship between matroids and different algorithms for solving problems
• Calculate the solutions to problems related to difference equations
• Identify the complexity class of a problem

• Implement a numerical approximation to a solution of an initial value problem;
• Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);
• Compare the error from a numerical calculus approximation to the corresponding error estimate;

Evaluate systems for stability, causality, and linearity in discrete time

• Model both open and closed-loop systems using both time and frequency domain methods.
• Model linear dynamical systems with state-space methods.
• Design a closed-loop system that meets specified transient and steady state error goals.
• Design a P, PI, and PID controller to meet steady state tracking error requirements.

• Implement a program that uses an array to solve a problem.
• Write, compile and execute a complete program for a given problem.

CLO 1: Determine the value of thermodynamic function to physical situations

Program a memory management simulation.

Work with the applications of geometric transformations in the sciences

CLO 1: Apply physical rate laws for simple systems

Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions

• Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)
• Recognize the role of the condition number of a matrix as a measure of the sensitivity of the solution to the related linear system of equations;

Apply iterative methods for solving systems of equations of at least two non-linear equations

Perform reductions and simplifications of linear models

• Construct model equations from a description of a biological system
• Use mathematical software to approximate solutions of biological models
• Interpret dynamics of discrete and continuous models

• Apply classical solution techniques to differential equation models of physical systems
• Construct partial differential equation models for physical systems
• Contextualize partial differential equation models of physical systems
• Visualize models graphically

Perform reductions and simplifications of linear models

Work with the applications of geometric transformations in the sciences

Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

• Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
• Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.

Explain the relationship between matroids and different algorithms for solving problems

• Utilize qualitative methods to analyze linear and non-linear systems of differential equations
• Utilize quantitative methods to analyze linear and non-linear systems of differential equations

Independently research mathematical concepts

• Model linear dynamical systems with state-space methods.
• Model both open and closed-loop systems using both time and frequency domain methods.

Devise a hypothetical research project for an AI topic of your choice

Apply group theoretic concepts to solve mathematical problems

• Write rigorous correctness proofs for algorithms.
• Analyze the asymptotic performance of algorithms.

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

Evaluate systems for stability, causality, and linearity in discrete time

• Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)
• Demonstrate the ability to use a matrix factorization to solve a linear system;
• Recognize the role of the condition number of a matrix as a measure of the sensitivity of the solution to the related linear system of equations;

Apply the techniques of multiple integration and partial derivatives to applied problems

• Apply classical solution techniques to differential equation models of physical systems
• Construct partial differential equation models for physical systems
• Contextualize partial differential equation models of physical systems

• Utilize qualitative methods to analyze linear and non-linear systems of differential equations
• Utilize quantitative methods to analyze linear and non-linear systems of differential equations
• Illustrate changes in the solution structure via a bifurcations diagram
• Perform linear stability analysis

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

• identify separable and linear first-order differential equations and solve those differential equations using separation of variables and the integrating factor, respectively.
• use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.

Apply basic linear algebra to economic problems.

Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.

Implement a program that uses an array to solve a problem.

Design a closed-loop system that meets specified transient and steady state error goals.

Calculate the solutions to problems related to difference equations

Describe each of the following system categories: Linear, nonlinear, time-invariant, time-varying, causal, noncausal, memoryless, continuous-time, discrete-time etc.

Analyze circuits in time domain and frequency domain using Z-trasform, DTFT, and DFT in discrete time.

• Independently research mathematical concepts
• Synthesize pertinent mathematical background material

Apply group theoretic concepts to solve mathematical problems

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.

• Construct model equations from a description of a biological system
• Use mathematical software to approximate solutions of biological models

• Visualize models graphically
• Contextualize partial differential equation models of physical systems
• Apply classical solution techniques to differential equation models of physical systems
• Construct partial differential equation models for physical systems

Work with the applications of geometric transformations in the sciences

Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Demonstrate knowledge of relationships between exponents and logarithms and their derivatives

Perform reductions and simplifications of linear models

Independently research mathematical concepts

• Use mathematical software to approximate solutions of biological models
• Interpret dynamics of discrete and continuous models
• Construct model equations from a description of a biological system

Work with the applications of geometric transformations in the sciences

• Visualize models graphically
• Construct partial differential equation models for physical systems

Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

• Interpret output from statistical software correctly
• Perform reductions and simplifications of linear models

Program a memory management simulation.

• Construct partial differential equation models for physical systems
• Apply classical solution techniques to differential equation models of physical systems
• Contextualize partial differential equation models of physical systems

• Utilize qualitative methods to analyze linear and non-linear systems of differential equations
• Utilize quantitative methods to analyze linear and non-linear systems of differential equations

• Apply non-parametric statistical tests
• Interpret model assumptions
• Perform reductions and simplifications of linear models

Model both open and closed-loop systems using both time and frequency domain methods.

• Construct model equations from a description of a biological system
• Interpret dynamics of discrete and continuous models

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

• Perform reductions and simplifications of linear models
• Interpret model assumptions

Write rigorous correctness proofs for algorithms.

Construct model equations from a description of a biological system

Visualize models graphically

• Apply non-parametric statistical tests
• Interpret output from statistical software correctly

Write a professional report adhering to scholarly standards

• Write a professional report adhering to scholarly standards
• Summarize the professional report in an oral presentation

Apply group theoretic concepts to solve mathematical problems

Implement a program that uses an array to solve a problem.

Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Program a memory management simulation.

Write a professional report adhering to scholarly standards

Implement an iterative method to solve a problem (e.g. matrix decomposition, solution of a linear system of equations, determining eigenpairs of a matrix)

Apply group theoretic concepts to solve mathematical problems