2010-2011 Catalog [ARCHIVED CATALOG]
Courses
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MAE 5125 - Advanced Dynamics 3 Credits (Minimum) 3 Credits (Maximum)
Analytical dynamics: Lagrange’s equations, Hamilton’s principle and variational calculus, Routh’s method, Hamilton’s equations. Applications in rigid bodies and continuous, nonautonomous, and nonlinear systems. Stability of nonlinear systems with Liapunov’s direct method. Prer., MATH 4470 and MAE 4402.
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MAE 5130 - Advanced Fluid Dynamics 3 Credits (Minimum) 3 Credits (Maximum)
Mechanics of fluids. Governing equations: conversation laws, flow kinematics, and basic theorems. Ideal fluid flow: 2D and 3D potential flows and surface waves. Viscous flows of incompressible fluids: exact solutions, low-Reynolds number approximations, and boundary layer theory. Compressible flow of inviscid fluids: shock waves, 1-D and multi-dimensional flows. Prer., MAE 2301, MAE 3130, ,MAE 3302, MAE 3310. Co-req., MAE 5011. Grad standing or consent of instructor.
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MAE 5131 - Computational Fluid Dynamics 3 Credits (Minimum) 3 Credits (Maximum)
Computational fluid dynamics (CFD) has become an industry standard, ranging from CFD solvers coupled with CAD packages such as Solidworks, to highly sophisticated standalone packages for advanced engineering applications (Fluent, Star-CCM, etc.). This introductory course provides an overview of the underlying numerical methods used in CFD: e.g., how we can solve the Navier-Stokes equations numerically. Students will utilize MATLAB and a commercially available CFD package: MATLAB to develop/implement a basic CFD program, providing insights and hands-on experience with the underlying methods used in CFD and the resulting limitations of CFD software; commercial software will be used to explore the broad range of enginering applications that can benefit from CFD analysis. Prer., MAE 3130, MATH 3130, MATH 3400, or graduate standing in MAE. Meets with MAE 4131.
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MAE 5140 - Compressible Flow 3 Credits (Minimum) 3 Credits (Maximum)
Compressible flow dynamics are investigated including the conservation equations for inviscid and viscous flows. Study of shock and expansion waves including methods for solving scenarios involving high Mach number flows. High temperature gas dynamics will also be introduced. Prer., MAE 2301, MAE 3130, MAE 3302, MAE 3310; coreq., MAE 5011; Graduate students only.
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MAE 5150 - Advanced Vibrations 3 Credits (Minimum) 3 Credits (Maximum)
A second course in vibrations covering the following topics: multiple-degree of freedom systems, undampedand damped, harmonic and forced, numerical solutions, continuous systems, and the finite-element method. Prer., MATH 3130 and MATH 3400; MAE 4150/5190.
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MAE 5155 - Mechanics of Composite Materials 3 Credits (Minimum) 3 Credits (Maximum)
Polymer, metal, and ceramic matrix composites. Anisotropic and orthotropic elasticity, rotation andlayering of laminas, properties of laminate structures. Failure theories: Tsai-Hill and Tsai-Wu. Hygrothermal and piezoelectric strains/stresses in composites. Computation of composite behavior. Prer., MAE 4150 or MAE 5190 and MATH 4470.
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MAE 5160 - Finite Element Analysis for Mechanics 3 Credits (Minimum) 3 Credits (Maximum)
An introduction to finite element analysis (FEA) procedures in mechanics, beginning with vectors, matrices and tensors, and continuing with formulation and calculation of FEA for solid mechanics, static and dynamic structural mechanics, heat transfer, electric fields, and incompressible fluid flow analysis. Students will do a significant amount of programming in the language of their choice. Prer., MATH 4470, MAE 4150/MAE 5190, and programming competency.
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MAE 5165 - Microelectromechanical Systems (MEMS) 3 Credits (Minimum) 3 Credits (Maximum)
Integration of electrical and mechanical processes to design micromachines. Properties of materials. Structural design: fundamental mechanics, systems,and vibrations. Transducer and actuator principles. Sensor design integration and applications. Prer., MATH 3130, MATH 3400, MAE 4402 or MAE 5493, ECE 2220 or equivalent.
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MAE 5167 - Mems Design and Fabrication Laboratory 3 Credits (Minimum) 3 Credits (Maximum)
Integration of electrical and mechanical design processes to build micro machines. Process design: wet chemical etching, wafer bonding, RIE and CMP. Surface micro machining. Sensor design integration and application. Prer., MAE 5165.
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MAE 5201 - Solid Mechanics 3 Credits (Minimum) 3 Credits (Maximum)
Analysis of structures using fundamental concepts of continuum mechanics, theory of elasticity, energy principles, variational methods, and finite element analysis. Prer., Graduate standing or consent of instructor.
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MAE 5205 - Fracture Mechanics 3 Credits (Minimum) 3 Credits (Maximum)
Fundamental concepts of structural failure. Stress intensity, energy criterion, cracking, and damage tolerance. Linear Elastic Fracture Mechanics: stress concentrations, Griffith energy, energy release rates, K/G and J-integrals, crack tip plasticity. Plane stress/strain, and mixed-mode failure. Graduate credit requires the solution and presentation of a class project. Prer., MATH 3130, MATH 3400 and MAE 2102. Meets with MAE 4210.
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MAE 5210 - Advanced Fracture Mechanics 3 Credits (Minimum) 3 Credits (Maximum)
Review of linear elastic fracture mechanics. Dynamic fracture mechanics: arrest and branching, energy release rates, contour integrals, and examples. Elastic-plastic fracture mechanics, including Dugdale’s model, J-integrals, CTOD, and mixed-mode failure. Introduction to computational technique. Prer., MAE 4210 and MATH 4470.
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MAE 5301 - Advanced Thermodynamics 3 Credits (Minimum) 3 Credits (Maximum)
First and second laws of thermodynamics including heat transfer, work transfer, property relationships, and maximum entropy. Entropy generation including lost work, mechanisms, and minimization. Power plant, solar power, and refrigeration processes including thermodynamic formulation, maximum power, reversible and irreversible processes, and optimization. Entropy generation minimization. Prer., MAE 2301, MAE 3302, MAE 3130, MAE 3310. Graduate standing or consent of instructor.
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MAE 5310 - Intermediate Heat Transfer 3 Credits (Minimum) 3 Credits (Maximum)
Fundamental treatment of conduction, convection, and radiation based on exact and numerical finite-difference/element solutions to the governing partial differential equations. Steady-state and transient conduction, laminar/turbulent boundary layer flows, radiation, and coupling between thethree modes of heat transfer. Prer., Graduate standing or consent of instructor.
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MAE 5391 - Rocket Propulsion 3 Credits (Minimum) 3 Credits (Maximum)
Basic theory of rocket propulsion, nozzle performance, propellant characteristics. Primary emphasis on the engine system design process, based on mission requirements. Chemical, as well as nuclear, electric, and advanced propulsion concepts are treated. Prer., MATH 3400 and MAE 2301. Meets with MAE 4316.
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MAE 5402 - System Dynamics 3 Credits (Minimum) 3 Credits (Maximum)
Kinematics, relative motion, and rotation of particles and rigid bodies, including inertia tensors, Euler’s angles and equations. Variational principles, work, energy expressions, and Lagrange’s equations. Electrical circuits and electromechanical systems. Prer., MAE 4402.
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MAE 5410 - Astrodynamics 3 Credits (Minimum) 3 Credits (Maximum)
Rigorous development and application of the fundamental principles of astrodynamics to satellite motion. Study of coordinate systems, time keeping, computation of orbits, introduction to perturbation theory, Kepler’s and Lambert’s problems, linear orbit theory, patched conics method. Prer., MAE 4402 or consent of instructor.
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MAE 5411 - Space Operations Analysis 3 Credits (Minimum) 3 Credits (Maximum)
An advanced class in astrodynamics and space mission operations. The primary goal is to present numerical methods useful in evaluating spacecraft trajectories. This will include methods of orbit determination, numerical vehicle targeting, and statistical estimation theory. Prer., MAE 4410/5410.
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MAE 5412 - Atmospheric Flight Control 3 Credits (Minimum) 3 Credits (Maximum)
Feedback control of aerospace vehicles operating in the atmosphere (aircraft and missiles). Aircraft and missile stability augmentation and autopilots. Frequency-domain analysis and synthesis, Bode/Nyquist, loop shaping. Prer., MAE 3420 and MAE 4415/MAE 5415.
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MAE 5415 - Flight Dynamics 3 Credits (Minimum) 3 Credits (Maximum)
Advanced treatment of the flight dynamics of atmospheric flight vehicles and spacecraft. Rigorous development of non-linear equations of motion, including environmental and propulsive forces. Linearization via small-perturbation methods - limitations. Transient response, stability, natural modes. Intro to simulation techniques. Prer., MAE 3401, MAE 4402 recommended by the instructor. Meets with MAE 4415.
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MAE 5417 - Analysis of Mechanical and Aerospace Dynamic Systems 3 Credits (Minimum)
Unified approach to dynamic systems analysis; method for development of lumped-parameter analytical models for mechanical and electromechanical systems, vehicles, robots, power systems; energy-based state-space formulations; simulation of linear and non-linear systems; perturbation techniques and neighboring trajectories; controllability concepts; modal analysis.
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MAE 5418 - Multivariable Modeling and Control of Mechanical and Aerospace Systems 3 Credits (Minimum) 3 Credits (Maximum)
Modeling, system representation, and control for multivariable mechanical and aerospace systems. Topics include system representation, observability, controllability, decoupling, and controller design. Prer., MAE 5417.
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MAE 5419 - Trajectory Optimization 3 Credits (Minimum) 3 Credits (Maximum)
Optimization of the non-linear dynamics governing trajectories of aerospace vehicles or robots. Calculus of variations and numerical algorithms. Optimal orbit transfer, launch, re-entry, and interplanetary trajectories; robot path planning. Treatment of equality and inequality constraints (e.g., heating, loads). Projects in numerical optimization. Prer., MATH 3130, MATH 3400, MAE 2102, and Graduate level linear algebra and astrodynamics recommended.
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MAE 5421 - Digital Control of Mechanical and Aerospace Systems 3 Credits (Minimum) 3 Credits (Maximum)
A laboratory-based course addressing the feedback control of aerospace vehicles, with special focus on the fact that the control systems will be implemented digitally. Z-domain systems analysis, discrete loop-shaping synthesis techniques; sample-rate selection; quantization effects. Real-time code generationand implementation. Hardware-in-the-loop testing and validation. Aircraft and missile stability augmentation and autopilots, spacecraft attitude control, and control of flexible systems. Prer., MAE 4421 or ECE 4510.
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MAE 5424 - Spacecraft Attitude Dynamics and Control 3 Credits (Minimum) 3 Credits (Maximum)
Three-dimensional rigid body rotational spacecraft kinematics, Euler angle, quaternions, axis/angle. Euler’s equations of motion, torque-free and constant torque behavior. Gravity gradient equilibria and stability. Spin stabilization, gyrostats, momentum exchange devices, reaction thrusters, magnetic torquers. Prer., MAE 4421, MAE 5417. Graduate standing or consent of instructor.
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MAE 5425 - Spacecraft Attitude Control 3 Credits (Minimum)
Graduate-level treatment of attitude feedback-control techniques. Review of attitude dynamics and conventional control analysis and synthesis methods. Loop-shaping design techniques; control-system requirements. Safe-hold algorithms, tracking, regulation control and maneuvering.
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MAE 5450 - Robotics 3 Credits (Minimum) 3 Credits (Maximum)
Dynamics, kinematics, and automatic control of robotic devices. Force and position control, path planning. Prer., MATH 3130, MATH 3400, MAE 3401, and MAE 4421. Meets with MAE 4450.
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MAE 5455 - Flight Mechanics 3 Credits (Minimum) 3 Credits (Maximum)
A fundamental study of the trajectory dynamics of aerospace vehicles operating in the atmosphere (aircraft and missiles). Rigid-body equations of motion; vehicle-carried coordinate systems; aerodynamic and propulsive forces; maneuvering flight; introduction to trajectory simulation. Prer., MAE 4402/MAE 5493, MATH 3130 and MATH 3400. Meets with MAE 4455.
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MAE 5456 - Spacecraft Actuators and Sensors 3 Credits (Minimum) 3 Credits (Maximum)
Modeling of spacecraft actuators, including momentum wheels, reaction wheels, gas jets, and magnetic torque bars. Modeling of spacecraft sensors, including sun sensors, star sensors, earth sensors, magnetometers, gyros, and GPS. Prer., MAE 5402 and MATH 3400.
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MAE 5460 - GPS Principles and Applications 3 Credits (Minimum) 3 Credits (Maximum)
Course will focus primarily on GPS (Global Positioning Satellite) navigation system and its limits and applications in navigation on earth and near-space. Effects of atmospheric propagation will be included. Surveys of usage for such navigational systems to the military and civilian sectors will be given. Prer., MAE 4410/5410 and MATH 3810 or ECE 3610. Meets with MAE 4460.
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MAE 5495 - Launch Vehicle Analysis 3 Credits (Minimum)
Theory of rocket performance, nozzle performance, propellant characteristics, staging, throw-weight analysis, launch trajectory analysis, orbit injection. Development of launch-vehicle requirements based on mission requirements.
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MAE 5510 - Engineering Design I 1 Credits (Minimum) 1 Credits (Maximum)
Design principles with the realistic constraints of economy, safety, reliability, aesthetics, ethics and social impact. Project and team organization to meet design goals. Professional oral and written communication of the design through presentations, memos, reports, and e-mail. Prer., Senior/Graduate standing. Meets with MAE 4510.
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MAE 5511 - Engineering Design II 3 Credits (Minimum) 3 Credits (Maximum)
Project laboratory for the senior or graduate student for the design of a mechanical or electromechanical component, with emphasis on the identification, selection, design, and simulation or fabrication of the component. A successful project is required for completion of the course. Prer., MAE 4510/MAE 5510. Meets with MAE 4511.
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MAE 5559 - Manufacturing Technology and the Factory of the Future 3 Credits (Minimum) 3 Credits (Maximum)
Engineering and technology issues are integrated with management methods and international interaction to examine future developments in manufacturing. Topics include: computer-integrated manufacturing, robotics, flexible automation, expert systems, integration of design and production through databases and telecommunications, the human-machine interface, and manufacturing management information systems. Prer., MAE 4541/MAE 5574 and MAE 4542/ MAE 5575.
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MAE 5560 - Engineering Project Management 3 Credits (Minimum) 3 Credits (Maximum)
Capstone course involving all components of the manufacturing systems engineering curriculum. Focus on mathematical programming, networks, dynamic programming and tools such as PERT/CPM to model projects, systems and timelines. A major portion of the course is a hands-on project. Written and oral reports are required that meet publication standards for completeness, clarity and technical integrity. Prer., Graduate status. Meets with ENGR 5050.
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MAE 5570 - Design for Manufacture 3 Credits (Minimum) 3 Credits (Maximum)
Theories and practice for achieving manufacturable designs. Topics include: introduction to manufacturing processes, creativity and design, DFM concepts, design philosophy, company DFM programs,group technology, cost and value analysis, life-cycle engineering, assembly strategies, and human factors. Prer., ENGR 3420 and MAE 2501. Meets with MAE 3560.
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MAE 5571 - Analysis and Design of Experiments 3 Credits (Minimum) 3 Credits (Maximum)
Statistical methods to design experiments for the design of effective manufacturing systems. Balanced treatment of traditional and modern techniques in experiment design, with emphasis on real-world applications. Processes of planning, collecting data, and analyzing the data are covered. Prer., Senior/Graduate standing and either ECE 3610 or MATH 3810. Meets with MAE 4561.
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MAE 5574 - Cellular Manufacturing 3 Credits (Minimum) 3 Credits (Maximum)
Cellular manufacturing has become an essential part of most world-class strategies. Investigation of analysis design and implementation of high-performance manufacturing cells. Topics include: key cell design issues, simulation in cell design, techniques for economic evaluation, group technology, just-in-time strategies, and team building in cellular manufacturing. Prer., MAE 3560/MAE 5570, MAE 4561/MAE 5571 and MAE 4506/MAE 5596. Meets with MAE 4541.
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MAE 5575 - Contemporary Issues in Manufacturing 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to world class manufacturing including interaction with customers and suppliers, integrated and concurrent manufacturing, and just-in-time production meeting customer requirements, using case analysis, field study, and experiential learning. Prer., MAE 3560/MAE 5570, MAE 4561/MAE 5571 and MAE 4506/MAE 5596. Meets with MAE 4542.
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MAE 5593 - Space Sensor Systems 3 Credits (Minimum)
Introduction to airborne and space based sensor systems and data fusion techniques. The sensor design and performance characteristics of microwave and millimeter wave radar systems, infrared (IR) thermal imagers, and electro-optical (EO) devices will be covered. Additionally, multiple sensor systems, data fusion, and tracking will be discussed.
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MAE 5595 - Space Mission Analysis 3 Credits (Minimum)
Space environment, spacecraft communication constraints. Orbit selection, launch requirements, communication requirements. Development of spacecraft design requirements, as driven by the mission requirements.
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MAE 5596 - Space Mission Design 3 Credits (Minimum)
A capstone course which includes some review of engineering subsystem technology. Students will be asked to configure and design a spacecraft bus to fulfill missions specified.
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MAE 6415 - Robust Multivariable Control 3 Credits (Minimum) 3 Credits (Maximum)
Theory and application for multivariable feedback control systems, limitations of achievable performance and stability robustness in the face of uncertainty in the dynamics of the controlled system. Characterization of uncertainty, and robustness analysis. Multivariable synthesis techniques, applications to control of electromechanical systems and spacecraft. Prer., ECE 5520.
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MAE 6430 - Optimal Estimation Theory 3 Credits (Minimum) 3 Credits (Maximum)
Theory of optimal estimation, with applications to aerospace navigation. Kalman filtering, and complementary filters, continuous and discrete formulations. Observability issues, sensor selection, numerical methods. Prer., ECE 4610 or ECE 5610.
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MAE 6432 - Advanced Astrodynamics 3 Credits (Minimum)
Special and general perturbations including geopotential expansions and other perturbing forces are covered. Also included are circular restricted three-body problems; Jacobi integral and zero velocity curves, and Hamiltonian mechanics including canonical transformations and the Hamilton-Jacobi equation applied to two-body motion. Open to graduate students only.
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MAE 7000 - Master’s Thesis 1 Credits (Minimum) 12 Credits (Maximum)
For master’s thesis in mechanical and aerospace engineering. Prer., Prior agreement with faculty advisor.
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MAE 7500 - Master’s Research 1 Credits (Minimum) 12 Credits (Maximum)
Research credit for master’s program in mechanical and aerospace engineering. Prer., Prior agreement with faculty advisor.
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MAE 8000 - Doctoral Dissertation 1 Credits (Minimum) 12 Credits (Maximum)
For doctoral dissertation in mechanical and aerospaceengineering. Prer., Prior agreement with faculty advisor.
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MAE 9110 - Special Topics: Undergraduate 1 Credits (Minimum) 3 Credits (Maximum)
An opportunity for students to study special subjectsin mechanical and aerospace engineering, undergraduate level. Prer., Prior agreement with faculty advisor.
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MAE 9400 - Independent Study: Undergraduate 1 Credits (Minimum) 6 Credits (Maximum)
Provides opportunity for independent study in mechanical and aerospace engineering by one or more students on topics determined by a faculty member. Prer., Prior agreement with faculty advisor.
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MAE 9500 - Independent Study: Graduate 1 Credits (Minimum) 6 Credits (Maximum)
Provides opportunity for independent study in mechanical and aerospace engineering by one or more graduate students on topics determined by a faculty member. Prer., Prior agreement with faculty advisor.
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MAE 9510 - Special Topics: Graduate 1 Credits (Minimum) 3 Credits (Maximum)
An opportunity for students to study special subjectsin mechanical and aerospace engineering, graduate level. Prer., Prior agreement with faculty advisor.
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MAE 9520 - Graduate Seminar 1 Credits (Minimum) 3 Credits (Maximum)
Allows graduate students credit for attending department seminars and workshops. Prer., Prior agreement with faculty advisor.
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MAE 9990 - Candidate for Degree 0 Credits (Minimum) 0 Credits (Maximum)
Candidate for degree. Prer., Prior agreement with faculty advisor.
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MAE 9999 - Candidate for Degree 0 Credits (Minimum)
Candidate for degree.
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MATH 90 - Algebra I: Fundamentals of Algebra 4 Credits (Minimum) 4 Credits (Maximum)
Graph and solve first-degree equations and inequalities; convert word problems into first-degree problems; add, multiply, and divide polynomials; use scientific notation; factor and solve word problems involving quadratic expressions; use algebra and coordinate geometry to solve problems involving one or more lines; manipulate algebraic fractions. Administered through the Department of Mathematics. Does not count toward BA or BS degree. Prer., Placement exam.
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MATH 99 - Algebra II: Intermediate Algebra 4 Credits (Minimum) 4 Credits (Maximum)
Equations and inequalities; graphs and functions; systems of equations and inequalities; polynomials and polynomial functions; rational expressions and equations; roots, radicals, and complex numbers; quadratic functions. Administered through the Department of Mathematics. Does not count toward BA or BS degree. Prer., MATH 90 with a grade of “C” or higher, or Placement exam.
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MATH 1040 - College Algebra 3 Credits (Minimum) 3 Credits (Maximum)
An in-depth study of algebraic equations and inequalities. Comprehension of the underlying algebraic structure will be stressed as well as appropriate algebraic skills. The study will include polynomials, rational, exponential, and logarithmic functions as well as systems of equations/inequalities. Prer., Score 12 or more on algebra diagnostic exam. *** See Mathematics Department prerequisite policy. ***
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MATH 1050 - Elementary Functions of Calculus 4 Credits (Minimum) 4 Credits (Maximum)
An intensive study of the elementary functions required for calculus. These functions will include polynomial, rational, exponential, logarithmic, and trigonometric functions. Emphasis is on their algebraic structure and graphs. Analysis of conic sections and analytic geometry will be included. GT-MA1. Prer., MATH 1040 or score 20 or diagnostic exam. **see Mathematics Department prerequisite policy. ***
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MATH 1110 - Topics in Linear Algebra 3 Credits (Minimum) 3 Credits (Maximum)
For business and economics students. Systems of linear equations, matrix algebra, linear programming, probability, statistics. Prer., MATH 1040 or score 17 or more on algebra diagnostic exam. **see Mathematics Department prerequisite policy**
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MATH 1120 - Calculus for Business and Economics 3 Credits (Minimum) 3 Credits (Maximum)
Calculus for business and economics students. Prer., MATH 1040 or score 17 or more on algebra diagnostic exam. **see Mathematics Department prerequisite policy**
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MATH 1200 - Reasoning About Data 3 Credits (Minimum) 3 Credits (Maximum)
Helps students develop quantitative and qualitative reasoning skills by applying inductive and deductive reasoning, mathematics, and statistics to real world data. This course is one of the means to satisfy the Qualitative and Quantitative Reasoning requirement.
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MATH 1310 - Calculus I with Refresher Precalculus Part A 3 Credits (Minimum) 3 Credits (Maximum)
See MATH 1350 for calculus topics covered. Algebraic and elementary function topics are covered throughout, as needed. MATH 1310 and 1320 together are equivalent to MATH 1350. The sequence MATH 1310 - 1320 is designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for MATH 1350. Credit not granted for both this course and MATH 1350. Prer., 4 years high school math (algebra, geometry, trigonometry or their equivalents). The equivalents of MATH 1040 (College Algebra) and MATH 1050 (Elementary Functions for Calculus) or score 20 or more on the Algebra Placement Exam and score 10 or more on the Calculus Readiness Exam. Most students with 4 years of high school mathematics (Algebra I and higher) will qualify.
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MATH 1320 - Calculus I with Refresher Precalculus Part B 3 Credits (Minimum) 3 Credits (Maximum)
Continuation of MATH 1310. See MATH 1350 for calculus topics covered. Algebraic and trigonometric topics are studied throughout, as needed. Credit not granted for both this course and MATH 1350. Prer., MATH 1310, the equivalents of MATH 1040(College Algebra) and MATH 1050 (Elementary Functions for Calculus) or score 20 or more on the Calculus Readiness exam. Most students with 4 years of high school mathematics (Algebra I or higher) will qualify.
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MATH 1350 - Calculus I 4 Credits (Minimum) 4 Credits (Maximum)
Selected topics in analytical geometry and calculus. Rates of change of functions, limits, derivatives ofalgebraic and transcendental functions, applications of derivatives, and integration. Prer., MATH 1050 or score 20 or more on the Algebra Placement Exam and score 10 or more on the Calculus Readiness Exam. *** See Mathematics Department prerequisite policy. ***
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MATH 1360 - Calculus II 4 Credits (Minimum) 4 Credits (Maximum)
Continuation of MATH 1350. Transcendental functions, techniques and applications of integration, Taylor’s theorem, improper integrals, infinite series, analytic geometry, polar coordinates. Prer., MATH 1350.
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MATH 2150 - Discrete Math 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to most of the important topics of discrete mathematics, including set theory, logic, number theory, recursion, combinatorics, and graph theory. Much emphasis will be focused on the ideas and methods of mathematical proofs, including induction and contradiction. Prer., MATH 1350.
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MATH 2350 - Calculus III 4 Credits (Minimum) 4 Credits (Maximum)
Continuation of MATH 1360. Parametric curves, vector functions, partial differentiation, multiple integrals, Green’s Theorem and Stoke’s Theorem. Prer., MATH 1360.
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MATH 2650 - Introduction to Computational Mathematics 1 Credits (Minimum) 1 Credits (Maximum)
An introduction to the use of computers in mathematics using the Matlab computer algebra system. Representation of equations and functions using arrays. Visualization of data and functions. Matlab programs, including general program organization, subprograms, files, and built-in mathematical functions. Prer., MATH 2350.
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MATH 2810 - Introduction to Basic Statistics 3 Credits (Minimum) 3 Credits (Maximum)
Study of the elementary statistical measures. Introduction to probability, statistical distributions, statistical inference and hypothesis testing. Prer., MATH 1040 or equivalent.
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MATH 3010 - Mathematics for Elementary Teachers I 3 Credits (Minimum) 3 Credits (Maximum)
Covers the whole number, integer, and rational number systems that are of prime importance to the elementary teacher. For students planning on elementary teacher certification.
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MATH 3020 - Mathematics for Elementary Teachers II 3 Credits (Minimum) 3 Credits (Maximum)
Intuitive and logical development of the fundamental ideas of geometry such as parallelism, congruence, and measurement. Includes study of plane analytical geometry. For students planning on elementary teacher certification.
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MATH 3100 - Statistics for the Sciences 3 Credits (Minimum) 3 Credits (Maximum)
Descriptive probability, hypothesis testing, nonparametric methods. Discrete and continuous random variables, mean and variance, confidence limits, correlation and regression. Prer., MATH 1350.
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MATH 3110 - Theory of Numbers 3 Credits (Minimum) 3 Credits (Maximum)
A careful study, with emphasis on proofs, of the following topics associated with the set of integers: divisibility, congruencies, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes. Prer., MATH 1360 and MATH 2150.
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MATH 3130 - Introduction to Linear Algebra 3 Credits (Minimum) 3 Credits (Maximum)
Systems of linear equations, matrices, vector spaces, linear independence, basis, dimension, determinants, linear transformations and matrices, eigenvalues and eigenvectors. Prer., MATH 1350.
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MATH 3400 - Introduction to Differential Equations 3 Credits (Minimum) 3 Credits (Maximum)
First order differential equations, linear differential equations, the Laplace transform method, power series solutions, numerical solutions, linear systems. Prer., MATH 2350.
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MATH 3410 - Estimation, Convergence and Approximation 3 Credits (Minimum) 3 Credits (Maximum)
Sequences, numerical series, and power series. Integrals and the analysis of functions defined by integrals. This course provides a thorough introduction to proofs in analysis, and is strongly recommended for students planning to take MATH 4310. Prer., MATH 2350.
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MATH 3500 - Graph Theory 3 Credits (Minimum) 3 Credits (Maximum)
Standard material on the theory of both directed and undirected graphs, including the concepts of isomorphism, connectivity, trees, traversability, planar graphs, coloring problems, relations and matrices. Prer., MATH 2150.
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MATH 3510 - Topics in Combinatorial Analysis 3 Credits (Minimum) 3 Credits (Maximum)
A survey of important areas of combinatorics. Topics may include enumeration techniques, recurrence relations, combinatorial designs, graph theory, machining and optimization. Prer., MATH 2150.
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MATH 3810 - Introduction to Probability and Statistics 3 Credits (Minimum) 3 Credits (Maximum)
The axioms of probability and conditional probability will be studied as well as the development, applications and simulation of discrete and continuous probability distributions. Also, expectation, variance, correlation, sum and joint distributions of random variables will be studied. The Law of Large Numbers and the Central Limit Theorem will be developed. Applications to statistics will include regression, confidence intervals, and hypothesis testing. Prer., MATH 2350.
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MATH 4050 - Topics in Mathematics Secondary Classroom 1 Credits (Minimum) 3 Credits (Maximum)
The topics covered will vary from one offering to the next. Topics will be chosen to meet the needs of secondary mathematics teachers for additional training to teach to the Colorado Model Content Standards. Prer., One semester of calculus, or instructor approval. Meets with MATH 5050.
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MATH 4100 - Technology in Mathematics Teaching and Curriculum 3 Credits (Minimum) 3 Credits (Maximum)
Methodology for using technology as a teaching/learning tool for high school and college math courses. Use of graphing calculators, computer algebra systems, computer geometry systems and the internet will be emphasized. Students are required to develop and present a portfolio of in-depth projects. Prer., MATH 1360. Meets with MATH 5100.
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MATH 4130 - Linear Algebra I 3 Credits (Minimum) 3 Credits (Maximum)
Vector spaces, linear transformations and matrices, determinants, eigenvalues, similarity transformations, orthogonal and unitary transformations, normal matrices and quadratic forms. Prer., MATH 3130. Meets with MATH 5130.
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MATH 4140 - Modern Algebra I 3 Credits (Minimum) 3 Credits (Maximum)
A careful study of the elementary theory of groups, rings, and fields. Mappings such as homomorphisms and isomorphisms are considered. The student will be expected to prove theorems. Prer., MATH 2150 and MATH 3130. One of MATH 3110, MATH 3500, or MATH 3510 (preferably MATH 3110) is strongly recommended.
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MATH 4150 - Modern Algebra II 3 Credits (Minimum) 3 Credits (Maximum)
Continuation of MATH 4140 through Galois theory. Prer., MATH 4140. Meets with MATH 5150.
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MATH 4210 - Higher Geometry 3 Credits (Minimum) 3 Credits (Maximum)
Axiomatic systems. The foundations of Euclidean and Lobachevskian geometries. Prer., MATH 3110 or MATH 3130. Meets with MATH 5210.
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MATH 4230 - Fractal Geometry 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to iterated function systems and mathematical aspects of fractal sets. Includes metric spaces and the space fractals live in, transformations, contraction mapping and Collage Theorem, chaotic dynamics, shadowing theorem, fractal dimension, fractal interpolation, and measures on fractals. Prer., MATH 2350 and MATH 3130. Meets with MATH 5230.
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MATH 4250 - Introduction to Chaotic Dynamical Systems 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to dynamical systems or processes in motion, that are defined in discrete time by iteration of simple functions, or in continuous time by differential equations. Emphasis on understanding chaotic behavior that occurs when a simple non-linear function is iterated. Topics include orbits, graphical analysis, fixed and periodic points, bifurcations, symbolic dynamics, chaos, fractals, and Julia sets. Prer., MATH 2350. Meets with MATH 5250.
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MATH 4310 - Modern Analysis I 3 Credits (Minimum) 3 Credits (Maximum)
Calculus of one variable, the real number system, continuity, differentiation, integration. Prer., MATH 2150 and MATH 2350, MATH 3410 is strongly recommended.
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MATH 4320 - Modern Analysis II 3 Credits (Minimum) 3 Credits (Maximum)
Sequence and series, convergence, uniform convergence; Taylor’s theorem; calculus of several variables including continuity, differentiation, and integration. Prer., MATH 4310. Meets with MATH 5320.
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MATH 4420 - Optimization 3 Credits (Minimum) 3 Credits (Maximum)
Linear and nonlinear programming, the simplex algorithm and other approaches to linear optimization, minimax theorems, convex functions, introduction to calculus of variations. Prer., MATH 3130 and MATH 3400. Meets with MATH 5420.
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MATH 4430 - Ordinary Differential Equations 3 Credits (Minimum) 3 Credits (Maximum)
Linear systems of differential equations, existence and uniqueness theorems, stability, periodic solutions, eigenvalue problems, and analysis of equations important for applications. Prer., MATH 3130 and MATH 3400.
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MATH 4450 - Complex Variables 3 Credits (Minimum) 3 Credits (Maximum)
Theory of functions of one complex variable includingintegrals, power series, residues, conformal mapping and special functions. Prer., MATH 2350. Meets with MATH 5450.
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MATH 4470 - Methods of Applied Mathematics 3 Credits (Minimum) 3 Credits (Maximum)
Boundary value problems for the wave, heat, and Laplace equations, separation of variables methods, eigenvalue problems, Fourier series, orthogonal systems. Prer., MATH 2350, MATH 3130 and MATH 3400. Meets with MATH 5470.
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MATH 4480 - Mathematical Modeling 3 Credits (Minimum) 3 Credits (Maximum)
The use of diverse mathematical techniques to analyze and solve problems from science and engineering, particular problems likely to arise in nonacademic settings such as industry or government. Converting a problem to a mathematical model. Commonly encountered classes of mathematical models, including optimization problems, dynamical systems, probability models and computer simulations. Communication of results of mathematical analysis. Prer., MATH 3130, MATH 3400, and MATH 3100 or MATH 3810 or ECE 3610. Meets with MATH 5480.
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MATH 4650 - Numerical Analysis 3 Credits (Minimum) 3 Credits (Maximum)
Error analysis, root finding, numerical integration and differentiation, numerical methods for ordinary differential equations, numerical linear algebra and eigenvalue problems. Prer., CS 1150, MATH 3130, and MATH 3400. Meets with MATH 5650.
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MATH 4670 - Scientific Computation 3 Credits (Minimum) 3 Credits (Maximum)
Description and analysis of algorithms used for numerical solutions of partial differential equations of importance in science and engineering. The main emphasis is on theoretical analysis, but some practical computations are included. Prer., MATH 2350, MATH 3130, MATH 3400, and CS 1150 or equivalent. Meets with MATH 5670.
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MATH 4810 - Mathematical Statistics I 3 Credits (Minimum) 3 Credits (Maximum)
Exponential, Beta, Gamma, Student, Fisher and Chi-square distributions are covered in this course, along with joint and conditional distributions, moment generating techniques, transformations of random variables and vectors. Prer., MATH 2350 and MATH 3130. Meets with MATH 5810.
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MATH 4820 - Mathematical Statistics II 3 Credits (Minimum) 3 Credits (Maximum)
Point and confidence interval estimation, principles of maximum likelihood, sufficiency and completeness; tests of simple and composite hypotheses. Linear models and multiple regression analysis. Other topics will be included. Prer., MATH 3810 or MATH 3100. Meets with MATH 5820.
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MATH 4830 - Linear Statistical Models 3 Credits (Minimum) 3 Credits (Maximum)
Methods and results of linear algebra are developed to formulate and study a fundamental and widely applied area of statistics. Topics include generalized inverses, multivariate normal distribution and the general linear model. Applications focus on model building, design models and computing methods. The “Statistical Analysis System” (software) is introduced as a tool for doing computation. Prer., MATH 3810 or ECE 3610, or MATH 3100 and MATH 3130. Meets with MATH 5830.
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