MATH 347 — INTRODUCTORY DIFFERENTIAL EQUATIONS
Learning Objectives & Matches
1. use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.
Perform computations and apply methods of numerical analysis to data.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Program computer numerical control machines.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Create novel computational approaches and analytical tools as required by research goals.
Perform complex calculations as part of the analysis and evaluation of data, using computers.
Confer with numerical control programmers to check and ensure that new programs or machinery will function properly and that output will meet specifications.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
3. identify separable and linear first-order differential equations and solve those differential equations using separation of variables and the integrating factor, respectively.
Teach physics to students.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Prepare and deliver lectures to undergraduate or graduate students on topics such as linear algebra, differential equations, and discrete mathematics.
Remove objects from solutions at periodic intervals and observe objects to verify conformance to specifications.
Remove objects from solutions at periodic intervals and observe objects to verify conformance to specifications.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Remove objects from solutions at periodic intervals and observe objects to verify conformance to specifications.
Devise or apply independent models or tools to help verify results of analytical systems.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Observe the current system in operation, and gather and analyze information about each of the component problems, using a variety of sources.
4. understand the difference between a family of solutions to a differential equation and a specific solution of an initial value problem.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Design computer simulations to model physical data so that it can be better understood.
Analyze problems to develop solutions involving computer hardware and software.
Simulate or model fuel cell, motor, or other system information, using simulation software programs.
Prepare and deliver lectures to undergraduate or graduate students on topics such as linear algebra, differential equations, and discrete mathematics.
Remove objects from solutions at periodic intervals and observe objects to verify conformance to specifications.
Perform complex, dynamic, and integrated mathematical modeling of ecological, environmental, or economic systems.
Devise or apply independent models or tools to help verify results of analytical systems.
Remove objects from solutions at periodic intervals and observe objects to verify conformance to specifications.
Prepare and deliver lectures to undergraduate or graduate students on topics such as linear algebra, differential equations, and discrete mathematics.
5. understand the role of the characteristic and particular solution to solve homogeneous and nonhomogeneous differential equations.
6. 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.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
Create complex and dynamic mathematical models of population, community, or ecological systems.
Educate staff in the use of mathematical models.
Perform complex, dynamic, and integrated mathematical modeling of ecological, environmental, or economic systems.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Determine voices, instruments, harmonic structures, rhythms, tempos, and tone balances required to achieve the effects desired in a musical composition.
Create mechanical models to simulate mechatronic design concepts.
7. employ Laplace transforms to solve differential equations with discontinuous forcing terms.
Apply elements of music theory to create musical and tonal structures, including harmonies and melodies.
Plan or implement research methodology or procedures to apply principles of electrical theory to engineering projects.
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
Conduct analyses of ships, such as stability, structural, weight, and vibration analyses.
Develop or use mathematical models to track changes in biological phenomena, such as the spread of infectious diseases.
Solve problems in a number of engineering fields, such as mechanical, chemical, electrical, civil, nuclear, and aerospace.
Design computer simulations to model physical data so that it can be better understood.
Study physical principles of living cells or organisms and their electrical or mechanical energy, applying methods and knowledge of mathematics, physics, chemistry, or biology.
Design, integrate, or test photonics systems or components.
Provide feedback to students, using positive reinforcement techniques to encourage, motivate, or build confidence in students.