MATH347 — Introductory Differential Equations
Introduces ordinary differential equations including analytical and numerical solution methods, Laplace transforms, and mathematical modeling.
Learning Objectives & Matches
Use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica
Create graphs, charts, or other visualizations to convey the results of data analysis using specialized software.
Present the results of mathematical modeling and data analysis to management or other end users.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
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.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Analyze problems to develop solutions involving computer hardware and software.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Solve ordinary differential equations using analytical methods
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Educate staff in the use of mathematical models.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Develop or use mathematical models to track changes in biological phenomena, such as the spread of infectious diseases.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Make use of mathematical software to perform qualitative analysis of nonlinear first order differential equations
Write program code to analyze data with statistical analysis software.
Develop software applications or programming for statistical modeling and graphic analysis.
Analyze problems to develop solutions involving computer hardware and software.
Perform computations and apply methods of numerical analysis to data.
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Design, develop and modify software systems, using scientific analysis and mathematical models to predict and measure outcomes and consequences of design.
Deliver oral or written presentations of the results of mathematical modeling and data analysis to management or other end users.
Write new functions or applications in programming languages to conduct analyses.
Apply Laplace transforms to solve differential equations
Identify separable and linear first-order differential equations and solve those differential equations using separation of variables and the integrating factor, respectively
Use numerical methods including Euler's method and Runge-Kutta methods
Understand the difference between a family of solutions to a differential equation and a specific solution of an initial value problem
Develop mathematical models for physical, biological, and engineering systems
Understand the role of the characteristic and particular solution to solve homogeneous and nonhomogeneous differential equations
Analyze stability and behavior of dynamical systems
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 systems of differential equations to model coupled phenomena
Employ Laplace transforms to solve differential equations with discontinuous forcing terms
Use computational tools to solve and visualize differential equations
Develop data models describing data elements and how they are used, following procedures and using pen, template, or computer software.
Develop data model describing data elements and their use, following procedures and using pen, template or computer software.
Use the computer in the analysis and solution of business problems, such as development of integrated production and inventory control and cost analysis systems.
Complete models and simulations, using manual or automated tools, to analyze or predict system performance under different operating conditions.
Develop or implement data analysis algorithms.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Educate staff in the use of mathematical models.
Analyze information processing or computation needs and plan and design computer systems, using techniques such as structured analysis, data modeling, and information engineering.
Develop or use mathematical models to track changes in biological phenomena, such as the spread of infectious diseases.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.