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ASEN 5227: Aerospace Mathematics 1
Description
AeroMath 1 provides an introduction to the methods of advanced engineering analysis with an aerospace engineering emphasis. The elements of vector and tensor analysis form the basis for the theoretical development of advanced continuum mechanics that includes fluid mechanics and solid mechanics. Linear ordinary differential equations arise in virtually all aerospace engineering topics, particularly in control theory and mechanics. The calculus of variations and variational methods are an integral part of many methods of optimization and finite-element analysis.
Outline
1.Elements of Vector and Tensor Analysis and Linear Algebra
Vector algebra
Topics of linear algebra
Coordinate systems and vector calculus
Dyadics and Tensors
2. Linear Ordinary Differential Equations (ODEs)
Classification
Qualitative behavior
Initial value problems
Systems of ODEs
Boundary value problems
3. Calculus of Variations and Variational Methods
Extrema of functions
Extrema of functionals and the Euler-Lagrange equation
Variational methods of approximation
Benefits
- Introduction to the mathematics used in advanced engineering analysis.
- Application of the programming, graphics, and symbolic manipulation capabilities of advanced computing environments.
- Develop math skills for systems control and navigation.
- Develop tools to determine system stability.
Objectives
Introduce the methods and mathematics of advanced engineering analysis tailored to aerospace engineering applications.
Prerequisites
Undergraduate calculus, differential equations, and simple programming skills, particularly with MATLAB and/or Mathematica.
Education Officer (EO)
Not Required
Textbooks
Harman et al., Advanced Engineering Mathematics with MATLAB, 2nd ed., Brooks/Cole, 2000, ISBN 0534371647.
References:
References:
- Borisenko and Tarapov, Vector and Tensor Analysis with Applications, Dover, 1968.
- Hildebrand, Methods of Applied Mathematics, 2nd ed., Prentice-Hall, 1965.
- Kreyszig, Advanced Engineering Mathematics, 8th ed., Wiley, 1999.
- Reddy and Rasmussen, Advanced Engineering Analysis, Wiley, 1982, Reprint, Krieger, 1990.
Hardware & Software
MATLAB or Mathematica and e-mail required.
Syllabus
Sample Lectures
| Lecture Title | Semester | Year |
| Wed, Aug 26, 08 54 AM | Fall | 2009 |
| Mon, Aug 24, 08 57 AM | Fall | 2009 |
Upcoming & Previous Offerings
Meeting Days Legend: Monday (M), Tuesday (T), Wednesday (W), Thursday (R), Friday (F), Saturday (S), Sunday (U)
Summer Terms: M = Maymester, A = 1st 5 weeks, B= 2nd 5 weeks, C = 8 weeks, D= 10 weeks
Refer to the Academic Calendar for specific dates.
| Semester | Term | Time | Days | Location | Instructor | Additional Instructors |
| Fall 2009 | 09:00 AM - 09:50 AM | MWF | ECCS 1B14 | Hussein, M | ||
| Fall 2007 | 09:30 AM - 10:45 AM | TR | ECCS 1B12 | Argrow, B | ||
| Fall 2006 | 09:30 AM - 10:45 AM | TR | ECCS 1B12 | Argrow, B | ||
| Fall 2005 | 09:30 AM - 10:45 AM | TR | ECCS 1B28 | Argrow, B | ||
| Fall 2004 | 09:30 AM - 10:45 AM | TR | ECCS 1B28 | Argrow, B |
