Engineering Mathematics II | |||
ENGR MATH II | |||
CLASS CODE: | MATH 316 | CREDITS: 4 | |
DIVISION: | PHYSICAL SCIENCE & ENGINEERING | ||
DEPARTMENT: | MATHEMATICS | ||
GENERAL EDUCATION: | This course does not fulfill a General Education requirement. | ||
DESCRIPTION: | Matrices, determinants, eigenvalues and eigenvectors, first and second order ordinary differential equations, power series and Fourier series methods, systems of linear ordinary differential equations, introduction to numerical solution of the above. Emphasis on methods and applications. Math 316 and Math 371 cannot both be taken for credit. | ||
TAUGHT: | Winter, Fall | ||
CONTENT AND TOPICS: | (Note: As many as possible of the following topics are accompanied by applications.) Matrix arithmetic including multiplicative inverses. Linear independence, rank of a matrix, determinants and Gauss-Jordan elimination. Eigenvalues and eigenvectors. Notions of "vector space," "inner product" and "linear transformation." First order ordinary differential equations (ODEs) and initial value problems (IVPs), including separable, exact and linear equations. Modeling. Homogeneous second order linear ODEs and IVPs. Non-homogeneous ODEs and undetermined coefficients. Free, forced and damped oscillation. Resonance. Homogeneous stystems of linear ODEs with constant coefficients and the phase plane. Solution of ODEs and IVPs by power series methods. Bessel functions (without reference to the method of Frobenius) and the gamma function. Solution of IVPs by LaPlace transform methods, including the first and second shifting theorems and the use of Dirac's delta function. Fourier series of functions of any period. As many of the following as time permits: numerical error propagation, solution of equations by iteration, numerical differentiation, numerical integration, numerical methods for the solution of systems of linear equations by Gaussian elimination, iteration, LU factorization, curve-fitting by the method of least squares, eigenvalues by iteration, numerical solution of IVPs and systems thereof. | ||
GOALS AND OBJECTIVES: | 1. Learn the fundamental mathematics that is needed in engineering. 2. Learn the importance of careful, accurate, and precise work. 3. Practice working together as a team on significant problems. 4. Develop both oral and written communication skills. 5. Examine applications of the material. 6. Acquire skills in using technology where appropriate. |
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REQUIREMENTS: | All students must have their own text. If a graphing calculator is to be used, the student must obtain their own. Assignments and exams are required by all faculty. Some faculty may require attendance, participation, projects, working in groups, graphing calculators, computer lab assignments or other forms of assessment. | ||
PREREQUISITES: | Math 215 or equivalent. | ||
OTHER: | |||
EFFECTIVE DATE: | January 2003 |