This course is designed for students majoring in science or engineering. It is a combination course for engineering students and not intended for students majoring in mathematics. It will develop foundations for a understanding and working knowledge of ordinary differential equations and linear algebra as they relate to modeling problems in science and engineering. This course will include standard classical techniques of solving ordinary differential equations including first order equations, second and higher order linear equations, systems, Laplace transforms. Further study will examine the qualitative nature of solutions and numerical methods to obtain solutions. Applications include population models, motion and resonance, equilibrium solutions, and electric circuits. The linear algebra portion includes the study of systems which may have none, one, or infinitely many solutions; vectors, determinants, matrices, and eigenvalues as they relate to solving systems of linear equations and systems of differential equations.
PREREQUISITES FOR THE COURSE:
MATH 1220 (Calculus II) with a "C" or better.
GENERAL COURSE INFORMATION:
Topics to be covered include:
Identification of dependent, independent, linear, and non-linear equations.
Separation of variables.
Substitution techniques.
Integrating Factors.
Higher Order Differential Equations.
Application of Differential Equations.
Eigenvalues and Eigenvectors.
Undetermined Coefficients.
Laplace Transforms.
Inverse Transforms.
Linear Systems and Matrices.
Vector Spaces.
COURSE OUTCOMES:
At the conclusion of the course, the student will be able to:
Classification of differential equations.
Plot phase planes.
Determine equilibrium solutions and stability.
Solve differential equations using separation of variables.
Find solutions using substitution methods.
Complete solutions of differential equations using integrating factors.
Compute solutions for higher order differential equations.
Use the method of variation of parameters to solve equations.
Introduction to numerical solutions of differential equations using Euler's method and the Runge-Kutta method.
Solve applications involving damping, boundary-value problems and circuits.
Use Laplace transforms and inverse Laplace transforms to solve differential equations.
Translate and graph the unit step function.
Perform Matrix operations.
Find linear combinations and determine linear independence.
Use real and complex eigenvalues and eigenvectors to solve systems of differential equations.
