7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of Math. 31 or equivalent with a grade of "C" or better

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

Math. 32 recommended

9b. Catalog Description:

First and second order ordinary differential equations, linear differential equations, numerical methods and series solutions, Laplace transforms, modeling and stability theory, systems or linear equations, matrices, determinants, vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors. (CAN MATH 24)

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

1. solve first order differential equations with the variety of
classical methods;
2. solve higher order differential equations by utilizing the linear
model;
3. recognize and construct the solution space of a differential
equation as spanned by basis vectors of a vector space;
4. understand and utilize the practical and physical meaning and
import technical concepts such as linearity, similarity, independence,
orthogonality, eigenspace, transformations, Greens'' functions, null
and column spaces, convolution, Wronskian;
5. follow rigorous mathematical proofs and the development of the
theory throughout the course measured by classroom discussion;
6. be able to change basis, diagonalize matrices, and effect
transformations to solve problems and to become familiar with
appropriate representations, viz., principle axes systems;
7. be able to chose an appropriate method of solution for a
particular problem and solve it, i.e., Laplace transforms for
initial-value problems, power series for non-constant coefficient
differential equations, etc.;
8. work linear algebra and differential algebra problems as
encountered in science and engineering and other applied fields;
9. be able to form determinants, invert matrices, and solve systems
of equations using traditional methods;
10. demonstrate ability to generalize from the equation and its
solution to insight and patterns for general solutions measured
by classroom discussions, homework assignments and exams;
11. be able to set-up the algorithms for the numerical analysis of
both differential equations and linear algebra problems and to use
electronic technology to solve problems;
12. be able to determine the dimension of the solution space of a
differential equation based on linearity and order, and to determine
the dimension of the solution space of a linear system using the
rank and nullity theorem;
13. become familiar with special functions and orthogonal polynomials
differential equations, e.g., Bessel functions and Legendre
polynomials;
14. apply the filtering and switching properties of Dirac delta
functions and Heavyside step functions by homework assignments,
exams, and classroom discussions; and
15. acquire greater understanding of applied problems measured by
homework assignments, exams and classroom discussions.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. First Order Differential Equations
II. Elements of Linear Algebra
III. Linear Transformations and Linear Differential Operators
IV. Linear Differential Equations
V. Equations with Constant Coefficients
VI. Laplace Transformations
VII. Series Solutions
VIII. Matrices and Systems of Linear Equations
IX. Systems of Linear Differential Equations

12. Typical Assignments: (Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour. List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

c. Other (Terms projects, research papers, portfolios, etc.)

SECTION D

SECTION E

SECTION F

SECTION G