MATH2350

Meets MN Transfer Curriculum Goal Area 4: Mathematics/Logical Reasoning. This course is designed for students who have sound skills in single-variable calculus. The primary goal of this course is to help individuals acquire a solid foundation in the basic theory of differential equations and linear algebra. Students will apply skills to solve authentic real-world problems which are used to enhance students' understanding of higher lever concepts.Student Learning Outcomes

• Recognize and work with first order and higher order linear and nonlinear differential equations.
• Model real-life situations using first order and higher order differential equations.
• Find numerical solutions of ordinary Differential Equations including Euler's Method.
• Apply Existence and Uniqueness Theorem.
• Solve boundary/initial value problems.
• Solve systems of linear equations using matrix methods including Gaussian Elimination, Gauss-Jordan Elimination, and by matrix equation representation.
• Interpret the determinant of a matrix and its properties, and apply them to linear independence, areas, volumes, orientation, invertibility, Cramer's Rule, and the adjoint of a matrix.
• Identify a vector space from the axioms and prove that a non-empty subset of a vector space is a subspace.
• Create a basis for a nonzero finite dimensional vector space and find its dimension.
• Compute the coordinate vector of a vector relative to a finite basis.
• Construct bases for the row, column, and null space of a matrix. Relate their dimensions to one another, and to the rank and nullity of the matrix.
• Compute, explain, and apply key properties and definitions related to eigenvalues and eigenvectors of a matrix.
• Express a dynamical system as a mathematical model.
• Use direction fields to illustrate solutions of differential equations. Solve differential equations using direction fields?
• Solve systems of differential equations.
• Solve problems using the Laplace Transform.