MATH2082 — Linear Algebra and Differential Equations
MATH 2082 - Linear Algebra and Differential Equations MATH 2082 - Linear Algebra and Differential Equations Hours/Week: Lecture 5 Lab 0 Course Description: This is a first course in Differential Equations including ordinary differential equations, slope fields, existence and uniqueness, boundary and initial-value problems, Laplace transforms, characteristic equations, homogeneous and nonhomogeneous equations, undetermined coefficients, power series solutions, matrix formulation of linear systems of differential equations, phase planes and stability. The companion topics from Linear Algebra include systems of linear equations and matrices, matrix operations, determinants, singular and non-singular matrices, inverse matrices, row space, column space, and null space, rank and kernel, vector spaces and subspaces, independence, bases, linear transformations, eigenvalues and eigenvectors. Use of a 3-D graphing calculator, such as a TI-Nspire CX CAS, is required. Limited use of a computer algebra system will be made. MnTC Goals None Major Content 1. Systems of Linear Equations and Matrices a. Solve linear systems i. Gaussian elimination ii. Gauss-Jordan elimination iii. Matrix equations b. Matrix operations c. Calculate determinants d. Singular and non-singular matrices e. Inverse matrices 2. Vector Spaces and Linear Transformations a. Definition, axioms, and properties of vector spaces b. Subspaces c. Row space and column space d. Linear independence e Linear combinations of vector
Prerequisites: MATH1082