Mathematics I (MATH 203)
The course continues the topics in calculus of a single variable. Infinite sequences, series and series expansions like Taylor and Maclaurin expansions are the basis of approximations and solution strategies for first and second order differential equations. The next step is to generalize the framework of calculus by general concepts from linear algebra. The basic elements like vectors and matrices are introduced.
Applications of these objects are discussed to represent linear systems of equations. The different solution strategies for linear systems of equations are presented and the advantages of the solution approaches shown. Based on these techniques the general structure of a linear vector space is introduced and consequences derived for the solution strategies. In addition linear transformations, eigenvalues, eigenvectors as well as the spectral theorem are used in applications. The theoretical structure of linear vector spaces is extended to functions and applications for linear difference and differential equations.