Multivariable Mathematics: Linear Algebra, Vector Calculus, and Differential Equations

Catalog description

Prerequisite: Calculus II: Further Study of Motion and Change (MATH 3010) or equivalent or a score of four or five on the Calculus BC Advanced Placement Exam Rarely is a quantity of interest—tomorrow’s temperature, unemployment rates across Europe, the cost of a spring- break flight to Fort Lauderdale—a simple function of just one primary variable. Reality, for better or worse, is mathematically multivariable. This course will introduce an array of topics and tools used in the mathematical analysis of multivariable functions. The intertwined theories of vectors, matrices, and differential equations and their applications will be the central themes of exploration. Specific topics to be covered will include the algebra and geometry of vectors in two, three, and higher dimensions; dot and cross products and their applications; equations of lines and planes in higher dimensions; solutions to systems of linear equations, using Gaussian elimination; theory and applications of determinants, inverses, and eigenvectors; volumes of three-dimensional solids via integration; spherical and cylindrical coordinate systems; and methods of visualizing and constructing solutions to differential equations of various types. Conference work will involve an investigation of some mathematically-themed subject of the student’s choosing. Modern Mathematics: Proof, Sets, Logic, and Abstract Algebra