Differential Equations
Discrete Mathematics
The Differential Equations course focuses on equations that describe and solve many real world problems, including many from the fields of engineering, the physical sciences, and the social sciences. This course will demonstrate the usefulness of ordinary differential equations in a wide array of situations. Some topics we will explore are: First order differential equations, second order linear equations, the Laplace Transform, mathematical modeling, and higher order linear equations.
Discrete Mathematics is not the name of a branch of mathematics, like number theory, algebra, or calculus. Rather, it is a description of a set of branches of mathematics that all have in common the feature that they are “discrete” rather than “continuous.” Some topics we will explore are: Logic and Boolean algebra, set theory, relations and functions, sequences and series, algorithms and theory of computation, number theory, matrix theory, induction and recursion, counting and discrete probability and graph theory (including trees).
Linear Algebra Linear Algebra is a powerful field of mathematics that is used in a wide range of fields such as physics, computer graphics, cryptography, and sociology. Linear Algebra is traditionally introduced to university students after they have completed their basic Calculus courses. This abbreviated course will introduce some potent problem solving techniques. Some topics we will explore are: Vectors in a plane, matrix algebra and solving linear equations, vector spaces, determinants, linear transformations, eigenvalues, and eigenvectors.
Multivariable Calculus The Multivariable Calculus course focuses on the extension of calculus concepts to three or more dimensional spaces. This course will begin with an overview of three-dimensional coordinate systems before moving on to the analysis of spatial motion and curves. Additional topics we will explore include partial differentiation, multiple integrals, vector fields including Green’s Theorem and Stokes’ Theorem, and second order differential equations.
Upper School Curriculum Guide
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