This course covers differential, integral, and vector calculus for functions or more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics. The course opens with a unit on vectors, which introduces students to this critical component of advanced calculus and will culminate in Green’s Stokes’ and Gauss’ Theorems. We will study partial derivatives, double and triple integrals, and vector calculus in both two and three dimensions. Students are expected to develop fluency with vector and matrix operations. Understanding of parametric curves as a trajectory described by a position vector is an essential concept, and this allows us to break free from one-dimensional calculus and investigate paths, velocities, and other applications of science that exist in three-dimensional space. We study derivatives in multiple dimensions, we use the ideas of the gradient and partial derivatives to explore optimization problems with multiple variables, and we consider constrained optimization problems using Lagrangians. After our study of differentials in multiple dimensions, we move to integral calculus. We use line and surface integrals to calculate physical quantities especially relevant to mechanics and electricity and magnetism, such as work and flux, and we employ volume integrals for calculations of mass and moments of inertia.
The study of systems of linear equations, the algebra of matrices, determinants, vector spaces, linear transformations, the algebra of linear transformations with an introduction to dual spaces, eigenvalues and eigenvectors, and the applications of vectors and matrices to linear equations and linear transformations.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations (UC/CSU Subject C Approval Pending)