Topics include real vector spaces, subspaces, linear dependence, span, matrix algebra, determinants, basis, dimension, inner product spaces, linear transformations, eigenvalues, eigenvectors, and proofs. Ordinary differential equations and first-order linear systems of differential equations; explicit solutions; qualitative analysis of solution behavior; linear structure, existence, and uniqueness of solutions. Partial differential equations.
Set theory, logic, proof techniques, mathematical induction, relations and functions, recursion, combinatorics, elementary number theory, trees and graphs, analysis of algorithms. Emphasis on topics of relevance to mathematics and computer science majors.
Advanced calculus course focusing on vectors, curves and surfaces in 3-dimensional space, differentiation and integration of multivariate functions, line and surface integrals, and, in particular, the theorems of Green, Stokes, and Gauss.
Advanced calculus course focusing on vectors, curves and surfaces in 3-dimensional space, differentiation and integration of multivariate functions, line and surface integrals, and, in particular, the theorems of Green, Stokes, and Gauss.
Advanced calculus course focusing on vectors, curves and surfaces in 3-dimensional space, differentiation and integration of multivariate functions, line and surface integrals, and, in particular, the theorems of Green, Stokes, and Gauss.
A second course in single-variable calculus. Applications of integration, techniques of integration, numerical integration, indeterminate forms, improper integrals, parametrized curves, polar coordinates, infinite sequences and series, and power series.
A second course in single-variable calculus. Applications of integration, techniques of integration, numerical integration, indeterminate forms, improper integrals, parametrized curves, polar coordinates, infinite sequences and series, and power series.
First course in a three-semester calculus sequence, this course covers differential calculus through the study of limits, continuity, differentiation, applications of differentiation, and an introduction to integration.
First course in a three-semester calculus sequence, this course covers differential calculus through the study of limits, continuity, differentiation, applications of differentiation, and an introduction to integration.
First course in a three-semester calculus sequence, this course covers differential calculus through the study of limits, continuity, differentiation, applications of differentiation, and an introduction to integration.