Course Description
Vector algebra and geometry, fundamental concepts of linear algebra, linear transformations, differential calculus of functions of several variables, solutions of linear systems and linear independence, extremum problems and projections. This course and its sequel give an integrated and more proof-oriented treatment of the material in Multivariable Calculus and Introduction to Linear Algebra.
Athena Title
Multivariable Mathematics I
Equivalent Courses
Not open to students with credit in MATH 3500H
Prerequisite
MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Course Objectives
In addition to learning the customary computational skills in calculus and linear algebra, the student will be exposed to mathematics as mathematicians view it. Students will learn to write proofs and think more rigorously about mathematics, and will come to grips with challenging concepts and problems. In that regard, this course is an excellent preparation for students considering a career in law, medicine, or the sciences.
Topical Outline
1. Vectors, dot product, subspaces, linear transformations and matrices; introduction to determinants and cross product. 2. Scalar- and vector-valued functions, topology of euclidean space, limits and continuity. 3. Differentiation: directional derivatives, differentiability, differentiation rules, the gradient, curves, and higher-order partial derivatives. 4. Implicit and explicit solutions of linear systems: Gaussian elimination, elementary matrices and inverses, linear independence, basis, and dimension, the four fundamental subspaces associated to a matrix. 5. Extremum problems: compactness and the maximum value theorem, maximum/minimum problems, the second derivative test, Lagrange multipliers (with an introduction to eigenvalues), projections and least- squares solution of inconsistent systems.
Syllabus