Math 375 - Multi-Variable Calculus & Linear Algebra
VAN VLECK B239, 11:00 - 12:15 AM, TuTh
HOMEWORK/MATERIAL COVERED IN CLASS
Professor: Tullia Dymarz
Office: Van Vleck 509
Office hours: After class or Thursdays 2:30-3:30 or by appointment
Prerequisites: One variable Calculus
- 25% Midterm 1 (Thursday October 1, 2015, In class)
Homework: I will assign homework every week and it will be due Wednesday in section. You are encouraged to work on homework problems in groups but each assignment must be written up individually.
Important dates: See the registrar's web page for drop deadlines etc.
Linear spaces: Definitions and examples of vector spaces, Subspaces, Dependence and linear independence, Bases and dimension, Inner products and orthogonality
Linear transformations and matrices: Linear transformations, null space and range, Inverses, Matrix representation of a linear transformation, Matrix multiplication, Inverse linear transformations and matrices
Differential calculus of scalar and vector valued functions: Scalar and vector functions, Limits and continuity, The derivative as a linear transformation, Partial derivatives, The gradient, The chain rule, Implicit differentiation
Determinants: A set of axioms for the determinant function, Proof of existence and uniqueness, Determinants of products of matrices, Transposed matrices, Minors and cofactors, Cramer's rule
Eigenvalues and Eigenvectors: Eigenvalues and Eigenvectors of a linear transformation, Calculation of eigenvectors and eigenvalues, Diagonalization, Similar matrices, Spectral theorem for symmetric and Hermitian linear transformations, Quadratic forms, Unitary transformations
Application of the differential calculus: Maxima, minima and saddle points, Lagrange multipliers
More Math! See http://uwdrp.weebly.com/ to find out about the directed reading program.
So you think you might want to be a math major. Check out the math major requirements. The math major is very flexible, for example for an option 1 major you only need 6 math classes beyond Math 375 while under the option 2 math major you only need 5 math classes more and 4 classes in an area of application (more details here). The page also describes an honors math and an applied math degree. If you are thinking of going to graduate school then you should plan your degree so that you have a chance to take one or more graduate classes by the end of your degree.