Prerequisites: One variable Calculus
Course description: http://www.math.wisc.edu/node/329
Textbook: Calculus Vol 2 - Apostol

Grades:

- 25% Midterm 1 (Thursday October 1, 2015, In class)
- 25% Midterm 2 (Tuesday November 10, 2015, In class)
- 25% Midterm 3 (Tuesday December 15, 2015, In class)
- 25% Section grade (Howework due in Section on Wednesday)

Sections TAs:
Megan Maguire - mmaguire2@math.wisc.edu http://www.math.wisc.edu/~mmaguire2
Chandan Biswas - cbiswas@math.wisc.edu

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.

Course Content:

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