Math 2130

Syllabus MATH 2130 / Fall 2020

This is an attempt. Things may change as we go.

August

DateTopics
Aug. 24First definitions: linear systems, solutions, classification of linear systems;
Solving linear systems: the basic rules, equivalent linear systems
Aug. 26Matrix encoding: LS as a matrix, echelon form of matrices, row reduction to echelon form.
Aug. 28The row reduction algorithm
Aug 31Vector equations

September

DateTopics
Sep. 02The matrix equation Ax=b
Sep. 04Solution sets
Sep. 07Labor day (no class)
Sep. 09Linear independence – I
Sep. 11Linear independence – II
Sep. 14Introduction to linear transformations
Sep. 16The (standard) matrix of a linear transformation; or the matrix of a linear transformation according to the canonical basis
Sep. 18Matrix operations
Sep. 21The inverse of a matrix
Sep. 23Subspaces of \mathbb{R}^n – I
Sep. 25Subspaces of \mathbb{R}^n – II
Sep. 28Midterm I review
Sep. 30Midterm I

October

DateTopics
Oct. 02Dimension and Rank
Oct. 05 Introduction to Determinants
Oct. 07Properties of Determinants
Oct. 09Cramer’s Rule, Volume and Linear Transformations
Oct. 12Vector Spaces and Subspaces
Oct. 14Null Spaces, Column Spaces – I
Oct. 16Null Spaces, Column Spaces – II
Oct. 19Linearly Independent sets; Bases – I
Oct. 21Linearly Independent sets; Bases – I
Oct. 23Coordinate Systems
Oct. 26Coordinate Systems
Oct. 28The Dimension of a vector space
Oct. 30Rank

November

DateTopics
Nov. 02Change of Basis – I
Nov. 04Change of Basis – II
Nov. 06Eigenvectors and Eigenvalues
Nov. 09The Characteristic equation
Nov. 11Midterm II Review
Nov. 13Midterm II
Nov. 16Diagonalization
Nov. 18Eigenvectors and Linear Transformations – I
Nov. 20Eigenvectors and Linear Transformations – II
Nov. 23Inner Product, Length and Orthogonality
Nov. 25Orthogonal sets
Nov. 27Thanksgiving (no class)
Nov. 30Orthogonal Projections

December

DateTopics
Dec. 02The Gram-Schmidt Process
Dec. 04Least-Square problems
Dec. 07Final Exam Review
Dec. 09Final Exam

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