Instructor: Craig Sutton

Course on canvas.dartmouth.edu

Syllabus

Date Topic

Reading

Complete prior to Class

Notes
March 31 Course Overview; Sets & Functions; Vector Space Axioms Vector Space Axioms & SubspacesDownload Vector Space Axioms & Subspaces
April 2 Basic Properties of Vector Spaces; Subspaces Smith Chp. 2 -4

April 7

Linear Independence, dimension & bases Smith Chp. 5 & 6 Linear Independence, dimension & basesDownload Linear Independence, dimension & bases
April 9 Linear Independence, dimension & bases  Smith Chp. 5 & 6
April 14 Dimension & Bases Smith Chp. 6 & 7
April 16 Linear Transformations: Definition & Examples (abbreviated class)  Smith Chp. 8 Introduction to Linear TransformationsDownload Introduction to Linear Transformations

April 17

(x-hour)

Linear Transformations: Basic Properties, Kernel & Image, Examples Smith 8.1 - 8.4
April 21

Kernel & Image of Linear Transformations; Building Linear Transformations; Vector Space of Linear Transformations; Isomorphisms

No Class (Watch Video)

Smith 8.4 - 8.6, 9.1
April 23 NO CLASS

April 24

(x-hour)

Wrap-up Intro to Linear Transformations; Matrices & Linear Transformations Smith 91.-9.3; 10.1 -  Matrices & Linear TransformationsDownload Matrices & Linear Transformations

April 27

Exam I

6:00PM

Kemeny 007 

April 28

April 30

May 5

May 7

Linear Transformations & Matrices Smith 11.1-11.3

May 8

(X-Hour)

Smith 12.1 & 12.2

May 12

System of Linear Equations & Gaussian  Smith 13.1 & 13.2 Systems of Linear Equations & Gaussian EliminationDownload Systems of Linear Equations & Gaussian Elimination

May 14

System of Linear Equations & Gaussian Elimination ; Eigenvalues & Eigenvectors Smith 13.1 & 13.2; 14.1 & 14.2 Eigenvalues & Eigenvectors Download Eigenvalues & Eigenvectors 

May 18

Exam II

6:00 PM

Kemeny 007

May 19

Eigenvalues & Eigenvectors; The determinant & isomorphisms Smith 14.1-14.5

May 21

The Determinant & Oriented Volume (not in text); Characteristic polynomials and the eigenvalue problem; Intro to Inner Product Spaces Smith 14.1-14.5 Inner Product SpacesDownload Inner Product Spaces

May 26

Inner Product Spaces: Examples; Schwarz Inequality & triangle inequality; orthogonal sets & linear independence; Return Exam II Smith 15.1 - 15.4

May 28

Inner product Spaces
: Gram-Schmidt Process; Isometries & Riesz Representation Theorem; Self-Adjoint Maps
Smith 15.1 - 15.4; 16.1 & 16.2 Self-Adjoint Maps & the Spectral TheoremDownload Self-Adjoint Maps & the Spectral Theorem

May 30

(x-hour)

Self-Adjoint Maps & the Spectral Theorem Smith 16.1 & 16.2

June 2

Self-Adjoint Maps & the Spectral Theorem; Wrap-up Smith 16.1 & 16.2