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 | |
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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 |
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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 | ||
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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 |
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April 27 |
Exam I 6:00PM Kemeny 007 |
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April 28 |
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April 30 |
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May 5 |
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May 7 |
Linear Transformations & Matrices | Smith 11.1-11.3 | |
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May 8 (X-Hour) |
Smith 12.1 & 12.2 | ||
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May 12 |
System of Linear Equations & Gaussian | Smith 13.1 & 13.2 | Systems of Linear Equations & Gaussian EliminationDownload Systems of Linear Equations & Gaussian Elimination |
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May 14 |
System of Linear Equations & Gaussian Elimination ; Eigenvalues & Eigenvectors | Smith 13.1 & 13.2; 14.1 & 14.2 | Eigenvalues & Eigenvectors Download Eigenvalues & Eigenvectors |
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May 18 |
Exam II 6:00 PM Kemeny 007 |
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May 19 |
Eigenvalues & Eigenvectors; The determinant & isomorphisms | Smith 14.1-14.5 | |
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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 |
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May 26 |
Inner Product Spaces: Examples; Schwarz Inequality & triangle inequality; orthogonal sets & linear independence; Return Exam II | Smith 15.1 - 15.4 | |
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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 |
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May 30 (x-hour) |
Self-Adjoint Maps & the Spectral Theorem | Smith 16.1 & 16.2 | |
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June 2 |
Self-Adjoint Maps & the Spectral Theorem; Wrap-up | Smith 16.1 & 16.2 |