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Department:

MATH

Course Number:

2605

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

2

Hours - Total Credit:

4

Typical Scheduling:

Not regularly scheduled

Topics in linear algebra and multivariate calculus and their applications in optimization and numerical methods, including curve fitting, interpolation, and numerical differentiation and integration.

Course Text:

Level of *Thomas' Calculus, Early Transcendentals*, by Thomas, Weir, Haas (13th Edition) Addison Wesley, Inc. 2009, [Thomas]; Web-notes: *Linear Algebra for* MATH2601; *Theory* [Notes:Th]; Web-notes: *Linear Alg. for* MATH2601; *Numerical Methods* [Notes:Num]. Web-notes

Flow chart describing textbook choices for fall 2015.

Topic Outline:

Topic | Text Sections | Lectures |
---|---|---|

Lines and planes. Scalar and vector product | 12.1-12.5 in [Thomas] | 3 |

Review of elementary linear algebra | 1-4, 8 in [Notes:Th] | 3 |

Vectorspaces, maps and their matrices, change of basis | 5 in [Notes:Th] | 6 |

Review of Gram-Schmidt, QR and least squares | 6 in [Notes:Th] | 3 |

Diagonalization, spectral theorem, SVD | 7 in [Notes:Th] | 3 |

Introduction to numerical methods | 1 in [Notes:Num] | 1 |

Partial pivoting, LU factorization | 2 in [Notes:Num] | 2 |

Householder and Givens methods for QR | 3 in [Notes:Num] | 2 |

Fixed point method | 4 in [Notes:Num] | 1 |

Iterative methods for Ax=b and eigenvalues/vectors | 4, 5 in [Notes:Num] | 3 |

Vector calculus, curves | 13.1-13.4 in [Thomas] | 3 |

Functions in several variables, partial derivative | 14.1-14.4 in [Thomas] | 3 |

Linearization of functions; gradient, Jacobian, Newton iteration. | 14.5-14.6 in [Thomas] | 3 |

Min-max problems | 14.7-14.8 in [Thomas] | 2 |

Double integral | 15.1-15.4 in [Thomas] | 4 |