#### About

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.

Note: This course was previously called "Mathematical Methods for Engineers I".

**Course Homepage** 18.085 Computational Science and Engineering I Fall 2007

**Course features at MIT OpenCourseWare page**:
*Syllabus
*Assignments
*Exams
*Study Materials
*Related Resources
*Download Course Materials

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## Uploaded videos:

### Lecture 1: Positive definite matrices K = A'CA

Nov 24, 2008

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26360 Views

### Lecture 2: One-dimensional applications: A = difference matrix

Nov 24, 2008

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13639 Views

### Lecture 3: Network applications: A = incidence matrix

Nov 24, 2008

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10671 Views

### Lecture 4: Applications to linear estimation: least squares

Nov 24, 2008

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17841 Views

### Lecture 5: Applications to dynamics: eigenvalues of K, solution of Mu'' + Ku = F...

Nov 24, 2008

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7928 Views

### Lecture 6: Underlying theory: applied linear algebra

Nov 24, 2008

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### Lecture 7: Discrete vs. continuous: differences and derivatives

Nov 24, 2008

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### Lecture 8: Applications to boundary value problems: Laplace equation

Nov 24, 2008

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### Lecture 9: Solutions of Laplace equation: complex variables

Nov 24, 2008

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10876 Views

### Lecture 10: Delta function and Green's function

Nov 24, 2008

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13036 Views

### Lecture 11: Initial value problems: wave equation and heat equation

Nov 24, 2008

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8056 Views

### Lecture 12: Solutions of initial value problems: eigenfunctions

Nov 24, 2008

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### Lecture 13: Numerical linear algebra: orthogonalization and A = QR

Nov 24, 2008

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10910 Views

### Lecture 14: Numerical linear algebra: SVD and applications

Nov 24, 2008

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14235 Views

### Lecture 15: Numerical methods in estimation: recursive least squares and covaria...

Nov 24, 2008

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### Lecture 16: Dynamic estimation: Kalman filter and square root filter

Nov 24, 2008

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### Lecture 17: Finite difference methods: equilibrium problems

Nov 24, 2008

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6757 Views

### Lecture 18: Finite difference methods: stability and convergence

Nov 24, 2008

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### Lecture 19: Optimization and minimum principles: Euler equation

Nov 24, 2008

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### Lecture 20: Finite element method: equilibrium equations

Nov 24, 2008

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### Lecture 21: Spectral method: dynamic equations

Nov 24, 2008

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7862 Views

### Lecture 22: Fourier expansions and convolution

Nov 24, 2008

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9432 Views

### Lecture 23: Fast fourier transform and circulant matrices

Nov 24, 2008

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13453 Views

### Lecture 24: Discrete filters: lowpass and highpass

Nov 24, 2008

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10868 Views

### Lecture 25: Filters in the time and frequency domain

Nov 24, 2008

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9757 Views

### Lecture 26: Filter banks and perfect reconstruction

Nov 24, 2008

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9950 Views

### Lecture 27: Multiresolution, wavelet transform and scaling function

Nov 24, 2008

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30117 Views

### Lecture 28: Splines and orthogonal wavelets: Daubechies construction

Nov 24, 2008

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11891 Views

### Lecture 29: Applications in signal and image processing: compression

Nov 24, 2008

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12301 Views

### Lecture 30: Network flows and combinatorics: max flow = min cut

Nov 24, 2008

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12624 Views

### Lecture 31: Simplex method in linear programming

Nov 24, 2008

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21364 Views

### Lecture 32: Nonlinear optimization: algorithms and theory

Nov 24, 2008

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12296 Views