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."
Computational Science and Engineering I
Massachusetts Institute of Technology via MIT OpenCourseWare
Overview
Syllabus
- Course Introduction
- Lecture 1: Four Special Matrices
- Recitation 1: Key Ideas of Linear Algebra
- Transcript – Lecture 1
- Transcript – Recitation 1
- Lecture 2: Differential Eqns and Difference Eqns
- Recitation 2
- Transcript – Lecture 2
- Transcript – Recitation 2
- Lecture 3: Solving a Linear System
- Recitation 3
- Transcript – Lecture 3
- Transcript – Recitation 3
- Lecture 4: Delta Function Day
- Recitation 4
- Transcript – Lecture 4
- Transcript – Recitation 4
- Lecture 5: Eigenvalues (Part 1)
- Recitation 5
- Transcript – Lecture 5
- Transcript – Recitation 5
- Lecture 6: Eigen Values (part 2) and Positive Definite (part 1)
- Recitation 6
- Transcript – Lecture 6
- Transcript – Recitation 6
- Lecture 7: Positive Definite Day
- Recitation 7
- Transcript – Lecture 7
- Transcript – Recitation 7
- Lecture 8: Springs and Masses
- Recitation 8
- Transcript – Lecture 8
- Transcript – Recitation 8
- Lecture 9: Oscillation
- Recitation 9
- Transcript – Lecture 9
- Transcript – Recitation 9
- Lecture 10: Finite Differences in Time
- Recitation 10
- Transcript – Lecture 10
- Transcript – Recitation 10
- Lecture 11: Least Squares (part 2)
- Recitation 11
- Transcript – Lecture 11
- Transcript – Recitation 11
- Lecture 12: Graphs and Networks
- Recitation 12
- Transcript – Lecture 12
- Transcript – Recitation 12
- Lecture 13: Kirchhoff's Current Law
- Recitation 13
- Transcript – Lecture 13
- Transcript – Recitation 13
- Lecture 14: Exam Review
- Transcript – Lecture 14
- Lecture 15: Trusses and A^(T)CA
- Transcript – Lecture 15
- Lecture 16: Trusses (part 2)
- Transcript – Lecture 16
- Lecture 17: Finite Elements in 1D (part 1)
- Transcript – Lecture 17
- Lecture 18: Finite Elements in 1D (part 2)
- Transcript – Lecture 18
- Lecture 19: Quadratic/Cubic Elements
- Transcript – Lecture 19
- Lecture 20: Element Matrices; 4th Order Bending Equations
- Transcript – Lecture 20
- Lecture 21: Boundary Conditions, Splines, Gradient, Divergence
- Transcript – Lecture 21
- Lecture 22: Gradient and Divergence
- Transcript – Lecture 22
- Lecture 23: Laplace's Equation
- Transcript – Lecture 23
- Lecture 24: Laplace's Equation (part 2)
- Transcript – Lecture 24
- Lecture 25: Fast Poisson Solver (part 1)
- Transcript – Lecture 25
- Lecture 26: Fast Poisson Solver (part 2); Finite Elements in 2D
- Transcript – Lecture 26
- Lecture 27: Finite Elements in 2D (part 2)
- Transcript – Lecture 27
- Lecture 28: Fourier Series (part 1)
- Transcript – Lecture 28
- Lecture 29: Fourier Series (part 2)
- Transcript – Lecture 29
- Lecture 30: Discrete Fourier Series
- Transcript – Lecture 30
- Lecture 31: Fast Fourier Transform, Convolution
- Transcript – Lecture 31
- Lecture 32: Convolution (part 2), Filtering
- Transcript – Lecture 32
- Lecture 33: Filters, Fourier Integral Transform
- Transcript – Lecture 33
- Lecture 34: Fourier Integral Transform (part 2)
- Transcript – Lecture 34
- Lecture 35: Convolution Equations: Deconvolution
- Transcript – Lecture 35
- Lecture 36: Sampling Theorem
- Transcript – Lecture 36
Taught by
Prof. Gilbert Strang
