Computational Science and Engineering I

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 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