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Course Info
Instructor
Prof. Gilbert Strang
Departments
Mathematics
As Taught In
Spring 2006
Level
Graduate
Topics
Engineering
Systems Engineering
Computational Science and Engineering
Mathematics
Applied Mathematics
Differential Equations
Linear Algebra
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Lecture Videos
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18.086 | Spring 2006 | Graduate
Mathematical Methods for Engineers II
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More Info
Syllabus
Calendar
Video Lectures
Readings
Assignments
Projects
Study Materials
Related Resources
Lecture Videos
video
Lecture 1: Difference Methods for Ordinary Differential Equations
video
Lecture 2: Finite Differences, Accuracy, Stability, Convergence
video
Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability
video
Lecture 4: Comparison of Methods for the Wave Equation
video
Lecture 5: Second-order Wave Equation (including leapfrog)
video
Lecture 6: Wave Profiles, Heat Equation / point source
video
Lecture 7: Finite Differences for the Heat Equation
video
Lecture 8: Convection-Diffusion / Conservation Laws
video
Lecture 9: Conservation Laws / Analysis / Shocks
video
Lecture 10: Shocks and Fans from Point Source
video
Lecture 11: Level Set Method
video
Lecture 12: Matrices in Difference Equations (1D, 2D, 3D)
video
Lecture 13: Elimination with Reordering: Sparse Matrices
video
Lecture 14: Financial Mathematics / Black-Scholes Equation
video
Lecture 15: Iterative Methods and Preconditioners
video
Lecture 16: General Methods for Sparse Systems
video
Lecture 17: Multigrid Methods
video
Lecture 18: Krylov Methods / Multigrid Continued
video
Lecture 19: Conjugate Gradient Method
video
Lecture 20: Fast Poisson Solver
video
Lecture 21: Optimization with constraints
video
Lecture 22: Weighted Least Squares
video
Lecture 23: Calculus of Variations / Weak Form
video
Lecture 24: Error Estimates / Projections
video
Lecture 25: Saddle Points / Inf-sup condition
video
Lecture 26: Two Squares / Equality Constraint Bu = d
video
Lecture 27: Regularization by Penalty Term
video
Lecture 28: Linear Programming and Duality
video
Lecture 29: Duality Puzzle / Inverse Problem / Integral Equations
Course Info
Instructor
Prof. Gilbert Strang
Departments
Mathematics
As Taught In
Spring 2006
Level
Graduate
Topics
Engineering
Systems Engineering
Computational Science and Engineering
Mathematics
Applied Mathematics
Differential Equations
Linear Algebra
Learning Resource Types
theaters
Lecture Videos
group_work
Projects with Examples
assignment_turned_in
Problem Sets with Solutions
Download Course