مجموعه ویدئوهای آموزشی کلاس های درس دانشگاه MIT توسط پروفسور Gilbert Strang که مباحث ریاضی مهندسی
وعلوم محاسباتیومهندسیرا شامل می شود. در ابتدای این دوره مروری بر جبر خطی، آمار و احتمال و محاسبات عددی
می شود و سپس مباحثی نظیر معادلات دیفرانسیل، لاپلاس، سری فوریه، تبدیل فوریه گسسته و … را پوشش می دهد.
بخش دوم فیلم های آموزشی کلاس های درس دانشگاه MIT شامل ۲۹ قسمت می شود که عبارتند از:
Lecture 1 – Difference Methods for Ordinary Differential Equations
Lecture 2 – Finite Differences, Accuracy, Stability, Convergence
Lecture 3 – The One-way Wave Equation and CFL / von Neumann Stability
lecture 4 – Comparison of Methods for the Wave Equation
Lecture 5 – Second-order Wave Equation (including leapfrog)
Lecture 6 – Wave Profiles, Heat Equation / point source
lecture 7 – Finite Differences for the Heat Equation
lecture 8 – Convection-Diffusion / Conservation Laws
Lecture 9 – Conservation Laws / Analysis / Shocks
Lecture 10 – Shocks and Fans from Point Source
Lecture 11 – Level Set Method
Lecture 12 – Matrices in Difference Equations (1D, 2D, 3D)
lecture 13 – Elimination with Reordering: Sparse Matrices
lecture 14 – Financial Mathematics / Black-Scholes Equation
lecture 15 – Iterative Methods and Preconditioners
ecture 16 – General Methods for Sparse Systems
Lecture 17 – Multigrid Methods
Lecture 18 – Krylov Methods / Multigrid Continued
Lecture 19 – Conjugate Gradient Method
Lecture 20 – Fast Poisson Solver
Lecture 21 – Optimization with constraints
Lecture 22 – Weighted Least Squares
Lecture 23 – Calculus of Variations / Weak Form
Lecture 24 – Error Estimates / Projections
ecture 25 – Saddle Points / Inf-sup condition
lecture 26 – Two Squares / Equality Constraint Bu = d
lecture 27 – Regularization by Penalty Term
lecture 28 – Linear Programming and Duality
lecture 29 – Duality Puzzle / Inverse Problem / Integral Equations
Lecture 2 – Finite Differences, Accuracy, Stability, Convergence
Lecture 3 – The One-way Wave Equation and CFL / von Neumann Stability
lecture 4 – Comparison of Methods for the Wave Equation
Lecture 5 – Second-order Wave Equation (including leapfrog)
Lecture 6 – Wave Profiles, Heat Equation / point source
lecture 7 – Finite Differences for the Heat Equation
lecture 8 – Convection-Diffusion / Conservation Laws
Lecture 9 – Conservation Laws / Analysis / Shocks
Lecture 10 – Shocks and Fans from Point Source
Lecture 11 – Level Set Method
Lecture 12 – Matrices in Difference Equations (1D, 2D, 3D)
lecture 13 – Elimination with Reordering: Sparse Matrices
lecture 14 – Financial Mathematics / Black-Scholes Equation
lecture 15 – Iterative Methods and Preconditioners
ecture 16 – General Methods for Sparse Systems
Lecture 17 – Multigrid Methods
Lecture 18 – Krylov Methods / Multigrid Continued
Lecture 19 – Conjugate Gradient Method
Lecture 20 – Fast Poisson Solver
Lecture 21 – Optimization with constraints
Lecture 22 – Weighted Least Squares
Lecture 23 – Calculus of Variations / Weak Form
Lecture 24 – Error Estimates / Projections
ecture 25 – Saddle Points / Inf-sup condition
lecture 26 – Two Squares / Equality Constraint Bu = d
lecture 27 – Regularization by Penalty Term
lecture 28 – Linear Programming and Duality
lecture 29 – Duality Puzzle / Inverse Problem / Integral Equations
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