Month: May 2024

Multivariable Calculus Notes for BS

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Multivariable calculus is a branch of calculus that extends the concepts of differential and integral calculus to functions of more than one variable. Functions of Several Variables: Partial Derivatives: Gradient: Directional Derivative: Tangent Plane and Normal Line: Double and Triple Integrals: Change of Variables in Multiple Integrals: Line Integrals: Surface Integrals: Vector Fields: A vector … Read more

Spectral Methods Notes for BS/MS

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Spectral methods (SM) are numerical techniques used to approximate solutions to partial differential equations (PDEs) and other mathematical problems. These methods rely on the properties of the spectral decomposition of certain operators, such as the Laplacian operator, to efficiently compute approximate solutions. Spectral Decomposition: Fourier Series: Chebyshev Polynomials: Galerkin Method: Collocation Method: Spectral Accuracy: Applications: … Read more