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MATH-207(a): Analysis IV (for SV, MT)

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Lectures in this course (33)

Convolution of Distributions and Differential Equations Log in to Mediaspace to watch this video

Explores the convolution of tempered distributions and solving differential equations using fundamental solutions.

Heat and Wave Equations: Analysis IV Log in to Mediaspace to watch this video

Covers the study of the heat and wave equations, including the process of separating variables to find solutions.

Wave Equation Separation of Variables Log in to Mediaspace to watch this video

Explores the method of separation of variables for the wave equation and the importance of Fourier coefficients in solving boundary and initial conditions.

Properties of Laplace Transform Log in to Mediaspace to watch this video

Covers the properties of the Laplace transform and its applications.

Inverse Fourier Transform: Verification and Properties Log in to Mediaspace to watch this video

Focuses on the inverse Fourier transform, verification, and properties.

Ordinary Differential Equations: Solving Examples and Special Cases Log in to Mediaspace to watch this video

Explores solving second-order ODEs with Laplace transforms and discusses special cases.

Inverse Laplace Transform and Cauchy Problem Log in to Mediaspace to watch this video

Introduces the inverse Laplace transform and the Cauchy problem for ordinary differential equations, emphasizing the importance of verifying the obtained results.

Fourier Series and Laplace Transform Log in to Mediaspace to watch this video

Covers Fourier series calculations and Laplace transform applications for periodic functions efficiently using tables and properties.

Fourier Transform and Residue Calculus Log in to Mediaspace to watch this video

Explores Fourier transform calculation and residue calculus in mathematical analysis.

Fourier Transform Interpretation and Reciprocity Theorem Log in to Mediaspace to watch this video

Explores the interpretation of Fourier transform and its application in signal modification.

Properties of Fourier Transform: Continuity, Linearity, Derivative Log in to Mediaspace to watch this video

Explores the properties of Fourier transformations, including continuity, linearity, and derivatives.

Analysis IV: Tempered Distributions and Dirac Functional Log in to Mediaspace to watch this video

Introduces tempered distributions, derivatives, and Dirac functional in analysis.

Fourier Transform of Tempered Distributions: Reflection and Translation Log in to Mediaspace to watch this video

Explores the Fourier transform of tempered distributions, emphasizing reflection and translation operations.

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