Fourier sine and cosine transform | Part 6

▶️ Full Playlist

👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8R_4z-ki48SWJIAXElNq-5

📘 What I Solve in This Video

In this video, we find the Fourier Sine Transform of the function

f(x) = e^(-modulus of x)

Using the obtained transform, we then deduce the value of
∫ from 0 to infinity of [sin(m x)/ (1 + x²) dx

▶️ Questions Solved in This Playlist

✔ Fourier sine and cosine transform of f(x) = x for 0 to 2
✔ Cosine transform of piecewise functions (VTU pattern)
✔ Sine and cosine transform of e^(−αx)
✔ Transforms of 2e^(−3x) + 3e^(−2x)
✔ Transform of e^(−|x|) and evaluation of standard integral
✔ Sine transform of e^(−ax)/x
✔ Inverse Fourier sine transform problems
✔ Integral equations using sine and cosine transforms
✔ Finding f(x) from given cosine transform
✔ Infinite cosine transform of e^(−x²)
✔ Self-reciprocal function under sine transform
✔ Cosine transform of e^(−ax), x e^(−ax) and standard integral
✔ Infinite cosine transform of 1/(1 + x²)
🎓 VTU Syllabus Coverage

✔ BMATE301 – Mathematics-III (EE)
Module 4: Fourier Transforms and Z-Transforms

✔ BMATEC301 – Mathematics-III (EC)
Module 2: Infinite Fourier Transforms

🚨 BMATE301 / BEE301 – Mathematics-III (VTU 2023–24) | EE Engineering

📌 Concept Playlists (Module-wise)

🔹 Module 1 – Higher Order Differential Equations
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8nhKT-E8Q52mEz9cxKGR9Z

🔹 Module 2 – Curve Fitting, Correlation & Regression
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9nwGI0eG1_MiBiOGWPv_Nz

🔹 Module 3 – Fourier Series
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-n1gfkoWEyKpMI2vO_9C6s

🔹 Module 4 – Fourier Transforms & Z-Transforms
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9__zLPC1XJkzw3av8J8qiOoi

🔹 Module 5 – Probability & Statistics
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9H07iTZ444aLxYqa1jerjz

📝 Model Question Papers – BMATE301 / BEE301

M1 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8iaRTjFpjFl3AZD693AWkh
M1 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8Zf8Ns5AIAOKgouEi_LwUa

M2 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-_DX0UIcTEzckrDGX00H0F
M2 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-wvid5ccQm27lU0Jd8jy1O

M3 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9Pp9GkOym7ZJP0ZVoOJUxM
M3 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8Gak58wHqMe1JIhitW4hIZ

M4 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-7uQvkFkev_3dDMEGZdhiW
M4 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-dFehdJsRoFMkX77xnlZ85

M5 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9__9TbsPTVjnDXXnzMuC8tsl
M5 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9__wHXoDNwUms-h9u_YGds56

🚨 BMATEC301 – Mathematics-III (VTU 2023–24) | EC Engineering

📌 Concept Playlists (Module-wise)

🔹 Module 1 – Fourier Series & Practical Harmonic Analysis
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-CnqEH2st5Qp6855UtsNjj

🔹 Module 2 – Infinite & Discrete Fourier Transforms
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9vdN85m0HlV5H1OIoWMPpF

🔹 Module 3 – Z Transforms
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_968Db9KUSXEyT8HxA-fuP8

🔹 Module 4 – Higher Order Differential Equations
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-C2b7AzvivRHjXkhyETypN

🔹 Module 5 – Curve Fitting, Correlation & Regression
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-5nG9CvvnYgzdhRgayF-iD

📝 Model Question Papers – BMATEC301 (EC)

🔸 M1 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-U0fcSyGnBg8h-u3Lf4k-y
🔸 M1 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9__1-U0NHsc38JKkLCVg0xMF

🔸 M2 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9__HNKtov9_K0z6u6guXmjcc
🔸 M2 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9HFZdbUub7fawDjOkQXUcB

🔸 M3 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-4oUG7SjotCpZVVRDyU34l
🔸 M3 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9__rV1k7ENC_5z8edT-M63xy

🔸 M4 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_94vEjINmkBJgC2TJVtKORP
🔸 M4 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9wcOKiXooibbz9cx-xvpft

🔸 M5 – P1 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_96-JBNYMQaHuTD77MOUOBL
🔸 M5 – P2 👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9-xW2ds4tYLrK6fLsd1N_T

🆕 High-Weight Playlists (Very Important)

⭐ Fourier Transform
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8qjYzY12oecM-xQ_jHLOUN

⭐ Fourier Sine & Cosine Transform
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8R_4z-ki48SWJIAXElNq-5

⭐ Z Transform
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9hLX3RcG3J0MBVjTB9KCG2

📌 Recommended Study Order
High-weight topics ➝ Concept playlists ➝ Model question papers
👉 Get all VTU Maths updates and video links on Telegram
https://t.me/vtumathswithmathematicstutor
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Видео Fourier sine and cosine transform | Part 6 канала Mathematics Tutor