Half Range Cosine Series | f(x) = x(l − x) | Fourier Series | VTU Maths

📘 Half Range Cosine Series | Fourier Series Problem Solved

In this video, we find the cosine half range series for the function
f(x) = x(l − x)
defined over the interval 0 to l.

This is a very important and frequently asked problem from Fourier Series, especially for VTU Engineering Mathematics examinations.

🎯 What you will learn in this video
• Meaning of half range cosine series
• Why even extension is used
• Formula for half range cosine expansion
• Step-by-step evaluation of Fourier cosine coefficients
• Final cosine series for x(l − x)
• Important VTU exam observations

📌 Problem Statement
Find the cosine half range series of the function
f(x) = x(l − x)
in the interval 0 to l.

📝 Important Exam Notes
• Half range cosine series contains cosine terms only
• The function is extended as an even function
• Interval length L is taken as l
• Very common question in VTU model papers and semester exams

👨‍🎓 Useful for
• VTU Engineering students
• Mathematics I and Mathematics II
• Fourier Series and Partial Differential Equations
• Semester exams and revision

🎓 VTU SYLLABUS

✔ BMATEC301 (EC) – Maths-III
Module-1: Fourier series and practical harmonic analysis.

✔ BMATE301 (EE) – Maths-III
Module-3: Fourier series.

🆕 HIGH-WEIGHT (Most IMPORTANT)

⭐ Fourier Transform
👉    • Fourier Transform  

⭐ Fourier Sine & Cosine
👉    • Fourier sine and cosine transform  

⭐ Z Transform
👉    • Z transform  

🚨 BMATEC301 – Maths-III (EC)

📌 Concept Playlists

M1 Fourier Series & PHA
👉    • Fourier Series & Practical Harmonic Analys...  

M2 Infinite & Discrete FT
👉    • Infinite & Discrete Fourier Transforms | B...  

M3 Z Transform
👉    • Z Transforms | BMATEC301 – Module 3 | Math...  

M4 Higher Order DE
👉    • Ordinary Differential Equations of Higher ...  

M5 Curve Fitting & Regression
👉    • Curve Fitting, Correlation & Regression | ...  

📝 Model Question Papers

M1 P1 👉    • Bmatec301 module 1 Model Question Paper 1  
M1 P2 👉    • Bmatec301 module 1 Model Question Paper 2  

M2 P1 👉    • Bmatec301 module 2 Model Question Paper 1  
M2 P2 👉    • Bmatec301 module 2 Model Question Paper 2  

M3 P1 👉    • Bmatec301 module 3 Model Question Paper 1  
M3 P2 👉    • Bmatec301 module 3 Model Question Paper 2  

M4 P1 👉    • Bmatec301 module 4 Model Question Paper 1  
M4 P2 👉    • Bmatec301 module 4 Model Question Paper 2  

M5 P1 👉    • Bmatec301 module 5 Model Question Paper 1  
M5 P2 👉    • Bmatec301 module 5 Model Question Paper 2  

🚨 BMATE301 / BEE301 – Maths-III (VTU 2023–24)

📌 Concept Playlists

M1 Higher Order DE
👉    • Ordinary Differential Equations of Higher ...  

M2 Curve Fitting, Correlation, Regression
👉    • Curve Fitting, Correlation & Regression | ...  

M3 Fourier Series
👉    • Fourier Series | BMATE301/BEE301 – Module ...  

M4 Fourier & Z Transforms
👉    • Fourier Transforms & Z-Transforms | BMATE3...  

M5 Probability & Statistics
👉    • Probability Distributions & Sampling Theor...  

📝 Model Question Papers

M1 P1 👉    • Bmate301 module 1 Model Question Paper 1  
M1 P2 👉    • Bmate301 module 1 Model Question Paper 2  

M2 P1 👉    • Bmate301 module 2 Model Question Paper 1  
M2 P2 👉    • Bmate301 module 2 Model Question Paper 2  

M3 P1 👉    • Bmate301 module 3 Model Question Paper 1  
M3 P2 👉    • Bmate301 module 3 Model Question Paper 2  

M4 P1 👉    • Bmate301 module 4 Model Question Paper 1  
M4 P2 👉    • Bmate301 module 4 Model Question Paper 2  

M5 P1 👉    • Bmate301 module 5 Model Question Paper 1  
M5 P2 👉    • Bmate301 module 5 Model Question Paper 2  


📌 Study Order
High-weight → Concepts → Model Papers

👉 Telegram (VTU Maths updates)
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👉 WhatsApp (VTU Maths updates)
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