Fourier Series of x² | Full Solution & Deductions for VTU Exams

VTU Fourier Series | x² in −π less than or equal to x less than or equal to π | 1BMATEE301 Module 2 | 1BMATEC301 Module 1 | 1BMATME301 Module 1 In this video, you'll learn how to obtain the Fourier Series of x² in −π less than or equal to x less than or equal to π and deduce three important series — an important VTU 3rd Semester exam topic. Step-by-step solution for VTU 2025 Scheme students. ━━━━━━━━━━━━━━━━━━━━━━ APPLICABLE FOR VTU SUBJECT CODES ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATEE301 – Module 2: Fourier Series 🔹 1BMATEC301 – Module 1: Fourier Series 🔹 1BMATME301 – Module 1: Fourier Series ━━━━━━━━━━━━━━━━━━━━━━ SYLLABUS TOPIC ━━━━━━━━━━━━━━━━━━━━━━ Fourier Series – Periodic Functions, Dirichlet's Conditions, Fourier Series of Periodic Functions ━━━━━━━━━━━━━━━━━━━━━━ PROBLEM SOLVED IN THIS VIDEO ━━━━━━━━━━━━━━━━━━━━━━ Obtain the Fourier Series for the function x² in −π less than or equal to x less than or equal to π. Hence deduce that: (i) 1/1² − 1/2² + 1/3² − 1/4² + ... = π²/12 (ii) 1/1² + 1/2² + 1/3² + 1/4² + ... = π²/6 (iii) 1/1² + 1/3² + 1/5² + 1/7² + ... = π²/8 ━━━━━━━━━━━━━━━━━━━━━━ PREVIOUS VIDEO ━━━━━━━━━━━━━━━━━━━━━━ Fourier Series of f(x) = (π − x)/2    • Don't Miss This! Fourier Series f(x) = (π ...   ━━━━━━━━━━━━━━━━━━━━━━ NEXT VIDEO IN THIS SERIES ━━━━━━━━━━━━━━━━━━━━━━ Fourier Series of f(x) = x(2π − x) in 0 less than or equal to x less than or equal to 2π    • Last Minute Revision: Fourier Series of x(...   ━━━━━━━━━━━━━━━━━━━━━━ COMPLETE PLAYLISTS BY SUBJECT CODE ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATEE301: ▶️ Module 1 – Complex Analysis    • 1BMATEE301 Module 1 | Complex Analysis Pro...   ▶️ Module 2 – Fourier Series    • 1BMATEE301 Module 2 | Fourier Series Compl...   ▶️ Module 3 – Fourier Transforms & Z-Transforms    • 1BMATEE301 Module 3 | Fourier Transforms &...   ▶️ Module 4 – Probability Distributions & Sampling Theory    • 1BMATEE301 Module 4 | Probability distribu...   ▶️ Module 5 – Linear Programming Problems    • 1BMATEE301 Module 5 | Linear Programming P...   ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATEC301: ▶️ Module 1 – Fourier Series    • 1BMATEC301 Module 1 | Fourier Series Compl...   ▶️ Module 2 – Fourier Transforms    • 1BMATEC301 Module 2 | Fourier Transforms C...   ▶️ Module 3 – Z-Transforms    • 1BMATEC301 Module 3 | Z-Transforms Complet...   ▶️ Module 4 – Linear Programming Problems    • 1BMATEC301 Module 4 | Linear Programming P...   ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATME301: ▶️ Module 1 – Fourier Series    • 1BMATME301 Module 1 | Fourier Series Compl...   ▶️ Module 2 – Fourier Transform & Z-Transform    • 1BMATME301 Module 2 | Fourier Transform & ...   ▶️ Module 3 – Partial Differential Equations    • 1BMATME301 Module 3 | Partial Differential...   ▶️ Module 5 – Statistics-2    • 1BMATME301 Module 5 | Statistics-2 Complet...   ━━━━━━━━━━━━━━━━━━━━━━ WHO IS THIS FOR? ━━━━━━━━━━━━━━━━━━━━━━ BE/B.Tech 3rd Semester VTU & Autonomous students (Karnataka) Subject Codes: 1BMATEE301, 1BMATEC301, 1BMATME301 Branch: EEE, ECE, Mechanical and allied branches For Autonomous colleges – if you have this in your syllabus, study this Students preparing for VTU internals, externals & backlog exams ━━━━━━━━━━━━━━━━━━━━━━ WHY WATCH THIS VIDEO? ━━━━━━━━━━━━━━━━━━━━━━ Step-by-step VTU exam solution Exam-focused VTU & Autonomous problems Simple, easy-to-understand method Covers repeated VTU exam questions Perfect for last-minute VTU revision ━━━━━━━━━━━━━━━━━━━━━━ STAY CONNECTED ━━━━━━━━━━━━━━━━━━━━━━ 💬 WhatsApp Channel: https://whatsapp.com/channel/0029Vb6c... 📩 Telegram: https://t.me/vtumathswithmathematicst... 📸 Instagram: https://www.instagram.com/_mathematic... Subscribe & hit the bell icon so you never miss a video! If this video helped you, LIKE, SHARE with your VTU classmates, and COMMENT which problem you want next! #VTU #VTUKarnataka #1BMATEE301 #1BMATEC301 #1BMATME301 #FourierSeries #EngineeringMathematics #VTU2025 #VTU3rdSem #VTUMaths #VTU2025Scheme #VTUExams #VTUImportantQuestions #EEE #ECE #Mechanical #BETech #Autonomous