06-Unit-I-SPPU-EM-I-Taylor's Series with Examples

Engineering Mathematics Made Simple | Engineering Mathematics-I Playlist
Welcome to the ultimate learning resource for Engineering Mathematics-I! This playlist covers all essential topics from the curriculum, specifically tailored for first-year engineering students. Whether you're preparing for exams or strengthening your mathematical foundation, this series is for you.
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What Makes This Playlist Unique?
✅ Concise Videos: Each lecture is under 20 minutes, making learning efficient and manageable.
✅ Exam-Focused: Includes solutions to previous years’ examination questions.
✅ Simplified Learning: Definitions and key concepts are explained clearly during problem-solving sessions.
✅ Easy English: We use simple and accessible language to ensure everyone can follow along.
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Topics Covered
Unit I: Single Variable Calculus
• Rolle’s Theorem & Mean Value Theorems
• Taylor's and Maclaurin's Series
• Indeterminate Forms and L'Hôpital's Rule
• Fourier Series and Harmonic Analysis
Unit II: Multivariable Calculus – Partial Differentiation
• Functions of Several Variables
• Limits, Continuity, and Partial Derivatives
• Euler's Theorem on Homogeneous Functions
• Total Derivatives and Change of Variables
Unit III: Applications of Partial Differentiation
• Jacobian and Its Applications
• Errors and Approximations
• Maxima and Minima of Two Variables
• Lagrange's Method of Undetermined Multipliers
Unit IV: Linear Algebra – Matrices and System of Linear Equations
• Rank of a Matrix
• Linear Dependence and Independence
• Linear and Orthogonal Transformations
Unit V: Linear Algebra – Eigenvalues, Eigenvectors, and Diagonalization
• Eigenvalues and Eigenvectors
• Cayley-Hamilton Theorem
• Diagonalization and Quadratic Forms
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Who Should Watch This Playlist?
• First-Year Engineering Students: Aligns perfectly with your syllabus and helps ace your exams.
• Self-Learners: Build a strong mathematical foundation at your own pace.
• Engineering Aspirants: A must-watch for students aiming to master engineering concepts.
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Resources & References
📚 Based on textbooks such as Higher Engineering Mathematics by B.S. Grewal and Thomas’ Calculus by George B. Thomas.