MFC-3-Unit-II-41-What is Linear Differential Equation

MFC-III: Mathematical Foundation for Computing-III (Video Series) Welcome to the Mathematical Foundation of Computing - III (MFC-III) video series, meticulously designed for Third / Fourth Semester Engineering Students of MIT School of Computing, MIT Art Design and Technology University, Pune. This playlist is your ultimate resource for mastering mathematical concepts essential for computational applications, as outlined in the syllabus for the course 23ASH1109. Each video is thoughtfully created to ensure learning is simple, efficient, and directly aligned with the course objectives. Key Features of This Playlist: 1. Short and Engaging Videos: Each video is under 20 minutes, ensuring focused and effective learning. 2. Exam-Centric Content: Includes detailed solutions to previous years' questions to help you prepare confidently for assessments. 3. Simplified Explanations: Delivered in very simple English, making it easy for students of all backgrounds to grasp the material. 4. Formula and Concept Integration: Important definitions and formulas are explained and applied while solving problems. 5. Interactive Chapter-Wise MCQ Tests: After completing each chapter, take quizzes to test your understanding and reinforce key concepts. What You’ll Learn: Unit-I: Linear Algebra-III : Eigen Values and Eigen Vectors, Diagonalization of Matrices, LU decomposition and Cholesky Method, Inner Product Space, Principal Component Analysis. Unit-II: Differential Equations: Order and Degree, Formation of Ordinary Differential Equation, Solution of Differential Equations: Variable Separable Form, Exact Differential Equations, Reducible to Exact Differential Equations, Linear Differential Equation, Reducible to Linear Differential Equation, Bernoulli’s Differential Equations, Growth and Decay of some Real-life Problems. Unit-III: Partial Differentiation and Applications : Partial Derivatives: Introduction of Partial Derivatives, Homogeneous Functions, Euler’s Theorem, Implicit Functions, Composite Functions, Total derivatives, Change of Independent Variables. Application of Partial Derivatives: Jacobian, Maxima and Minima of function of two Variables, Lagrange’s method of Undetermined Multipliers. Unit-IV: Integral Calculus and Tracing of Curves: Differentiation Under Integral Sign, Error Function, Tracing of Cartesian, Parametric and Polar Curves, Rectification of Curves. Unit-V: Multiple Integral and its Applications: Introduction of Double Integrals, Change of Order of Double Integrals, Change of Variables, Triple Integrals, Applications of Multiple integral to find Area and Volume. Why This Playlist? This series simplifies complex mathematical concepts and provides students with tools for problem-solving in engineering fields. The engaging format ensures you stay motivated while gaining a deep understanding of each topic. Whether you’re preparing for exams, working on projects, or exploring the mathematical foundations of computing, this playlist is the perfect guide.