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This textbook has been designed to meet the needs of B.Sc. Third Semester students of Mathematics as per Common Minimum Syllabus prescribed for Patna University and other Universities and Colleges under the recommended National Education Policy 2020 in Bihar. The book is divided into two parts. First Part: Real Analysis of the book dive deep into the world of Real Analysis with this comprehensive guide, structured precisely to enhance your understanding of the fundamental concepts. This part comprehensively covers important topics such as Algebraic and Order Properties of R, Suprema and Infima, Limit Points and Types of Sets, Limit Inferior and Limit Superior, Cauchy Sequence and Convergence, Infinite Series and Convergence, Alternating Series etc. Second Part: Ordinary Differential Equations embark on a journey through the details of Ordinary Differential Equations with this detailed textbook. This part covers the topics such as Formulation of Differential Equation, Order and Degree, Variable Separable and Homogeneous Differential Equations, First and second Order Linear and First Order Higher Degree Differential Equations, Cauchy-Euler and Legendre Equations, Laplace and Inverse Laplace Transform etc. The book enhances your mathematical skill with this essential resource for mastering real analysis and ordinary differential equations. Whether you're a student or a professional, these books are designed to provide you with a thorough understanding and practical approaches to these crucial areas of mathematics.