Linear Algebra and Differential Equations

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This textbook provides a unified introduction to two foundational areas of mathematics essential for students in science, engineering, and applied fields. Beginning with the core concepts of linear algebra-vector spaces, matrices, linear transformations, eigenvalues, and eigenvectors-the book builds the structural tools needed to understand and solve systems of equations. It then develops differential equations from first principles, covering first-order equations, higher-order linear equations, systems of differential equations, and qualitative analysis of solutions. Throughout the text, linear algebra and differential equations are integrated to show how the two subjects reinforce each other, especially in modeling real-world systems. Designed for a one-or two-semester course, the book emphasizes conceptual understanding, computational techniques, and practical applications, supported by examples, exercises, and clear explanations.