Fundamentals of Linear Algebra for University Students
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Linear algebra isn’t just about calculations, it’s a powerful lens to see the world. This foundational course introduces university students to the core principles of linear algebra, offering a comprehensive exploration of fundamental concepts and applications. Designed to cultivate a strong mathematical framework, the curriculum spans key topics essential for understanding vector spaces, matrices, tensors and linear transformations. Students will delve into the mathematical structures that underpin these concepts, gaining proficiency in operations such as addition, multiplication, and inversion of matrices. The course places a significant emphasis on practical problem-solving, thus guiding students through the application of linear algebra in real-world scenarios, including computer graphics, optimization, data science and data analysis.
The exploration of eigenvalues and eigenvectors forms a crucial component of the course, providing students with a deeper understanding of diagonalization and its diverse applications across disciplines. Through a combination of theoretical instruction and hands-on exercises, students will be able to develop analytical skills and critical thinking that allows them to approach complex problems with confidence.
Upon completion, students will possess a solid foundation in linear algebra, equipping them for advanced coursework in mathematics, computer science, physics, engineering, and various other fields where linear algebra plays a pivotal role.
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Scalar Fields vs. Vector Fields -
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Scalar Field Gradient - Introduction
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Scalar Field Gradient - Example
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Scalar Field Laplacian - Introduction
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Scalar Field Laplacian - Example
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Vector Filed Divergence - Introduction
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Vector Filed Divergence - Example
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Vector Filed Curl - Introduction
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Vector Filed Curl - Example
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Vector Field Laplacian - Introduction
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Vector Field Laplacian - Example
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Matrix Operations - Introduction
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Matrix Trace - Introduction
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Matrix Trace - Example 1
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Matrix Trace - Example 2
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Matrix Transpose - Introduction
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Matrix Transpose - Example
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Matrix Complex Conjugate - Introduction
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Matrix Complex Conjugate - Example
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Matrix Hermitian Complex Conjugate - Introduction
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Matrix Hermitian Complex Conjugate - Example
