Linear Algebra and Calculus

Course Objective

Upon completion of the course, students will:

• Demonstrate a solid comprehension of fundamental concepts in Linear Algebra and Calculus, including vectors, matrices, linear systems, differentiation, and integration (Knowledge and Understanding).
• Apply mathematical techniques to solve basic exercises and problems across different levels of complexity within Linear Algebra and Calculus, such as solving linear systems or diagonalization, showcasing proficiency in computations and problem-solving strategies (Applying Knowledge and Understanding).
• Engage in rigorous mathematical reasoning by providing proofs of statements and theorems, and by explaining underlying concepts and principles (Applying Knowledge and Understanding; Making Judgments).
• Develop the ability to articulate mathematical solutions and explanations effectively, engaging clear communication of mathematical concepts (Communication Skills).
• Cultivate learning skills necessary for further study in mathematics and AI, including the ability to independently explore advanced topics, identify areas for improvement, and pursue self-directed learning opportunities (Learning Skills).

Course Content

Calculus:

• Limits
• Derivatives
• Partial derivatives
• Gradients
• Integrals

Linear Algebra:

• Linear systems of equations
• Row reduction
• Linear maps
• Matrix and vectors operations
• Vector spaces
• Determinants
• Eigenvalues, eigenvectors and diagonalization
• Inner product, orthogonalization and Gram Schmidt

Teaching Methods

Theory lectures and exercise tutorials each week.

Type of  Assessment

At least one final exam at the end of the course. Possibility of a midterm or other assessments.