Finite Element Method: Quadratic Elements

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Linear Differential Equations

Explores linear differential equations of the second order and the construction of linearly independent solutions.

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Covers the basics of ray tracing, including ray generation, intersection with geometric shapes, and distance calculations to planes, setting the foundation for implementing a ray tracer.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Knot Theory: The Quadratic Linking Degree

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

Linearly Independent Solutions and Quadratic Equations

Explores linearly independent solutions in quadratic equations and the role of constants in trigonometric solutions.

Quadratic Forms: Definitions, Examples

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

Numerical Analysis: Nonlinear Equations

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

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Finite Element Method: Applications and Formulations

Explores the application and formulation of the finite element method in solving various engineering problems.