General Surfaces: Definition and Examples

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Two-loop Computations: External Legs and Internal Propagators

Covers the computation of two-loop diagrams with external legs and internal propagators.

Geometric Examples: Triangles and Functions

Explores geometric examples of triangles and functions, demonstrating the variation of x and y within defined ranges.

Calculating Integrals in Multiple Dimensions

Explores the method of calculating integrals in multiple dimensions using a step-by-step approach and examples.

Generalized Integrals: Definitions and Criteria

Covers the definition of generalized integrals and comparison theorems for convergence.

Properties of Integrals

Covers properties of integrals and differentiation, focusing on exercise solutions and function behavior.

Surface Integrals: Orientation and Computation

Explores orientable surfaces, scalar field integrals, and practical applications through examples with a sphere and a cone.

Mathematical Complements: df or δf

Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Generalized Integrals: Bounded Interval

Introduces generalized integrals on a bounded interval, discussing convergence, divergence, comparison criteria, variable substitution, and corollaries.

Solutions to QCM 1-3

Covers the solutions to multiple-choice questions 1 to 3.