Lectures related to Twisted Partition Function: Instanton Pre-factor

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Riemann Integral: Techniques and Fundamentals

Explores Riemann integrability, the fundamental theorem of integral calculus, and various integration techniques.

Fundamental Theorem of Calculus: Integrability, Anti-derivatives, Integration by Parts

Covers integrability, anti-derivatives, and integration by parts in calculus.

Change of Variables: Examples

Explores examples of applying the change of variables formula to simplify integrals over different regions in the xy-plane.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Fundamental Theory of Integral Calculus

Covers the fundamental theory of integral calculus, integration methods, and the importance of finding primitive functions for integration.

General Mathematics I - Integration Techniques

Covers integration techniques like parts and substitution with illustrative examples.

Functions: Parametric, Integrals, Multi-variable

Covers parametric functions, integrals, and the origin of plasticity in metals.

Finite Element Method: Formulation and Approximations

Covers the strong and integral formulations, weak formulation, and approximation of temperatures.

Integration Techniques: Partial Integration and Substitution Rule

Covers integration techniques like partial integration and substitution rule, providing step-by-step explanations.

Properties of Definite Integrals: Fundamental Theorem of Analysis

Covers the properties of definite integrals and the fundamental theorem of analysis.

Integration Techniques: Change of Variable

Covers the formula for changing variables in integration and explores indefinite integrals with trigonometric substitutions.

Improper integrals: Techniques and Examples

Covers improper integrals techniques and examples, exploring convergence and absolute convergence.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Immediate Integration

Covers immediate integration methods for solving integrals directly without complex calculations.

Quantum Field Theory: Fermions and Grassmann Numbers

Explores quantum field theory, focusing on fermions and Grassmann numbers in the path integral formalism.

Complex Analysis: Derivatives and Integrals

Provides an overview of complex analysis, focusing on derivatives, integrals, and the Cauchy theorem.

Integration Techniques: Change of Variable

Covers integration techniques, focusing on the change of variable formula and exercises on integration by parts and rational functions.

Integrals in C: Curvilinear Integration

Explores curvilinear integration in the complex plane, including regular curves, properties, examples, antiderivatives, Cauchy theorem, and integrability criteria.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.