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Lecture
Laplace Method: Asymptotic Analysis
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Related lectures (32)
Limit Calculations Applications
MOOC: Analysis I
MOOC: Analysis I (part 6) : Study of functions, limited developments
Demonstrates efficient limit calculations using Taylor expansions and basic algebraic operations.
Laplace's Method: Exercises
Covers exercises related to Laplace's method and complex analysis.
Holomorphic Functions: Taylor Series Expansion
Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.
Composition of Taylor Expansions
Covers the computation of Taylor expansions composition up to order 4.
Developing Cosine Composition
MOOC: Analysis I
MOOC: Analysis I (part 6) : Study of functions, limited developments
Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.
Taylor Polynomials and Remainders
MOOC: Analysis I
MOOC: Analysis I (part 6) : Study of functions, limited developments
Explores Taylor polynomials, remainders, and various function expansions around a point.
Algebraic Operations and Taylor Expansions
Explores algebraic operations on Taylor expansions and the development of various functions.
Taylor Expansion
Covers Taylor expansion around 0, derivatives, integrals, and series in Analyse 1 2018 exam.
Taylor Expansion: Derivation and Application
Covers the derivation of a function near a critical point.
Taylor Expansions: First Order
MOOC: Introduction to optimization on smooth manifolds: first order methods
Explores Taylor expansions of first order in optimization on manifolds.
Gamma Function and Stirling's Approximation: Mathematical Methods
Discusses the gamma function, its properties, and Stirling's approximation for large factorials, emphasizing their significance in mathematical methods for physics.
Developing Limited Functions
MOOC: Warm-up for EPFL
Covers the concept of developing limited functions and includes physical examples.
Gradient and Hessian of Pullback
Explores the connection between Riemannian and Euclidean gradients and Hessians at critical points.
Derivatives of Functions
MOOC: Warm-up for EPFL
Introduces derivatives, composition of functions, Taylor expansion, velocity, acceleration, and temporal derivative notation in physics.
Approximation of Functions by Taylor Polynomials
Explores the theory and application of Taylor polynomials for function approximation and limit calculations.
Taylor Series: Derivatives and Integrals
Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.
Functions of Class Cn: Theorem 2
MOOC: Analysis I
MOOC: Analysis I (part 6) : Study of functions, limited developments
Focuses on Theorem 2 for functions of class Cn and their Taylor expansion around a.
Energy Efficiency in Buildings
Explores optimizing energy use in buildings through solar panels and solving nonlinear equations efficiently.
Functions Extension and Taylor Expansion
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Covers functions extension and Taylor expansion, exploring mathematical concepts in depth.
Laurent Series and Convergence: Complex Analysis Fundamentals
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Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.
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