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Lecture
Ordinary differential equations
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Explores Lipschitz conditions in differential equations and their implications on solutions and properties.
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Linear differential equations
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Explores linear differential equations of order n, including homogeneous and inhomogeneous equations, solutions, and linear independence.
Existence-and-uniqueness-theorem
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Covers the existence and uniqueness theorem for Cauchy problems and explores global solutions of differential equations.
Differential Equations: Solutions and Extensions
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Covers solving differential equations, local and global solutions, and uniqueness.
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Covers characteristic polynomials, roots, and associated solutions for differential equations.
Solving Differential Equations with Bernoulli's Equation
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Covers solving differential equations using Bernoulli's equation and variable transformations to simplify linear inhomogeneous forms.
Beam Deflection: Integrating Loads to Deformation
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Explores integrating loads to deform beams, emphasizing boundary conditions and practical applications in stress analysis.
Green's Function: Theory and Applications
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Covers the theory and applications of Green's function in solving differential equations.
Differential Equations: Solutions and Uniqueness
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Explores differentiability, continuity, solutions, and uniqueness in differential equations, emphasizing well-posed problems and real-world applications.
Notion of Transfer Function
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Introduces the concept of transfer function in dynamic systems analysis.
Laplace Transform: Complex Roots and Transfer Functions
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Covers complex roots, transfer functions for nonlinear systems, and Laplace transforms in forced responses.
Solving Differential Equations: Separable Equations
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Covers the method of separation of variables to find the general solution of differential equations.
Linear Differential Equations
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Covers the resolution of linear differential equations, focusing on equations of order n and constant coefficients.
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Differential Equations: Implicit Solutions
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Explores implicit solutions for differential equations and their applications in different scenarios.
Separable Differential Equations
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Explores the theorem of existence and uniqueness for differential equations and the method to find the general solution.
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