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Real Numbers and Functions
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Related lectures (51)
Analyse I: Summary
Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.
Analysis I Exam Solutions
Provides solutions to an Analysis I exam, covering various topics.
Real Analysis: Summary
Covers real numbers, sequences, series, functions, limits, derivatives, Taylor series, integrals, and more.
Advanced Analysis: Differential Equations Overview
Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.
Improper Integrals: Convergence and Comparison
Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.
Mathematics: Analysis and Algebra Overview
Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.
Convex Functions: Theorems and Examples
Discusses the theorems on convex functions and provides examples for better understanding.
Fundamental Analysis: Integrals and Primitives
Covers the fundamental concepts of integrals and primitives, including properties and examples.
Taylor Series: Derivatives and Integrals
Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.
Bernoulli's Hospital Rule
MOOC: Analysis I
MOOC: Analysis I (part 6) : Study of functions, limited developments
Covers the statement of the Bernoulli's Hospital Rule and its application.
Taylor Polynomial: Order 2
Presents the solution to finding the second-order Taylor polynomial of a function.
Calculus: Derivatives and Integrals
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Covers the fundamentals of calculus, focusing on derivatives and integrals.
Analysis I: Functions of a Variable
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Introduces fundamental concepts of Analysis I, focusing on functions of a variable and numerical sequences.
Introduction to Mathematics for Engineers
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Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.
Integration by Substitution
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Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.
Implicit Functions Theorem
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Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.
Laplacian in Polar and Spherical Coordinates: Derivatives
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Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.
Taylor Polynomials: Approximating Functions in Multiple Variables
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Covers Taylor polynomials and their role in approximating functions in multiple variables.
Complex Numbers: Operations and Polar Form
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Explores complex numbers, operations, absolute value, and polar form, along with the analysis and graphic representation of complex numbers.
Functions: Differentials, Taylor Expansions, Integrals
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Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.
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