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Integral Calculation
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Related lectures (40)
Exponential Functions: Important Examples
MOOC: Trigonometric, Logarithmic and Exponential Functions
Explores important examples of exponential functions and their limits, including lim (1 + ²)² = 0 and lim ex as x→∞.
Real Numbers and Functions
Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.
Derivatives and Approximations: Logarithmic Functions
Explores derivatives and approximations, focusing on logarithmic functions and their properties.
Definite Integrals: Properties and Interpretation
Covers the calculation of minimum points and the concept of definite integrals.
Gradient Analysis
Explores the calculation and analysis of gradients for various functions.
Rolle's Theorem: Applications and Examples
Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.
Improper Integrals: Convergence and Comparison
Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.
Derivatives: Chain Rule and Composed Functions
Covers derivatives, chain rule, and composed functions with examples and applications.
Introduction to Mathematical Concepts
Introduces fundamental mathematical concepts and their applications in equations and inequalities.
Convexity and Concavity
Covers the concepts of convexity and concavity in functions with examples.
Exact Linearization: Earth Dynamics and Stabilization
Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.
Integrals of Functions
MOOC: Warm-up for EPFL
Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.
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.
Applications of Theorems
Demonstrates the practical application of theorems in calculus through two clever examples.
Tangent to Graph of a Function
Explores finding the equation of the tangent line to a function's graph at a point.
Derivatives and Continuity in Mathematics
Covers derivatives, continuity, Rolle's Theorem, function examples, and extrema.
Derivative of an Integral with Parameter
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Covers deriving integrals with parameters and their derivatives, including special cases and proofs.
Differential Calculation: Trigonometric Derivatives
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Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.
Derivative of an Integral
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Covers the derivative of an integral dependent on a parameter and its fundamental properties.
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.
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