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Lecture
Derivatives of Functions
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Mechanics: Introduction and Calculus
Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.
Derivatives and Trigonometry Fundamentals
Introduces derivatives, trigonometry, and motion principles through basic and trigonometric functions differentiation.
Developing Limit Concepts
Explores developing limits using Taylor series for function approximations and understanding functions with derivatives approaching zero.
Taylor Polynomials: Calculating Limits and Derivatives
Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.
Mathematical Reminders: Derivatives, Primitives, Integrals
Covers mathematical reminders on derivatives, primitives, and integrals, including common functions and Taylor series expansions.
Implicit Functions and Taylor Polynomials
Covers implicit functions, Taylor polynomials, and tangent equations.
Calculus: Derivatives and Integrals
Covers the fundamentals of calculus, focusing on derivatives and integrals.
Taylor Polynomial: Order 2
Presents the solution to finding the second-order Taylor polynomial of a function.
Implicit Functions Theorem
Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.
Integrals of Functions
Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.