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Lecture
Derivatives and Convexity
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Differential Calculation: Trigonometric Derivatives
Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.
Taylor's Formula: Developments and Extrema
Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.
Convexity and Concavity: Inflection Points, Taylor Expansion, and Darboux Sums
Explores inflection points, convexity, concavity, and asymptotes in functions, with examples and applications.
Partial Derivatives: Taylor Formula
Explores partial derivatives, Taylor formula, examples, and extrema of functions.
Taylor's Formula: Developments and Applications
Explores Taylor's formula, polynomials, functions, and series applications.
Mathematical Methods for Materials Science: Integrals, Exact Differentials
Explores limits, derivation rules, integrals, and exact differentials for practical applications.
Applications of Differential Calculus
Explores applications of differential calculus, including theorems, convexity, extrema, and inflection points.
Chapter 5: Function Studies
Covers the study of functions, including limits, derivatives, and sign variations.
Function Studies: Limits, Derivatives, and Convexity
Covers the essential elements for studying a function, including its domain, behavior at boundaries, limits, derivatives, and points of inflection.
Integration: Taylor Approximation & Convex Functions
Covers Taylor approximation, convex functions, and integrable properties.