MATH-106(f): Analysis II

Lectures in this course (84)

Covers the calculation of the center of gravity for various shapes using mathematical formulas.

Explores cylindrical coordinates in R^3, emphasizing continuity and class C properties.

Explores functions, derivatives, classes in neighborhoods, and compound functions.

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Explores changing coordinates, bijective functions, Jacobian matrices, and reciprocal functions in analysis.

Covers linear approximations up to order 2 and the Hessian matrix.

Covers limited order 1 and 2 development, focusing on linearity and polynomial approximation.

Covers the Implicit Function Theorem for functions of two variables and explores graphical representations and tangent lines.

Covers the concept of differentiability, focusing on understanding limits and continuity.

Explores Taylor polynomials of orders 1 and 2 for linear function approximation around a point.

Covers extreme points, compact intervals, and optimization problems in analysis.

Covers necessary conditions for extrema and provides illustrative examples.

Covers the development of Taylor polynomials of order 2, including examples and calculations.

Explores constrained volume problems using Lagrange multipliers to find extrema under constraints in various examples.

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Explores iterated integrals, their order, properties, and applications in practical scenarios.

Explores the Intermediate Value Theorem, continuous functions, and the verification of their continuity in various examples.

Explores extreme values, constraints, Riemann's integral interpretation, and volume calculations of parallelipipeds in mathematics.

Explores the definition and properties of limits, including uniqueness and the two gendarmes theorem.

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