MATH-106(e): Analysis II

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Lectures in this course (103)

Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.

Fubini Theorem for Closed Sets

Explains the Fubini theorem for closed sets and volume calculations.

Volume Calculation in R^3

Covers the calculation of volumes of subsets in R^3 using double integrals.

Fubini Theorem: Double and Triple Integrals

Explores the Fubini theorem for double and triple integrals, focusing on regular domains and order of integration.

Change of Variables in Multiple Integrals

Explores changing variables in multiple integrals, with a focus on polar transformations and their applications in calculating areas.

Methods of Integration of Functions in Several Variables

Explores methods of integrating functions in several variables, emphasizing the importance of regular areas and changing variables to polar coordinates.

Spherical Coordinates: Integration and Change of Variables

Covers the integration of functions in multiple variables, focusing on spherical coordinates and examples of change of variables.

Cylindrical and Spherical Coordinates

Covers the integration of functions of multiple variables using cylindrical and spherical coordinates.

Multiple Integrals: Change of Variables and Polar Coordinates

Covers multiple integrals, change of variables to polar coordinates, and area calculations.

Differential Equations: Implicit Function Theorem

Explores the implicit function theorem and Taylor polynomials in differential equations.

Limits of Functions in R^n

Explores limits of functions in R^n and the importance of understanding derivatives in multiple dimensions.

Taylor Polynomials and Extrema

Explores Taylor polynomials, extrema, Lagrange multipliers, and critical points in multivariable calculus.

Taylor Polynomials and Function Properties

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Methods of Demonstrations: Examples and Solutions

Covers examples and solutions on methods of demonstrations, properties of subsets, continuity criteria, and propositions.

Linear Differential Equations

Explores linear differential equations, superposition of solutions, and verification methods.

Linearly Independent Solutions and Quadratic Equations

Explores linearly independent solutions in quadratic equations and the role of constants in trigonometric solutions.

Linear Differential Equations: Solution Methods

Covers solution methods for linear differential equations of second order with constant coefficients.

Open Subsets and Compact Sets

Discusses open subsets, compact sets, and methods for demonstrating openness in a space.

Limits of Functions

Discusses the concept of limits of functions and the conditions for their existence.

Limits of Functions

Explores the existence of limits of functions under specific conditions.

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