LUISS

Syllabus and Course Guidelines

Course and Exams Guidelines

Calculus

Sequences and Series

Introduction to sequences and series
The integral test and estimates of sums The comparison tests
Alternating series
Absolute convergence, ratio-and-root tests
Strategy for testing series
Power series and representation of functions
Taylor and Maclaurin series

Partial Derivatives

Functions of several variables
Limits and continuity
Polar coordinates and their properties
Partial derivatives, directional derivatives and the gradient vector
The chain rule
Maximum and minimum values
Lagrange multipliers

Integrals

Iterated integrals
Double integrals over rectangles or general regions
Integrals in polar coordinates
Triple integrals
Change of variables in multiple integrals

First Order Differential Equations

First order differential equations
Separable equations
Linear equations

Linear Algebra

Spaces and Subspaces

Bases and dimensions
Maximal sets
Abstract spaces and axiomatic approach

Eigenvectors and Eigenvalues

Diagonalization
Markov chains

Linear Operators

Linear transformations and matrix representations
Quadratic forms
Orthogonal operators
Inner product space

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