#advanced
10 concepts
Concepts
Complex Numbers
A number combining real and imaginary parts, written as a + bi where i² = -1.
Exponential Function
A function where the base is a positive constant and the exponent is the variable.
Logarithm
The inverse of exponential function, indicating how many times a base must be multiplied to get a number.
Series
The sum of terms in a sequence, which can be finite or infinite.
Conic Sections
Curves formed by intersecting a cone with a plane: circle, ellipse, parabola, and hyperbola.
Taylor Series
A series expansion that represents a function as an infinite polynomial.
Eigenvalues and Eigenvectors
For matrix A, λ is an eigenvalue and v is an eigenvector if Av = λv.
Linear Transformation
A function between vector spaces that preserves addition and scalar multiplication.
Vector Space
A set with vector addition and scalar multiplication satisfying specific axioms.
Basis and Dimension
A basis is a set of linearly independent vectors that span the space. Dimension is the number of basis vectors.