# Logarithms/exponents

## Key Points

• An exponent of −1−1 denotes the inverse function. That is, f−1(x)f−1(x) is the inverse of the function f(x)f(x).
• An inverse function is a function that undoes another function: If an input xx into the function ff produces an output yy, then inputting yy into the inverse function gg produces the output xx, and vice versa (i.e., f(x)=yf(x)=y, and g(y)=xg(y)=x).
• The logarithm to base bb is the inverse function of f(x)=bxf(x)=bx: logb(b)x=xlogb(b)=xlogb⁡(b)x=xlogb⁡(b)=x
• The natural logarithm ln(x)ln(x) is the inverse of the exponential function exex:b=elnbb=elnb

# Calculus

• Functions of a single variable, limit, continuity, differentiability
• Mean value theorems, indeterminate forms, L’Hospital’s rule
• Maxima and minima
• Product and chain rule
• Taylor’s series, infinite series summation/integration concepts
• Fundamental and mean value-theorems of integral calculus, evaluation of definite and improper integrals
• Beta and gamma functions
• Functions of multiple variables, limit, continuity, partial derivatives
• Basics of ordinary and partial differential equations

# Linear Algebra

• Basic properties of matrix and vectors: scalar multiplication, linear transformation, transpose, conjugate, rank, determinant
• Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse
• Special matrices: square matrix, identity matrix, triangular matrix, an idea about sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian and unitary matrices
• Matrix factorization concept/LU decomposition, Gaussian/Gauss-Jordan elimination, solving Ax=b linear system of equation
• Vector space, basis, span, orthogonality, orthonormality, linear least square
• Eigenvalues, eigenvectors, diagonalization, singular value decomposition
• Sinan Ozdemir-Principles of Data Science (Packt)

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