# Mathematics

MATH 42’s mathematical capabilities are being enhanced and expanded permanently — the mathematics coverage described below represents the coverage on September 1st 2016.

Should you have special mathematical requirements, which are not listed below, please ask us about it with a given example.

## Step-by-Step Solutions

### Term Transformation

• Simplyfing and expanding
• Factorization (Factoring out, application of the binomial formulas)
• Transforming powers and roots
• Adding fractions, multiplying fractions, reducing fractions, expanding fractions
• Computing the gcd and the lcm
• Trigonometric transformations (Is being enhanced)
• Logarithmic transformations (Is being enhanced)

### Functions

• Roots
• Y-axis intersection
• Domain of definition
• Extremes (Maximums, Minimums)
• Inflexion points
• Curve sketching
• Derivatives:
• factor rule, sum rule,
• product rule, quotient rule
• chain rule
• Integration:
• Fundamental Integrals
• integrate by substitution
• integrate by parts
• partial fraction decomposition

### Equations

• Linear equations
• Completing the square, quadratic formula
• pq-formula
• Special equations of higher degree
• Linear systems of equations
• Non-linear system of equations

### Matrices

• Multiplying matrices
• Transposing matrices
• Inverting matrices
• Computing determinants
• Computing characteristic polynomials
• Computing eigenvalues
• Computing eigenspaces
• Computing kernels
• Computing ranks
• Cross-product
• Gaussian elimination

## Exercises

The Assessment Center of MATH 42 provides exercises to the 3 following topics:

• Transformation of expressions
• Functions
• Equations

## Graphical Display

• Graphical curve sketching
• Domain, asymptotes
• roots
• intersection with the y-axis
• extremes
• inflexion points
• Derivatives
• Asymptotical functions
• Intersections between functions
• Deskewing of the graph