Математика

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

Matrices

  • Adding 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