TB0021 Mathematics for Technical Preparatory Year, online with meetings on campus I 12.0 credits

COURSE UNIT A: TENA

• Vectors; Arithmetical operations. Components of vectors. Coordinates. Vector length.
• Algebraic expressions and algebraic methods; Implication and equivalence. Polynomials. Exponentiations. Square roots. Absolute values. Equations. Factorial polynoms. Rational expressions. Linear equation systems. Linear inequalities.
• Functions; Linear functions. Direct proportionality. Quadratic functions. Exponential functions.
• Right-angle trigonometry.
• Uniformity; Similar triangles. Intercept theorem. Area and volume scale factors.

COURSE UNIT B: TENB

• Exponential functions.
• Logarithms Logarithm laws. Natural logarithms.
• Derivatives. Change rates. Limits. The definition of the derivative. Derivation rules.
• Derivatives and graphs; Extreme points and extreme values. Increasing and decreasing. Maximum and minimum values. Second derivative.
• The equation of the circle.
• Area theorem. Law of sines. Law of cosines.

The overall goal of the course is to give new students enough skills and understanding to be able to follow the mathematical courses that are included in the 3- and 5-year engineering programs. The courses should also contribute to a good introduction to higher education.

After passing the course, the students should be able to:

• use theorems and methods on mathematical problems and communicate the mathematical argumentation in writing.

’Mathematical’ refers to the part of the mathematics that is included in the course content.

If the course is discontinued, students may request to be examined during the following two academic years.

• TENA - Written exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F
• TENB - Written exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Final grades are based on the total number of points from both written examinations. For final grade, it is required that all examination parts are passed.

Monica Kemvall

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.