# HF0024 Mathematics for Technical Preparatory Year II 12.0 credits

### Offering and execution

#### No offering selected

Select the semester and course offering above to get information from the correct course syllabus and course offering.

## Course information

### Content and learning outcomes

#### Course contents *

MODULE: TEN1

Trigonometry; the Unit circle. Trigonometric identities. Addition and the subtraction theorems Trigonometric equations. Trigonometric graphs. Radians. Derivatives of trigonometric functions.

Proof techniques; Direct proofs. Indirect proofs.

Derivatives; derivatives of composite functions. Product rule. Quotient rule. Relationships between change rates. Asymptots.

Integral; Indefinite Integral. Definite Integral and Area.

MODULE: TEN2

Number sequences; Recursion formulae. Arithmetic number sequence. Geometric number sequence.

Complex numbers; Rectangular form. Complex conjugates. Absolute value. Arithmetic rules. The complex plane. Polar form. Exponential form. De Moivre's formula. Euler's formula.

Polynomial equations; Polynomial long division. The factor theorem.

Advanced studies of derivatives and integrals; Repetition of basic concepts. Linear approximation. Change rates. Extreme values. Integrals and area calculations. Partial integration. Solids of revolution

Differential equations; differential equations of the first order. Inhomogeneous differential equations. Differential equations of the second order. Separable differential equations.

#### Intended learning outcomes *

The overall goal of the course is to give new students enough skills and understanding that is required 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.

The student should be able to formulate, analyse and solve relevant mathematical problems and communicate in writing the mathematical reasoning. The problems can be based on realistic situations and/or include handling of mathematical procedures of standard character.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

Mathematics of the upper secondary school 3b, 3c, Mathematics C or Mathematics I for Technical preparatory education.

#### Recommended prerequisites

No information inserted

#### Equipment

No information inserted

#### Literature

Kurslitteratur anges senast 6 veckor innan kursstart. Information finns på kurshemsidan http://www.kth.se/student/programhemsidafortekniskbasutbildning?programme=tbk

### Examination and completion

A, B, C, D, E, FX, F

#### Examination *

• TENA - Examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F
• TENB - Examination, 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.

#### Other requirements for final grade *

TEN1 - Written examination, 6.0 credits, grade P/F

TEN2 - Written examination, 6.0 credits, grade P/F

Final grades are based on the total of points from both written examinations.

For final grade, it is required that all examination parts are approved.

#### Opportunity to complete the requirements via supplementary examination

No information inserted

#### Opportunity to raise an approved grade via renewed examination

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### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web HF0024

#### Offered by

CBH/Biomedical Engineering and Health Systems

#### Main field of study *

No information inserted

#### Education cycle *

Pre-university level