• Svenska

# ML0024 Mathematics for Technical Preparatory Year II 12.0 fup

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.

### For course offering

Spring 2025 Start 14 Jan 2025 programme students

### Target group

No information inserted

### Periods

P3 (6.0 fup), P4 (6.0 fup)

14 Jan 2025
2 Jun 2025

33%

Normal Daytime

Swedish

KTH Södertälje

### Number of places

Places are not limited

## Application

### For course offering

Spring 2025 Start 14 Jan 2025 programme students

61422

## Contact

### For course offering

Spring 2025 Start 14 Jan 2025 programme students

### Examiner

No information inserted

### Course coordinator

No information inserted

### Teachers

No information inserted
Headings with content from the Course syllabus ML0024 (Spring 2021–) are denoted with an asterisk ( )

## Content and learning outcomes

• Lectures

### Course contents

Course unit A: TENA

• Trigonometry; Unit circle. Trigonometric identities. The addition and subtraction theorems. Trigonometric equations. Trigonometric graphs. Radians. Derivatives of trigonometric functions.
• Proof techniques: Direct proofs. Indirect proofs. Proofs by contradiction.
• Derivatives. Derivatives of composite functions. Product rule. Quotient rule. Relationships between change rates. Asymptots.
• Integrals; Primitive function. Integrals and areas.

Course unit B: TENB

• Number sequences; Recursion formulae. Arithmetic number sequence. Geometric number sequence.
• Complex numbers; Rectangular form. Complex conjugates. Absolute values. Arithmetic rules. The complex plane. Polar form. Exponential form. De Moivre's formula. Euler's formula.
• Polynomial equations; Polynomial long division. The factor theorem.
• More of derivatives and integrals; Repetition of basic concepts. Linear approximation. 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 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.

On completion of the course, the student should

• be able to use theorems and methods on mathematical problems, also without digital aids, and communicate the mathematical argumentation in writing.

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

## Literature and preparations

### Specific prerequisites

No information inserted

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

• Matematik 5000+ Kurs 4. (Natur & Kultur 2020). ISBN 978-91-27-45577-1.
• Matematik 5000 Kurs 5. (Natur & Kultur 2015, 2a uppl.). ISBN 9789127441699.
• Formler och tabeller. (Natur & kultur 2019, 3e uppl.). ISBN 978-91-27-45720-1.

Recommended extra book:

• Matematik 1000. (Konvergenta 2010, 4e uppl.).  ISBN 978-91-973708-5-1.

## Examination and completion

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

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

### Examination

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

Final grades are based on the total of points from both 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

No information inserted

### Ethical approach

• 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.

## Further information

### Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

### Main field of study

This course does not belong to any Main field of study.

### Education cycle

Pre-university level