TB0024 Mathematics for Technical Preparatory Year, online with meetings on campus II 12.0 credits
This course will be discontinued.
Last planned examination: Spring 2024
Decision to discontinue this course:
The course is discontinued at the expiration of the spring semester 2024 according to a decision by the Vice President for Education: V-2022-0012.
Decision date: 18/01/2022
The course is given for the last time during the spring semester 2022. Final opportunity for examination in the course will be given during the spring semester 2024.
The examination in the course is carried out as written examination. At least two examination dates per academic year are offered until and including the spring semester 2024.
For information about when examination is given, when exam registration is possible and for exam registration please refer to the KTH web. Questions are referred to the Department of Sustainable production development via service-hpu@kth.se
Content and learning outcomes
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. 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 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
Recommended prerequisites
Equipment
Literature
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- 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.
Other requirements for final grade
Final grades are based on the total number of points from both written examinations. For final grade, it is required that all examination items are passed.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
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.