- Systems of linear equations. Gaussian elimination.
- Vectors, vector addition, scalar multiplication, dot product, cross product, and vector projections.
- Lines and planes in 3D space.
- Determinants.
- Matrices and matrix algebra. Matrix inverse.
- Functions and their graphs.
- Limits and continuity: limits, one-sided limits, limits at infinity, continuity.
- Differentiation: Derivatives, tangent lines and normal lines, differentiation rules, higher-order derivatives.
- Applications to behavior of functions: curve sketching, maxima and minima.
- Basic integration techniques and applications.
HF1901 Mathematics I 7.5 credits
Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus HF1901 (Autumn 2009–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
Upon completing this course students should be able to:
- Solve and apply systems of linear equations;
- Define, calculate and apply vector addition, scalar multiplication, dot product, vector product, and vector projections;
- Solve problems that include lines and planes in 3D space;
- Perform the matrix operations of addition, scalar multiplication, and multiplication, and find the transpose and inverse of a matrix;
- Demonstrate an understanding of the fundamental concepts of analysis: limits, continuity, differentiability and integrability of real-valued functions of a single real variable;
- Use the algebra of limits, and l’Hospital’s rule to determine limits of simple expressions;
- Apply the procedures of differentiation accurately, including implicit and logarithmic differentiation;
- Apply the differentiation procedures to solve extreme value problems;
- Sketch graphs, using function, its first derivative, and the second derivative;
- Calculate definite and indefinite integrals, using substitution and integration by parts;
- Understand and apply the procedures for integrating rational functions;
- Use integration to find areas and volumes;
Literature and preparations
Specific prerequisites
No information inserted
Recommended prerequisites
No information inserted
Equipment
No information inserted
Literature
Rodhe – Sollervall: Matematik för ingenjörer
or
Glyn James: Modern Engineering Mathematics
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
A, B, C, D, E, FX, F
Examination
- TEN1 - Examination, 7.5 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.
Opportunity to complete the requirements via supplementary examination
No information inserted
Opportunity to raise an approved grade via renewed examination
No information inserted
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.
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.
Offered by
Main field of study
Mathematics, Technology
Education cycle
First cycle
Add-on studies
No information inserted
Contact
Armin Halilovic, armin.halilovic@sth.kth.se