HF1903 Mathematics 1 7.5 credits

• 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.
• Functions of several variables. Partial derivatives. Maxima and minima.
• Double integrals in Cartesian and polar coordinates and applications: area, volume and moments of inertia.

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;
• Sketchgraphs, 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;
• Calculate partial derivatives;
• Apply partial derivatives for  finding extreme values;
• Calculate and apply double integrals for computing areas, volumes and moments of inertia;  

Completed upper secondary education including documented proficiency in Swedish corresponding to Swedish B and in English corresponding to English A.

And the specific requirements of mathematics, physics and chemistry corresponding to Mathematics D, Physics B and Chemistry A.

 Meddelas senast tre veckor innan kursstart.

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

• TEN1 - Examination, 3.5 credits, grading scale: A, B, C, D, E, FX, F
• TEN2 - Examination, 4.0 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.

Armin Halilovic

• 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.