SF1612 Mathematics, Basic Course 6.0 credits

• Computations involving real and complex numbers, algebraic expressions, inequalities, equation solving.
• Basic properties of transcendental functions, e.g. the natural logarithm, the exponential function, powers, trigonometric functions, the complex exponential function. Inverse functions.
• Mathematical reasoning, proofs, induction and recursion, the binomial theorem, sums, products.

After the course the student should be able to

• Simplify expressions by factoring or using laws of exponents and logarithms.
• Use the unit circle to derive trigonometric relations.
• Solve certain rational equations and inequalities using the factor theorem, polynomial division etcetera.
• Solve certain trigonometric equations, root equations and equations involving logarithms or absolute values.
• Interpret and use the summation symbol and the binomial theorem, and compute geometric and arithmetic sums.
• Carry out certain simple proofs, e.g. by induction.
• Use complex numbers, both in rectangular and polar form, including the use of the complex exponential function.
• Explain certain properties of the basic transcendental functions, domain of definition, range, especially the exponential function, the natural logarithm function, and trigonometric functions. Compute inverse functions.
• Present his/her calculations and arguments so that they are easy to follow even for someone who is not already involved in the problem.

In addition, the student should have achieved a study technique that simplifies further mathematical studies

Advanced mathematics (level A-D from a Swedish high school or equivalent).

For COPEN1

Persson&Böiers/Analys i en variabel.

LTH/Övningar i analys i en variabel.

For CDATE1:

Kompletteringskompendium i matematik

Samt särtryck ur följande alster:

Persson&Böiers/Analys i en variabel. (Kapitel 0-1) Appendix A och B 

LTH/Övningar i analys i en variabel. (Kapitel 0-1) Appendix A och B

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

• TEN1 - 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.

Written examination, possibly in conjunction with other assignments.

• 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.