Valid for: 2022/23
Faculty: Faculty of Engineering, LTH
Decided by: PLED F/Pi
Date of Decision: 2022-04-20
Compulsory for: IBYA1, IBYI1, IBYV1, IDA1, IEA1
Language of instruction: The course will be given in Swedish
The course aims at giving a basic treatment of one-dimensional calculus. Particular emphasis is put on the role which this plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies.
Knowledge and understanding
For a passing grade the student must
Competences and skills
For a passing grade the student must
Algebraic computations. Functions, equations, inequalities and modulus of a number. Complex numbers. Powers and logarithms. Trigonometry. Curve sketching: elementary functions and second degree curves.
Complex numbers and polynomials. The concept of a function. Properties of the elementary functions: graphs, formulas, limits. Limits with applications: the number e, series. Continuous functions. Derivatives: definition and properties, applications. Differentiation of the elementary functions. Properties of differentiable functions: the mean value theorem with applications. Curve sketching. Local extreme values. Optimization.
Primitive functions. Partial integration and change of variable. Partial fractions. Definition of the Riemann integral. Methods of integration. Riemann sums. Geometrical and other applications of integrals. Improper integrals. Differential equations of first order: linear and separable with applications. Linear differential equations of second order: solution of homogeneous and certain inhomogeneous equations, with applications. The Taylor and Maclaurin formulae. Power series expansions of the elementary functions, with applications.
Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Computer test on the subcourse Algebra, which graded only with Passed or Not passed. Written examinations on the subcourses Calculus 1 and 2. These are graded on a scale from 3.0 (passed) to 6.0 in steps of 0.1. The final grade is the integer part of the mean of these two grades (at most 5). The subcourse Algebra finishes with a short online examination in study week 5 of the first study period. The subcourse Calculus 1 begins in study week 6. A re-sit of the online examination is, besides the re-sit examination periods, offered during the ordinary exam period in October.
The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.
Code: 0117. Name: Algebra.
Credits: 3. Grading scale: UG. Assessment: Computer quiz, with grades Passed and Not passed. Contents: See above, Algebra. Further information: The computer quiz is scheduled after study week 5 in study period 1.
Code: 0217. Name: Calculus 1.
Credits: 6. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 1. Further information: The subcourse starts in study week 6 of study period 1.
Code: 0317. Name: Calculus 2.
Credits: 4,5. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 2.
The number of participants is limited to: No
The course overlaps following course/s: FMA415, FMAA01, FMAA05, FMA410, FMA645, FMAB65, FMAB70, FMAB45, FMAB50, FMAB60
Director of studies: Studierektor Anders Holst, Studierektor@math.lth.se
Course administrator: Studerandeexpeditionen, email@example.com
Teacher: Tanja Kimmerud, Tanja.Kimmerud@math.lth.se
Course homepage: http://www.maths.lth.se/course/analHbg/