| BML401 |
Mathematics 4 for Foundation Year, 8 ECTS credits.
/Matematik 4 för basår/
For:
Bas
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Prel. scheduled
hours: 64
Rec. self-study hours: 149
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Area of Education: Science
Main field of studies: Other subjects
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Advancement level
(G1, G2, A): 0
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Aim:
The course aim is to give a foundation in mathematics and a preparation for further university studies in mathematics.
After completion of the course, the student should be able to,
- handle simple algebraic expressions with real and complex numbers.
- set up and solve equations and inequalities.
- handle and use the principle for derivatives with applications.
- apply the definition of the derivative to illustrate general differentiation rules and handle differentiation rules.
- study the elementary functions with derivates and limits to draw conclusions regarding the properties of the functions.
- use standard techniques to calculate antiderivatives and definite integrals with applications.
- use the unit circle to defined trigonometric identities, solve trigonometric equations and graph trigonometric functions.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Matematics 3C for Foundation Year
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Mathematics Specialization for Foundation Year.
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Organisation:
The course is given in the form of lectures and tutorials. The lectures presents theories on the current course section and tutorials apply active student work with teacher supervision. The students homework, initiative and activity is of great importance. The examination consists of a written examination and continuous examinations (assignments and control test) during the course.
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Course contents:
Complex numbers in different forms, conjugate and absolute value of complex numbers, Euler´s formula, proof of de Moivre´s theorem with applications. Polynomials, polynomial equations with complex roots, power equations of degree one, two , three or more, factoring polynomials (Fundamental theorem of algebra), trigonometric expressions and identities, trigonometric functions, trigonometric equations, radians, logarithmic functions, absolute value function, derivatives of elementary functions (of powers, exponential and logarithmic functions, trigonometric functions), differentiation rules (sum rule, product rule, quotient rule, chain rule), study of functions, draw a curve, asymptotes. Primitive functions and integrals with applications, integration by parts,
differential equations and solutions.
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Course literature:
Lena Alfredsson, Kajsa Bråting, Patrik Erixon, Hans Heikne : Matematik 5000, Kurs 4 Blå lärobok. Natur & Kultur
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Examination: |
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Written examination
Optional written test
Assignments
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6 ECTS
0 ECTS
2 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Malgorzata Wesolowska
Link to the course homepage at the department
Course Syllabus in Swedish
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