| NMAA17 |
Mathematics, 6 ECTS credits.
/Matematik/
For:
Bio
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Prel. scheduled
hours: 50
Rec. self-study hours: 110
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Area of Education: Science
Main field of studies: Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
That you as a student will learn to feel confident with the mathematical expressions, reasoning and relations which are basic to scientific and technical subjects. After a completed course you should be able to:
- Read and interpret mathematical texts
- Explain definitions and expressions like local extremes, limits, continuity, derivatives, primitive functions and integrals
- Explain and use central theorems like The Fundamental Theorem of Calculus, Mean-Value Theorems, The Intermediate-Value Theorem and The Max-Min Theorem.
- Use mathematical laws for limits of functions, derivatives, antiderivatives and integrals.
- Perform investigations of functions using derivatives, limits and the properties of basic functions and from this draw conclusions regarding the properties of the functions
- Use standard techniques to calculate antiderivatives and definite integrals.
- Handle differential equations (first-order separable and first-order linear equations.)
- Use Maclaurin expansions to approximate functions and investigate limits.
- Solve linear systems of equations using elimination
- Carry out matrix computations
- Compute 2x2 and 3x3 determinants
- Define and compute eigenvalues and eigenvectors of matrices
- Perform checks of results and calculations to verify that they are correct and reasonable.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
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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Organisation:
Teaching is done in lectures and problem classes. Theory is followed up by problem-solving by the lecturer. The examination consists of a written test.
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Course contents:
Equations and systems of equations. Geometric and arithmetic series. Inequalities. Exponential functions and logarithms. Trigonometric functions. Derivative and the study of functions.Functions of a real variable. Polynomials. Elementary functions. Sequences, limits. Derivatives and continuity. Rules for differentiation. Properties of continuous functions. Study of functions. Antiderivatives. Integration and geometrical applications, including area. Improper integrals. Taylor's formula. Maclaurin expansions of elementary functions with applications to the calculation of limits. Linear ordinary differential equations of first order, separable equations. Systems of linear equations and matrices. Determinants. Eigenvalues and eigenvectors. Models of Population Biology and Leslie matrices
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Course literature:
Rodhe/Sigstam: Naturlig matematik. 4th edition.
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Magnus Berggren
Link to the course homepage at the department
Course Syllabus in Swedish
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