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01005 Advanced Engineering Mathematics 1 (Package version)
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Danish title: Matematik 1 (fagpakkeversion)
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Language: Danish
Credit points: 17,5 |
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No credit points with: 01000/01001/01002/01003/01010/01011/01012/01013/01014/01020/01021
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Recommended semester: 1st semester
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Scope and form: Pr.week: 2 lectures, 3h 20m tutorials.
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Examination: Written exam and mandatory problem (13-scale)
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Department: Department of Mathematics
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Aim: To form a basis for physical and technical applications,as well as for possible further study in pure and applied mathematics.
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Contents: Systems of linear equations. Matrix algebra. Determinants. Vector spaces.
Linear maps. The eigenvalue problem, and diagonalization of matricies.
Complex numbers, roots of polynomials, the complex exponential function.
First order linear differential equations. Elementary functions.
Second order linear differential equations with constant coefficients.
Continuity and differentiability of functions of one and several
real variables. Partial derivatives. Gradients. Taylor expansions
of functions of one and several real variables. Limits.
Inner product spaces. Symmetric matrices. Orthogonal matrices.
Quadratic forms. Conic sections. Tangents and tangent planes.
Level curves and level surfaces. The Jacobi matrix.
Extremum. Line integrals, surface integrals, volume integrals. The flux
of a vector field, circulation, divergence and curl. Gauss' theorem.
Stokes' theorem.
Applications of MAPLE in the above areas. Examples of applications in
engineering sciences.
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