| Recommended semester: 1st - 4th semester |
| Scope and form: Each week 1 lecture followed by tutorials. Also home problems. |
| Evaluation: Written exam
|
| Examination: 13-scale |
| No credit points with: 01000 / 01001 / 01002 / 01003 / 01010 / 01011 / 01012 / 01013 / 01014 / 01020 / 01021 |
| Aim: To form a basis for physical and technical applications, as well as for possible further study in pure and applied mathematics. |
Contents: Systems of linear equations. Matrix algebra. Derminants. 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 differentiablitity 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. |
| Remarks: The course is intended for students who have participated in 01005 without passing the combined examinations. The grade in 01006 replaces the grade from the 4-hours written examination in 01005. |
| Contact: Per W. Karlsson, building 303, (+45) 4525 3050, p.w.karlsson@mat.dtu.dk |
| Department: 001 Department of Mathematics |
| Course URL: http://www.mat.dtu.dk/courses/01006 |
| Keywords: Linear Algebra, Calculus |
| Updated: 18-01-2002 |
