SIF5010 - Matematikk 3 Våren 2002, Interessante linker Week 3, 14.01-20.01: Our theme is Complex numbers and the main book we use is Erwin Kreyszig: Advanced Engineering Mathematics, 8. utgave, 1999,chapters 12.1, 12.2. If you want to find more about complex numbers click to the links below. Complex Numbers and Electrical Enginneering An introduction to complex numbers S.O.S. Mathematics, Complex Variables If you want to play with complex numbers try the following link! Complex Applet Week 4, 21.01-27.01: Our theme is First order linear differential equations and the main book we use is Erwin Kreyszig: Advanced Engineering Mathematics, 8. utgave, 1999,chapters 1.6, 1.9, 19.1 ( Euler's method ). The brief introduction to the subject can be found below. S.O.S. Mathematics, First Order Linear Differential Equations Click to the following links to see how the Euler Method works! Euler's Method for dy/dx=axm+byn. First Order Differential Equation Solver The Effect of Step Size Week 5, 28.01-3.02: Our theme is Second order homogeneous linear differential equations with constant coefficients and the main book we use is Erwin Kreyszig: Advanced Engineering Mathematics, 8. utgave, 1999,chapters 2.1, 2.2, 2.3, 2.4. Find the relevant information on S.O.S. Mathematics, S.O.S. Mathematics, Homogeneous Linear Equations with Constant Coefficients Or see how the solution of homogeneous linear equation depends on the coefficients: Differential Equation Applet Week 6, 4.02-10.02: We continue with Second order homogeneous linear differential equations with constant coefficients and the main book we use is Erwin Kreyszig: Advanced Engineering Mathematics, 8. utgave, 1999,chapters 2.5, 2.7. First we consider applications to Mass Spring System and Electrical Circuits. Spring/Mass System Harmonic Oscillator Damped harmonic motion applet Damped harmonic oscillator applet Electric Circuits Then we discuss existence and uniqueness of solution to initial value problem. Look at the corresponding page in S.O.S. Mathematics. Linear Independence and the Wronskian Week 7, 11.02-17.02: We consider Second order nonhomogeneous linear differential equations and the main book we use is Erwin Kreyszig: Advanced Engineering Mathematics, 8. utgave, 1999,chapters 2.8 - 2.12. Nonhommogeneous Second Order Equations on S.O.S.Mathematics Method of Undetermined Coefficients Variation of Parameters Formula Applet for solving different types of differential equations including equation of Mass/Spring system and nonhomogeneous equations by the variation of parameters method Harmonic Oscillations and Resonance Week 8, 18.02-24.02: We switched to Systems of linear equations and to the book C. H. Edwards Jr. & David E. Penney: Elementary Linear Algebra. Our first theme is Gauss Elimination and Gauss-Jordan Elimination. Linear Systems and Gauss Elimination Calculus on the Web Click on Linear Algebra and then on Matrices to get some interactive exercises on echelon and reduced echelon matrices. Try some exercises on Visual Gauss Gauss-Jordan Elimination game Week 9, 25.02-03.03: We discussed Matrices and Matrix Operations following C. H. Edwards Jr. & David E. Penney: Elementary Linear Algebra. Matrix operations on S.O.S. Mathematics Some Historical Notes on Matrices Gauss-Jordan elimination and the Inverse Matrix The Inverse of a Square Matrix Week 10, 04.03-10.03: We studied the Determinants following the book C. H. Edwards Jr. & David E. Penney: Elementary Linear Algebra. Determinants (and their basic properties) from Mathworld Historical Notes on Matrices and determinants Cramer's Rule on S.O.S: Mathematics Do you want to know more about Johann Carl Friedrich Gauss, Marie Ennemond Camille Jordan, and Gabriel Cramer ? Read their biographies on The Mac Tutor History Week 11, 11.03-17.03: We introduced general Vector Spaces and discussed the space Rn following the book C. H. Edwards Jr. & David E. Penney: Elementary Linear Algebra. Vector Space from Mathworld Real Vector Spaces Vectors Glossary of Linear Algebra Terms Week 12, 18.03-24.03: We studied Bases for Vector Spaces following the book C. H. Edwards Jr. & David E. Penney: Elementary Linear Algebra. Basis for Vector Space from Mathworld Try interactive exercises on vector spaces, subspaces, and bases on WWW Interactive Mathematics Server Column space and column rank of a matrix Week 14, 1.04-7.04: We defined Dot Product of Vectors in Rn and discussed the Orthogonal Vectors following the book C. H. Edwards Jr. & David E. Penney: Elementary Linear Algebra. Dot Product from Mathworld Learn more about The Gram-Schmidt Algorithm on one of the following pages The Gram-Schmidt Algorithm Gram-Schmidt Orthogonalization on Planet Math The Gram-Schmidt Algorithm Simulation Do you want to know more about Augustin Louis Cauchy, Hermann Amandus Schwartz, Jorgen Pedersen Gram and Erhard Schmidt ? Read their biographies on The Mac Tutor History Week 15, 8.04-14.04: We defined Eigenvectors and Eigenvalues of squre matrices and discussed the Diagonalization of Matrices following the book C. H. Edwards Jr. & David E. Penney: Elementary Linear Algebra. Eigenvalues from Mathworld An introduction to Eigenvalues and Eigenvectors and Diagonalization from S.O.S. Math Eigenvalues and Eigenvectors Technique for system of differential equations EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION

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Last modified: Fri Jan 3 19:46:51 MET 2003