engineering with Analysis, Algebra etc, they will not be repeated in the
preparation week. 1. Analysis ... Stroud, K.A., Booth, D.J. Engineering
Mathematics.
Lehrstuhl Informatik VII Prof. Dr. Klaus Schilling
Background Knowledge Needed for Space Dynamics Remark 1: The following issues are required for understanding contents of the lecture “Space Dynamics”. Considering these are handled in the most studying fields of science and engineering with Analysis, Algebra etc, they will not be repeated in the preparation week. 1. Analysis • Differentiation: Sum, product, quotient and chain rules, derivative of the inverse of a function; •
Integration: definite and indefinite integral; Integration by substitution, Integration by parts, Integration by trigonometric substitution, Integration by partial fractions;
•
Partial differentiation, integration of functions of several variables;
• •
Infinite series: definition, convergence and criteria, power series; Taylor series: definition, properties, Taylor series for several variables, calculation; • Fourier series: definition, properties, Fourier series of a function. 2. Linear Algebra • Vector algebra: vector operation (addition, subtraction, multiplication); vector operation in 2- and 3-D space; scalar production and vector production; Norm of a vector; • Matrix: matrix norms, inverses and determinants, ranks, matrix power and exponentials, eigenvalues and eigenvectors, Cholesky, LU and QR factorizations; • Solving linear system of equations: Gaussian algorithm, solving a linear (m, n)-system of equation, square systems, over- and underdetermined systems. 3. Complex numbers and functions • Definition and presentation of complex numbers: algebraic-, trigonometricand exponential forms; • Calculation: addition, subtraction, multiplication, and geometric interpretation. Remark 2: The following issues will be handled / repeated in the preparation week. However it is helpful to have these as background. 4. Ordinary differential equations • Homogenous- and inhomogenous ODEs; • Solving first-order ODEs: general solutions, particular solution, variation of parameters; • Solving second-order ODEs; • Linear systems of differential equations. 5. Laplace transformation • Laplace transform as an extension of Fourier transform; • Definition of Laplace- and inverse Laplace transform; • Properties and theorems: linearity, differentiation, frequency division, frequency integration, integration, scaling, initial- and final value theorems, frequency- and time shifting, convolution,
Lehrstuhl Informatik VII Prof. Dr. Klaus Schilling
References Jeffrey, A. Mathematics for Engineers and Scientists. Chapman & Hall/CRC 2004 Stroud, K.A., Booth, D.J. Engineering Mathematics. Industrial Press 2001 Dettman, J.W. Introduction to Linear Algebra and Differential Equations. Dover Publications 1986. Golub, G.H., Van Loan, C.F. Matrix Computations (Johns Hopkins Studies in Mathematical Sciences). The Johns Hopkins University Press 1996 Brogan, W.L. Modern control theory. Prentice Hall Ogata, K. Modern Control Engineering. Pearson Education International 2002
