What is math 1
Contents Mathematics 1 (WS19 / 20)
Propositional logic and set theory,, (sets, relations and mappings). (Number systems: natural, whole, rational and real numbers,) powers, roots and logarithms of real numbers, equations and inequalities, calculating with sums, factorials and binomial coefficients, binomial theorem. Number sequences, limit value of a number sequence, land exchange O () - notation. Modular arithmetic, check digits. Real functions, limit value of a function, continuity, trigonometric functions. Differential calculus, differentiability, derivation, differential, derivation rules, Taylor's theorem, de l’Hospital rules, extreme values, turning points, curve discussion. Linear algebra, determinants, matrices, systems of linear equations (LGS) and their solvability, Gaussian methods, Gauss-Jordan methods, vectors, straight line equations, plane equations.
Integral calculus, definite integral, antiderivative, partial integration, substitution, improper integrals, geometric applications of integration. Functions of several variables, definition and forms of representation,, partial derivatives, total differential and its application, gradient, extreme values of functions of two variables, least squares method, optimization with Lagrange multipliers. Graph theory, paths in graphs, (search) trees, spanning trees, Kruskal algorithm, Huffman code, shortest paths, Dijkstra algorithm. Statistics, randomness and probability, descriptive statistics, characteristics, relative frequency, parameters of a sample, combinatorics, conditional probabilities, random variables, binomial distribution, uniform distribution, normal distribution,, central limit theorem. Complex numbers, Gaussian number plane, powers, roots of complex numbers, converting Cartesian form into polar form, fundamental theorem of algebra. . Differential equations (DGLs): Typing, solution of linear DGL with constant coefficient, initial value problems.
The above topics may be relevant for the exam (s) from July 1st, 2020.
As I said in the lecture, the topics can Derivation of functions, LGS (Gauss), Graph almost as "set" due to their importance for every exam. But of course the other content is also relevant. Just take a good look at the exercises and mock exams. I wish you success!
© Wolfgang Konen, June 25th, 2020
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