# There is an asymptot chapter in Kreyszig

### Analysis I (D-ITET)

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Check in the VVZ for a current information.

First lecture: Tuesday 15th September 2015.
First practice lesson: Monday September 21, 2015.
First quick exercise: Friday 25th September 2015.

Presence: Every Monday, Wednesday and Thursday, 12-13pm in HG G19.1 or HG G19.2. Further information can be found here.

 Assistants Days Burchert Conrad 5.10,12.10,19.10,9.11,18.11,19.11 Aron Philipp 7.10,8.10,15.10,11.11,12.11,16.11 Tailor Nick 14.10,22.10,29.10,26.11,10.12,17.12 Fynn von Kistowski 21.10,4.11,5.11,2.12,9.12,14.12 Ekin Ilseven 26.10,28.10,2.11,30.11,7.12,16.12

AMIV: Further information on D-ITET and old exams can be found on the AMIV homepage under the link.

### Content of the lecture

Week 1: Appearances of functions (pages 77-99) with the exception of complex-valued functions, product and faculty. Chapter 1.1-1.3 (up to page 19) in sheets.

Week 2: End of chapter 2.1 in Blatter, with the exception of complex-valued functions. Chapter 2.2 in Blatter.

Week 3: Continuity (p. 115-121), inner points, boundary points and termination of a set (p. 126), limit values ​​(p. 127-28), one-sided limit values ​​(p. 133-135).

Week 4: Improper limit values, calculation rules for limit values, asymptotes (pp. 129-139), complete induction (pp. 19-22).

Week 5: Alternating series (p. 145), absolutely convergent series (p. 146-147), function series and power series (p. 149-150), radius of convergence of a power series (p. 151 ff.), Complex numbers: calculation rules, polar form, Euler 's formula (pp. 65-71), calculation of the example on p. 146 by Blatter.

Week 6: Exponential function (pages 2.5): functional equation, logarithm, hyperbolic functions, exponential function in complex; Derivation (definition, examples and calculation rules) (sheet 3.1).

Week 7: Maxima and minima (sheet 3.2), mean value theorem, monotony criteria, rule from de l'Hôspital (sheet 3.3 p. 196-200), calculation of derivatives.

Week 8: Geometric interpretation of the second derivative, Bernoulli's inequality (Blatter 3.3, pp. 201-203), Taylor approximation (Blatter 3.4, pp. 206-213, 221-223); Analysis of critical points (sheet 3.4, p. 214-215), Newton method for determining the zero point (sheet 3.4, p. 216-220).

Week 9: Examples of differential equations, geometric interpretation of first-order differential equations (Blatter, pp. 226-236); Differential equations of higher order and systems, existence and uniqueness theorem (Blatter, pp. 238-240); Zeros of complex polynomials: fundamental theorem of algebra, quadratic equations, roots of unity (sheet 1.7, pp. 72-76); linear homogeneous differential equations with constant coefficients: solutions, characteristic equation (Blatter 3.6, pp. 243-246); Vector algebra: the cross product (leaves 1.6).

Week 10: Homogeneous differential equations with constant coefficients (Blatter 3.6 to p. 251), inhomogeneous linear differential equations (Blatter, p. 252-260), Euler's differential equations (Blatter, p. 261-263).

Week 11: The term integral (Blatter 4.1, pp. 3-11), measure of a subset of R ^ n, Riemann sums, definition and properties of the Riemann integral; The main theorem of differential and integral calculus (sheet 4.2).

Week 12: Integration techniques: partial integration and substitution (Blatter 4.3 pp. 35-47); Partial fraction decomposition and integration of rational functions (Blatter 4.3 pp. 47-55)

Week 13: Technique of integration, supplement to partial fraction decomposition: main parts in the case of a pair of conjugate complex zeros of the denominator (sheet 4.3 example 11), the case of simple zeros of the denominator (sheet 4.3 p. 55), integration of rational functions in e ^ x or in sin x), cos (x) (sheet 4.3 p. 56); Path length and curve integrals (pages 4.1, pages 23-25; line integrals (pages 6.1, pages 245-248).

Week 14: Separation of the variables in the one-dimensional wave equation (Kreyszig 11.3, without Fourier series), separable ordinary differential equations (Blatter 4.6 p. 113-119); Homogeneous differential equations (Blatter 4.6, pp. 121-124), orthogonal trajectories (Kreyszig 1.8).

### credentials

• Christian Blatter, Ingenieur Analysis 1, 2nd edition, Springer, 1996, available online on the homepage of Prof. Blatter (Ingenieur-Analysis, Chapters 1 to 3)
• Christian Blatter, Ingenieur Analysis 2, 2nd edition, Springer, 1996, available online on Prof. Blatter's homepage (Ingenieur-Analysis, Chapters 4 to 6)
• Kreyszig, Advanced Engineering Mathematics

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