# There is an asymptot chapter in Kreyszig

### Analysis I (D-ITET)

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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