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.
|Fynn von Kistowski||21.10,4.11,5.11,2.12,9.12,14.12|
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).
- 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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