This is the second part of an elementary calculus course. It covers integration technics, solution technics for ODEs, elementary transcendental functions, infinite series, Taylor- and Maclaurin series, Fourier Series, vectors in the plane and space, polar coordinates, and some more.

**Textbook:**R.L. Finney, M.D. Weir, F.R. Giordano: Thomas' Calculus, 10th edition, vol 1&**2**,
ISBN 978-7-04-014424-6 (Chinese HEP).

**Course home page:** www.grutzmann.de/calc2

Language: *English*

Lectures: MW 10:30-12:05, Fr 14:00-15:40 in A106 West Teaching Area (Chang'an campus)

Instructor: M. Grützmann (古梅西), e-mail:
x@nwpu.edu.cn, x=grutzmann, QQ-group: 162-423-552^{*} (2012西工大微积分).

Teaching assistants (grader): Ms Wu and Ms Zhang

Seminar: Fr 2nd lecture (same room)

Office hours: Fr after the seminar^{†}

Midterm: April 2012 during lecture time, in the class room

Final: TBA, begin of July 2013

^{*} When you add me (QQ: 109-235-1405 or via the discussion group), please send your name and the word calculus2. If you were already member last semester, you are automatically member (it's the same group).

^{†}The office hours are not a substitute for attending the lecture. You should first come to the lecture and try to understand material there. If there are questions left, ask me between/ after class (maybe I should also address them in the seminar)

The course grade constitutes from your homework (10%), one mid-term exam (30%) and the final (60%). Class attendance is mandatory if you got less than 70% in the last exam.

*Homework* is assigned every week and due on Tuesday the next week (hand in before the class). It will be graded by the TA and returned the following week. The maximal score of the homework is scaled to 10%.

I (10P) p. 474ff Nr. 1, 3, 10, 19, 22; 25, 31, 62, 65, 68;

II (10P) p. 464ff Nr. 1, 8, 10, 22, 66; 50, 57, 23, 73, 75--6;

I (7P) p.483ff Nr. 2, 14, 15, 26, 36, 37, 54a

II (6P) p.495ff Nr. 3, 5, 23, 31, 34, 38 (also Stokes friction)

III (7P) p.506ff Nr. 1, 6, 23, 27, 28, 30,31

If you failed the course last semester, there is a makeup exam in the 4th week (Mar 18–22). Conditions are the same as for the final exam last semester. Please start preparing by yourself. You can ask questions after class.

Numbers in parentheses give the approximate number of lectures.

- Differential equations and Transcendental functions (2 weeks)
- exponential functions (logarithms, 1)
- (ordinary) differential equations (Picard-Lindelöff theorem, 1)
- trigonometric functions (and their inverses, 2)
- first order separable ODEs (1)
- linear first and second order ODEs (complex numbers, 3)
- Numerical integration of ODEs (Euler's method; 1)
- hyperbolic functions (0.5)

- Technics of Integration (2weeks)
- basic integration formulas (0.5)
- Integration by parts (examples, integrals of log, and inverse trig & hyp fcts; 1)
- Integration of rational functions (partial fractions; 2)
- Trigonometric integrals (1)
- Integration by trig. substitution (1)
- Strategies for integration (0.5)
- Integration using tables and CAS (Computer Algebra Systems; 1)
- Numerical integration II (Monte-Carlo method, 1)
- Improper integrals (1)

- Infinite series (2 weeks)
- Limits of sequences of numbers (2)
- Subsequences, bounded sequences, and Picard's method (1)
- Infinite series (1)
- series of nonnegative terms and integral test (1)
- alternating series, absolute and conditional convergence (1)
- power series (1)
- Taylor and Maclaurin series (1)
- Application of power series (1)
- Fourier-series, sine and cosine series (2).
- Review session(s) midtem (2)

- Vectors in the plane & Polar coordinates (2weeks)
- vectors in the plane (2)
- scalar product (1)
- vector-valued functions (1)
- modeling projectile motion (1)
- polar coords, examples, area & length in polar coords (1)
- conic sections (carth & polar coords.; 2)

- Vectors and motion in space (2weeks)
- Vectors in space and carthesian coordinates (1)
- scalar and vector products (1)
- lines and planes (1)
- cylinders and quadric surfaces (1)
- vector valued functions, space curves (1)
- arc length, TNB frame, tangential and normal components of acceleration (2)
- planetary motion and satellites (1)
- Review sessions for the final (6)

This page is maintained by Melchior Grützmann.