This is the first part of an elementary calculus course. It covers differentiation, integration, applications, limits, differentiation rules, integration technics, and some more.

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

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

Language: *English*

Lectures: **MWF 8 ^{30}—10^{10}** at West Teaching Building C

Instructor: M. Grützmann (古梅西), e-mail: x@nwpu.edu.cn, x=grutzmann, QQ-group: 162-423-552

Teaching assistants (grader): Ms Zhang, Ms Wu

Seminar: Fr 9

Office hours: Wed+Fri after the lecture in C40x lecture building

Midterm: Wed November 21

Makeup exam: Tue January 1st, 2013 2:30–4:00pm in C407 教东楼 (lecture building).

Final: January 15, 2013, 2:30–4:30pm (120min) in 教西楼D105 (neighbor building of our lecture building, sample exam will be here)

^{*} The group secret (to be added) is my university e-mail address (the one on the course home page). When you add me (QQ: 109-235-1405 or via the discussion group), please send your name and the word “calculus”.

^{99}If you don't want to come on January 1st, you can come the day before, Mon Dec 31st, 2012, 2:30–4:00pm in C407 (our lecture building). Please let me know if you prefer to take the makeup exam on Monday.

The course grade constitutes from your homework (10%), one mid-term exam (30%) and the final exam (60%).

*Homework* is assigned every week and due on Monday 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%.

The exams take place at university. Personal presence is mandatory, please keep a photo ID (e.g. student ID card) at hand. No calculators or pre-written notes allowed. You may use an alphabetically sorted list of vocables / dictionary *without annotations*. A makeup exam with the same conditions at a later time is availalbe if you have a university-approved excuse^{3} and not yet taken the original exam.

I (10P) p.7ff^{‡} Nr. 3a,4b each i-iii; 5b;38 graphically or via computer/ calculator.

II (10P) p.20ff Nr. 1, 2, 5, 9, 30ab; ~~44a--d,f, e~~^{*}

^{‡} page 7 or on the next few pages.

I (6P) p.29ff Nr. 1–6, 28

II (7P) p.41ff Nr. 1–6, 8, 10, 17, 26, 28, 60

III (7P) p. 55ff Nr. 6, 7b, 10b, 14a, 21; 31^{*}

^{*} The last one may be harder, if you solve it, you get extra credit, if you cannot solve it, you don't lose points.

I (6P) p.65ff Nr. 6, 9, 17, 21, 23, 49

II (7P) p.95ff Nr. 5, 7, 13, 25, 29, 35

III (7P) p.108ff Nr. 2, 9, 14, 16a, 17, 19, 33

I (8P) p.122ff Nr. 1, 12, 15, 20, 26, 35, 59, 62

II (6P) p.132ff Nr. 2,8,17,22,24,36,37^{*}

III (6P) p.139ff Nr. 6,8, 16, 21, 25, 43

I (6P) p. 157ff Nr. 6 at `θ`=0, 10, 14, 15-18, 30, 34

II (7P) p. 169ff Nr. 4, 12, 14, 15, 19, 21

III (6P) p. 178ff Nr. 2, 6, 12, 26, 29, 30.

I (6P) p. 184ff Nr. 3, 4, 5, 15, 33, 41

II (7P) p. 195ff Nr. 3, 1, 7, 9, 12, 32, 36, 39

III (7P) p. 204ff Nr. 2, 6, 26, 27, 39, 46, 48.

I (6P) p. 212ff Nr. 2, 3, 5, 13, 14, 37

II (7P) p. 217ff Nr. 55, 87, 91-92, 95-96, 101, 104, 107

III (6P) do at least two questions in the sample midterm.

Erratum: Question 4c requires the average chocolate consumption in Switzerland, which is 10.6 kg/yr⋅cap.

No homework in the week of the mid-term. But please use the time to review all necessary material for the mid-term exam.

on Wed November 21^{st}, 2012, 8:30—10:10am in C206 (class time, class room). Please let me know a.s.a.p.^{2} if you have a time conflict. Given a university-approved excuse,^{3b} you are entitled to a makeup exam.^{5} The exam covers chapters 0—3. I will provide a sample exam here. If you feel unsure about the required vocables, check this list. In the exam however you may **not use** this detailed list, instead you are restricted to this alphabetically sorted translations without annotations. You may extend/ shorten this list, but not add annotations.

If you came to this class only 3 weeks before the mid-term (or later), please write me an e-mail stating your name, the word calculus and that you were admitted late. You will be entitled to the makeup exam, but you may *not attend the regular exam*. Please make sure you got some confirmation e-mail from me.

There will be additional “office” hours before the midterm: Mo 10^{20}–12^{00} in C40x (same building after class) and Tue 1^{30}pm–3^{00} in C40x. If you were admitted late to class, please review the course material (chapters 0–2) as soon as possible and see me during some office hours for additional questions.

^{2} as soon as possible

^{3b} such as acute sickness, cultural choke, family emergency or important religious holiday/ ceremony, …, severe late admission to class;^{4} only valid before starting the exam

^{4} No excuses are, e.g. slight tiredness before the exam, minor sickness (such as running nose), lack of performance due to lack of training, …, interrupting the exam due to feared failure.

^{5} somewhat different questions, same conditions, same difficulty, same points

I (6P) p. 234ff Nr. 1, 3, 4; 44, 50, 52–53, 55, 58;

II (7P) p. 243ff Nr. 1–5, 24, 32, 39, 44, 42, 46;

III (6P) p. 253ff Nr. 1, 4, 5; 7, 13, 37, 40, 59; Erratum: Q5 has an error, namely y'(2)=0, y''(2)∈**R** and y''(x)>0 with y'(x)<0 for all x∈(2,4) is not possible. You can either say why this is not possible or assume y'(x)>0 on (2,4). Please write what you assume. In either case it is still possible to draw a function on (-∞,2] and one on [4,∞).

If you have missed the mid-term, please talk to me as soon as possible (there is one makeup exam mid of December).

I (6P) p. 264ff Nr. 1, 5, 7, 12, 13, 15;

II (6P) p. 276ff Nr. 1–2, 3, 45, 52, 59, 62ac;

III (7P) p. 293ff Nr. 2, 6; 8cdf, 30, 31, 46, 50.

I (6P) p. 303ff Nr. 1, 8, 23, 28, 9, 30;

II (7P) p. 349ff^{+} Nr. 2, 3, 6; 7,^{&} 19, 32, 37-8, 39, 40;

III (6P) p. 361ff Nr. 13, 6, 11, 12; 14, 41, 51a–c, 52, 63–4.

^{+}There is no need to study §§4.1–4.3 before doing this homework.

^{&}You can do all 3 graphs into one diagram.

I (7P) p. 319ff Nr. 2a–c, 4a–c, 6a, 7b, 8a; 14, 24, 34, 44, 59–60;

II (6P) p. 371ff Nr. 1ab, 3ab, 4ab; 13, 14, 40, 42;

III (6P) p. 381ff Nr. I&II of 1, 3, 8; 11, 12; 22, 23, 31–32.

I (6P) p. 401ff Nr. 1b–d, 3, 5, 12; 56, 59, 60;

II (7P) p. 411ff Nr. 2,3,4,5, 32,33,35;

III (7P) p. 420ff Nr. 1,2,10, 16,17, 20,30.

I (7P) p. 428ff Nr. 7–8; 15, 23, 31, 32, 36, 38; Hint `T` = ½`mv`^{2} the kinetic energy

II (6P) p. 437ff Nr. 7, 8, 13ab,c^{*}, 14, 16, 21;

III (7P) p. 449ff Nr. 1, 2, 4 7, 9, 25; 39–42;

IV review the course material for the final and try the sample exam.

Please hand in all late homework by Jan 9^{th}. Later solutions may not be graded and thus cannot be considered for your grade.

on Tue January 15^{th}, 2013, 2:30—4:30pm in 教西楼 D105 (neighbor building of our class building). Please let me know a.s.a.p.^{2} if you have a time conflict. Given a university-approved excuse,^{3c} you are entitled to a makeup exam.^{5} The exam covers chapters 0—5. I will provide a sample exam here. If you feel unsure about the required vocables, check this list. In the exam however you may **not use this detailed list**, instead you are restricted to this alphabetically sorted translations without annotations. You may extend/ shorten this list, but not add annotations.

If you came to this class only 3 weeks before the final (or later), please consider cancelling the course as the time is not enough to learn all the material from new.

There will be additional “office” hours before the final exam: Mo,We,Fr 10^{20}–12^{00} in C40x (same building after class).

^{2} as soon as possible

^{3c} such as an exam at the same time, acute sickness, cultural choke, family emergency or important religious holiday/ ceremony, …;^{4} only valid before starting the exam

^{4} No excuses are, e.g. slight tiredness before the exam, minor sickness (such as running nose), lack of performance due to lack of training, …, interrupting the exam due to feared failure.

^{5} somewhat different questions, same conditions, same difficulty, same points

(Numbers in parenthesis give the approximate numbers of lectures)

- Functions and Models (2 weeks, vocables)
- Definition function; even, odd; examples. (1)
- classes of functions: polynomials, rational fcts., algebraic fcts., trig. (sum-angle formula), exp-log, other transcendental, piecewise fcts. (3)
- Parametrized curves (0.5)
- Modeling (0.5)

- Limits and Continuity (1.5 weeks, vocables)
- rates of change and limits (1, w ε-δ-definition)
- limit laws & one-sided limits (1)
- limits with ∞, horizontal and vertical asymptotes (indeterminate expressions; 1)
- continuity (intermediate value thm, range of a fct; 1.5)
- tangents: velocity and other rates of change (1)

- Derivatives (1.5weeks, vocables)
- derivative as a function (0.5)
- derivatives of polynomials and exp (sum rule; 0.5)
- product and quotient rule (power functions; 1)
- der. of trig. (1)
- chain rule (1)
- implicit diff. & inverse fct.; (log and roots; 1)
- related rates (0.5)
- Review session for the mid-term (3)

- Applications of Differentiation (1.5weeks, vocables)
- finding min/ max (1)
- mean value theorem (w/ proof; 1)
- curve sketching (min, max, cont/sing., range, asymptotes; 1)
- undefined expressions and l'Hospital's rule (1)
- graphical solutions of autonomous ODEs (1)
- modeling and optimization (1)
- lin. approx. & differentials (0.5)
- Newton's method for finding zeros (0.5)

- Integrals (1.5 weeks, vocables)
- Introduction: Areas and distances (0.5)
- The definite integral, Riemann sums, definition, approx. (1)
- Fundamental and mean value theorem of calculus (w/ proof, net change theorem, examples, ODEs; 2)
- integration rules (antiderivative, sum, substitution; examples; 1)
- numerical integration (trapezoid, Simpson's rule, error est., 1)

- Applications of Integration (1 week, vocables)
- disk integration of a body of revolution (1)
- integration by cylindrical shells of a body of revolution (1)
- length of a plane curve (1)
- springs, pumping, and lifting (1)
- fluid forces (0.5)
- moments and centroids (0.5)
- Review session for the final (6)

This page is maintained by Melchior Grützmann.