Všechny pravdy je snadné pochopit poté, co jsou objeveny. Potíž je v tom je objevit. (Galileo Galilei)

Home Page of Robert Mařík

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Mathematics

  • This is a webpage for Erasmus students at Faculty of Forestry and Wood technology and for students of Faculty of Regional Developement and International Studies.
  • The lectures are scheduled on Monday 15:00-19:00 and Tuesday 15:00-19:00, room Z7 in the building of the Faculty of Regional Develpement.
  • Lectures start on September 25. There are 5 weeks of lectures. The exam follows.

EXAMS, common informations

  • The exam is written, includes problem solving and theoretical questions, passing is 40%. Exam covers the topics from lectures.
  • Example of one old exam is here.

EXAMS, Erasmus students

  • Contact the teachers, all exams have to be finished before February 2018.
  • As soon as the terms of exams will be known, you have to register to the exam in the University Information System (UIS).

EXAMS, Faculty of regional development

  • The exams are organized by the faculty staff, as usual on this faculty. The lecturers just provide the problems for each term, correct solutions and graduation scale.
  • It is supposed that one term will be in the week after the lectures, one term in November or December and the other terms in January 2018.
  • As soon as the terms of exams will be known, you have to register to the exam in the University Information System (UIS).

Materials for year 2017 (September, October) - Monday's lecture

  1. (Sep. 25. 15-19, Z7) Precalculus (one-to-one functions, inverse functions, monotonicity), equations via inverse functions, continuity, theorem of Bolzano, solving inequalities using theorem of Bolzano. Calculus (evaluating derivatives)
  2. (Oct. 2. 15-19, Z7) Derivatives (linear approximation, derivative and continuity, related rates, derivative and monotonicity, derivative and local extrema)
  3. (Oct 9. 15-19, Z7) Derivatives (min-max problems, Newton-Raphson method for nonlinear equations)
  4. (Oct 16. 15-19, Z7) Derivatives (derivative and convexity, function investigation and curve sketching)
    • Homework 4
    • Curve sketching, also exercises for exam, (PDF, exercises from 15 to 34, skip 30)
    • Derivatives using Sagecell:
      • ((3*x^2+1)/x).factor().show() # factorization
      • ((3*x^2+1)/x).diff(x).factor().show() # f' and factorization
      • ((3*x^2+1)/x).diff(x,2).factor().show() # f'' and factorization
    • Derivatives using Wolfram Alpha:
      • factor (3x^2+1)/x
      • differentiate (3x^2+1)/x
      • second derivative of (3x^2+1)/x
  5. (Oct 23. 15-19, Z7) Summary of calculus (Robert Mařík)

Literature

Materials from years 2012--2016

Materials from year 2016 (September, October)

  1. (Sep. 21, 13-17) Precalculus (one-to-one functions, inverse functions, monotonicity), equations via inverse functions, continuity, theorem of Bolzano, solving inequalities using theorem of Bolzano. Calculus (evaluating derivatives)
  2. (Sep. 28) Canceled - public holliday in the Czech Republic
  3. (Oct. 5, 13-17) Derivatives (derivative and continuity, derivative and monotonicity, derivative and convexity, linear approximation, derivative and local extrema)
  4. (Oct. 12, 15-17) Derivatives (min-max problems, related rates) The lecture starts at 15:00, since from 13:00 to 15:00 there is a meeting of university staff with the rector and the rector canceled the lectures from 13 to 15.
  5. (Oct. 19, 13-17) Derivatives (function investigation and curve sketching, Newton-Raphson method for nonlinear equations)

Materials for year 2015 (November, December)

  1. (Fri, Nov 6, 13:00)
    Precalculus (Radka Smýkalová)
  2. (Fri, Nov 13, 13:00, room B44)
    Calculus, derivatives and applications of derivatives (related rates, linear approximation, nonlinear equations) (Robert Mařík)
    Materials from lecture
  3. (Fri, Nov 20, 13:00, room B44)
    Calculus, derivatives, limits and continuity (Bolzano theorem), applications of derivatives (maxima and minima) (Robert Mařík)
  4. (Fri, Nov 27, 13:00, room B44)
    Calculus, derivatives, curve sketching (Robert Mařík)
  5. (Fri, Dec 4, 13:00, room B44)
    Summary of calculus (Robert Mařík)

Materials for year 2014 (January)

Exam

  • Written, includes problem solving and theoretical questions, passing is 40%. Exam covers the topics from lectures.
  • You have to register to the exam in the University Information System (UIS). The deadline for submitting or canceling registration is about 24 hours before the exam (you will see the exact deadline in UIS).

Literature

Lectures by Robert Mařík (January 2014)

  1. Precalculus, Calculus;            PDF slides from the lecture

  2. Calculus;            PDF slides from the lecture

  3. Calculus;            PDF slides from the lecture
  4. Calculus;            PDF slides from the lecture

Outline of the lectures from January 2013 by Robert Mařík

  1. Precalculus, Calculus;            PDF slides from the lecture
  2. Calculus II;            PDF slides from the lecture
  3. Calculus III (Applications of derivatives);            PDF slides from the lecture
  4. Other selected topics;            PDF slides from the lecture

Other resources collected for course in January 2013

  • Online video tutorials
  • Applications: http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx
  • Min/max problems (external links)
    • link 1 (skip 22)
    • link 2
    • link 3 from 37 to 60
    • link 4 page 11-13, problems 2-27 (solved problems are from page 5) - page numbers reffer to PDF file, not numbers printed in the top of the pages.
  • Related rates problems (external links)
    • link 1
    • link 2
    • link 3
      • Water runs into a conical tank at the rate of 9 ft^3/min. The tank stands vertex down and has a height of 10 feet and a base radius of 5 feet. How fast is the water level rising when the water is 6 feet deep?
      • Two truck convoys leave a depot at the same time. Convoy A travels east at 40 mph and convoy B travels north at 30 mph. How fast is the distance between the convoys changing a) in 6 minutes b) in 30 minutes
      • Two commercial jets at 40,000 ft. are both flying at 520 mph towards an airport. Plane A is flying south and is 50 miles from the airport while Plane B is flying west and is 120 miles from the airport. How fast is the distance between the two planes changing at this time?
    • link 4
mathematics.txt · Poslední úprava: 2017/10/16 13:42 (upraveno mimo DokuWiki)

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