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.

Exam

• Written, includes problem solving and theoretical questions, passing is 40%. Exam covers the topics from lectures.
  • Example of one old exam is here.
  • Derivatives -- exercises for exam (PDF)
  • Curve sketching -- exercises for exam, (PDF, exercises from 15 to 34, skip 30)
• There will be three terms between January 30 and February 8. The exact room, date and time will be announced later.
• 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).
• Need more informations? Ask on the lecture or on a discussion platform in the University information system (RRMATA Mathematics in English for students of FRDIS). All students will see the question and the answer.

Literature

• Literature authored by Robert Mařík (precalculus, calculus, polynomials)
  • Paper-friendly textbook (PDF, approx 90 pages)
  • Screen-friendly textbook (PDF)
  • Presentations, real world applications, solved problems, quizzes
  • for slides from lectures see the section "Outline of the lectures"
• Literature authored by Simona Fišnarová (integral calculus, linear algebra)
  • Home page

Outline of the lectures by Robert Mařík

1. Precalculus, Calculus;            PDF slides from the lecture
   • Functions: basic elementary functions (short list, graphs), elementary functions, increasing/decreasing, one-to-one, inverse, (texbook/pages from 15 to 24, interactive exercises on inverse functions)
   • Introduction to limits (MIT online course)
     
     • Rough geometrical idea (animations)
     • Definition of limit (texbook)
   • Applications of limits (texbook)
     • Continuity, continuity of elementary functions (wikipedia)
     • Theorem of Bolzano (textbook/page 49, wikipedia)
     • Solving inequalitites using Theorem of Bolzano (textbook/page 52, interactive exercises)
     • Derivatives:
       • definition (texbook/page 57),
       • real world interpretation (texbook/page 61),
       • geometric interpretation (texbook/page 58),
       • (derivatives on SOS math)
2. Calculus II;            PDF slides from the lecture
   • Evaluating derivatives
     • refcard,
     • solved exercises,
     • interactive exercises,
     • online calculator with step by step solution,
     • more online calculators (in Czech))
   • Applications of derivatives
     • Differentiability implies continuity (wikipedia, textbook/page 62)
     • Tangent (wikipedia), linear aproximation (textbook/page 70, external link)
3. Calculus III (Applications of derivatives);            PDF slides from the lecture
   • Related rates of change (wikipedia), see also external links to exercises on related rates at the bottom of the page
   • Local extrema:
     • definition,
     • existence of derivative at local extremum implies stationary point,
     • 1-st derivative test
     • links: textbook/Chapter Caculus - Extremal problems, wikipedia, solved exercises, interactive exercises,
     • see also external links to exercises on min/max problems at the bottom of the page
   • Curve sketching: problems from 15 to 34, skip 30, solved problems
   • Derivatives -- exercises for exam (PDF)
4. Other selected topics;            PDF slides from the lecture
   • Algebraic equations, solvability and multiplicity of the solutions textbook, Chapter 3, only topics covered by the presentation from the lecture
   • Curve sketching: exercises, solved problems
   • Nonlinear equations
     • Root finding using bisection of interval (wikipedia)
     • Root finding using Newton-Raphson method (wikipedia)
   • Taylor polynomial (presentation, Chapters 1 and 3 only, wikipedia)
   • Least squares method (presentation, Chapters 1 and 3 only)

Other resources

• Online video tutorials
  • Patrick Jones
  • MIT
    • Gilbert Strang
    • David Jerison
  • Calculus I in 20 Minutes
• 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