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Vybrané modely a aplikace

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Mnoho nul je přesvědčených, že jsou elipsami, po kterých obíhá zem. (Stanislaw Jerzy Lec)

Doplňkové materiály

Vybrané modely a aplikace

Ostatní/Others

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.

- 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.

- 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).

- 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).

- (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)- Homework 1
- Derivatives, step by step solved problems
- Online calculator with step by step solution,
- Derivatives, exercises for exam
- Refcard,

- (Oct. 2. 15-19, Z7)
**Derivatives**(linear approximation, derivative and continuity, related rates, derivative and monotonicity, derivative and local extrema) - (Oct 9. 15-19, Z7)
**Derivatives**(min-max problems, Newton-Raphson method for nonlinear equations)- Homework 3
- Problems on minima and maxima
- Related rates problems
- Curve sketching, also exercises for exam, (PDF, exercises from 15 to 34, skip 30)

- (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`

- (Oct 23. 15-19, Z7)
**Summary of calculus**(Robert Mařík)

- Literature authored by Robert Mařík (precalculus, calculus, polynomials)
- Paper-friendly textbook (PDF, approx 90 pages)
- Shortened version of textbook (PDF, approx 20 pages)
- Screen-friendly textbook (PDF)
- Presentations, real world applications, solved problems, quizzes

- Literature authored by Simona Fišnarová (integral calculus, linear algebra)

- (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) - (Sep. 28)
**Canceled**- public holliday in the Czech Republic - (Oct. 5, 13-17)
**Derivatives**(derivative and continuity, derivative and monotonicity, derivative and convexity, linear approximation, derivative and local extrema) - (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.*- Related rates problems
- Curve sketching, also exercises for exam, (PDF, exercises from 15 to 34, skip 30)

- (Oct. 19, 13-17)
**Derivatives**(function investigation and curve sketching, Newton-Raphson method for nonlinear equations)- Related rates problems
- Curve sketching, aslo exercises for exam, (PDF, exercises from 15 to 34, skip 30)

- (Fri, Nov 6, 13:00)
**Precalculus**(Radka Smýkalová) - (Fri, Nov 13, 13:00, room B44)
**Calculus, derivatives and applications of derivatives (related rates, linear approximation, nonlinear equations)**(Robert Mařík)

Materials from lecture- Handwritten slides from the lecture
- Refcard,
- Derivatives, step by step solved problems
- Derivatives, exercises for exam
- Root finding using Newton-Raphson method (wikipedia)
- Kinetic energy, Einstein's formula and linear approximation

- (Fri, Nov 20, 13:00, room B44)
**Calculus, derivatives, limits and continuity (Bolzano theorem), applications of derivatives (maxima and minima)**(Robert Mařík) - (Fri, Nov 27, 13:00, room B44)
**Calculus, derivatives, curve sketching**(Robert Mařík)- Curve sketching -- exercises for exam, (PDF, exercises from 15 to 34, skip 30)
- Handwritten slides from the lecture

- (Fri, Dec 4, 13:00, room B44)
**Summary of calculus**(Robert Mařík)

- 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)

- 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 authored by Robert Mařík (precalculus, calculus, polynomials)
- Paper-friendly textbook (PDF, approx 90 pages)
- Shortened version of textbook (PDF, approx 20 pages)
- Screen-friendly textbook (PDF)
- Presentations, real world applications, solved problems, quizzes
- for slides from lectures see below

- Literature authored by Simona Fišnarová (integral calculus, linear algebra)

**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)

**Calculus; PDF slides from the lecture**- Evaluating derivatives
- Linear approximation
- Related rates prolems

**Calculus; PDF slides from the lecture**- Minima and maxima of function
- Curve sketching: problems for final exam (from 15 to 34, skip 30), solved problems
- Derivatives exercises for exam

**Calculus; PDF slides from the lecture**- Taylor polynomial (presentation, application, wikipedia)
- Nonlinear equations
- Algebraic equations, solvability and multiplicity of the solutions textbook, Chapter 3, only topics covered by the presentation from the lecture
- Least squares method (presentation)
- Summary

**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)

**Calculus II; PDF slides from the lecture**- Evaluating derivatives
- Applications of derivatives
- Differentiability implies continuity (wikipedia, textbook/page 62)
- Tangent (wikipedia), linear aproximation (textbook/page 70, external link)

**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)

**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
- Taylor polynomial (presentation, Chapters 1 and 3 only, wikipedia)
- Least squares method (presentation, Chapters 1 and 3 only)

- Online video tutorials
- Applications: http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx
- Min/max problems (external links)
- 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: 2020/03/05 07:36 (upraveno mimo DokuWiki)