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Applied Mathematics - Background

Instructions

1st week: Oct 1– Oct 5, 2018
Title of lecture: Functions, elementary functions.
Necessary knowledge: basic notation of set theory and sententional calculus, basic properties of real numbers.
Topic of exercises: Equations, inequalities, domains of elementary functions.
Necessary knowledge: algebraic manipulations, properties of elementary functions, solution of various types of equations and inequalities.
2nd week: Oct 8– Oct 12, 2018
Title of lecture: Limit and continuity, 1st derivative.
Necessary knowledge: intervals on the real line, graph of a function, line in the plane.
Topic of exercises: Differentiation of elementary functions (except of composite functions).
Necessary knowledge: formulae for differentiation.
3rd week: Oct 15 – Oct 19, 2018
Title of lecture: Monotony of a function, extreme values.
Necessary knowledge: computing derivatives, solving inequalities
Topic of exercises: Differentiation of more complicated elementary functions. Equations of a tangent line and a normal to the graph of a functin.
Necessary knowledge: formulae for differentiation, equations of lines in the plane, equations of tangent and normal to the graph of a function.
4th week: Oct 22 – Oct 26, 2018
Title of lecture: Convex and concave functions.
Necessary knowledge: computation of derivatives, solving equations and inequalities.
Topic of exercises: Monotony of a function, extreme values.
Necessary knowledge: differentiation, manipulation with expressions, solving equations and inequalities.
5th week: Oct 29 – Nov 2, 2018
Title of lecture: Antiderivatives and indefinite integral of a function.
Necessary knowledge: differentiation, manipulation with expressions.
Topic of exercises: Convexity, concavity and inflections.
Necessary knowledge: differentiation, manipulation with expressions, solving equations and inequalities.
6th week: Nov 5 – Nov 9, 2018
Title of lecture: Differential equations with separated variables.
Necessary knowledge: integration, basic couples of mutually inverse functions.
Topic of exercises: Indefinite integral.
Necessary knowledge: Formulae and rules for integration, manipulation with expressions.
7th week: Nov 12 – Nov 16, 2018
Title of lecture: Definite integral and its applications.
Necessary knowledge: computation of indefinite integrals.
Topic of exercises: Differential equations.
Necessary knowledge: method of solving separable equations, integration (by various methods), manimpulations with expressions, couples of mutually inverse elementary functions.
8th week: Nov 19 – Nov 23, 2018
Title of lecture: Introduction to linear algebra.
Necessary knowledge: no knowledge is necessary.
Topic of exercises: Definite integral.
Necessary knowledge: computation of integrals, solving equations (algebraic, logarithmic, exponential and trigonometric).
9th week: Nov 26 – Nov 30, 2018
Title of lecture: Systems of linear equations.
Necessary knowledge: matrix row operations, Gaussian elimination.
Topic of exercises: Arithmetic vector space, rank of a matrix.
Necessary knowledge: arithmetic vector space and its properties.
10th week: Dec 3 – Dec 7, 2018
Title of lecture: The algebra of matrices.
Necessary knowledge: Gaussian elimination method.
Topic of exercises: Solving systems of linear algebraic equations by the Gaussian elimination method.
Necessary knowledge: Gaussian elimination method.
11th week: Dec 10 – Dec 14, 2018
Title of lecture: Determinants, the Cramer rule.
Necessary knowledge: no knowledge is necessary.
Topic of exercises: Operations with matrices, a matrix inverse, matrix equations.
Necessary knowledge: matrix oparations, Jordan elimination method.
12th week: Dec 17 – Dec 21, 2018
Title of lecture: Information about examinations.
Necessary knowledge: all previous topics.
Topic of exercises: Determinants, the Cramer rule.
Necessary knowledge: evaluating determinants by various methoda, the Cramer rule.

Instructions how to use this page

The winter semester of the academic year 2018/19 is divided into 12 weeks. You can download for each week:

  • materials to the corresponding lecture clicking on Lecture,
  • important formulae clicking on Formulae,
  • exercises clicking on Exercises,

All the documents are PDF-files.

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