Detailní popis

Walk in the footsteps of Newton and Leibnitz!  An interactive text and graphing software combine with the exciting on-line course delivery to make Calculus an adventure. This course includes a study of limits, continuity, differentiation, and integration of algebraic, trigonometric and transcendental functions, and the applications of derivatives and integrals.

Study materials (e-books, Discovery Education, etc. ...) for FLVS Global courses are INCLUDED in the price of the course.

Calculus je důležitým a nezbytným nástrojem nejen pro matematiky. Bez porozumění funkcím a jejich vlastnostem, diferenciálnímu a integrálnímu počtu se jen těžko studuje fyzika, některé části chemie, ekonomie, ale také třeba biologie. Calculus je tak skutečně základním stavebním kamenem pro vybudování dalších, nejen matematických disciplín. V našem kurzu provedeme studenta světem funkcí a jejich vlastností, limitami, derivacemi i jejich aplikacemi. V kurzu jsou obsažena také témata, která se běžně nevyučují na našich středních školách, např. diferenciální rovnice.

RNDr. Ing. Jana Kalová, PhD., instruktorka CTM Online kurzů

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Calculus is an important and essential tool not just for mathematicians. Without understanding of functions and their properties, derivatives and integrals, it is very difficult to conduct further studies in Physics, certain parts of Chemistry, Economy or even Biology. Calculus is therefore truly the foundation for developing other, not only mathematical disciplines. In this course we will guide the student through the world of functions and their properties, limits, derivatives and their applications. The course also contains topics, which are not commonly parts of the Czech high school curriculum, such as differential equations.

RNDr. Ing. Jana Kalová, PhD., CTM Online instructor

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Struktura kurzu

Study Scope and Sequence

Module 01: Functions

Module 02: Limits and Continuity

Module 03: Differentiation

Module 04: Applications of Derivatives

                  ·  Introduction to Calculus 


                  ·  Review of Function Terminology 


                  ·  Graphing Calculators 


                  ·  Compositions and Transformations of Functions 


                  ·  Some Common Functions 


                  ·  Introduction to Limits 


                  ·  Properties of Limits 


                  ·  Limits Involving Infinity 


                  ·  Continuity 


                  ·  Applications of Limits 


                  ·  The Derivative 


                  ·  Rules of Differentiation 


                  ·  Trigonometric Derivatives and the Chain Rule 


                  ·  Inverse Functions 


                  ·  Exponential and Logarithmic Functions 


                  ·  Derivatives of Exponential, Logarithmic, and Inverse Trig Functions 


                  ·  Implicit Differentiation 


                  ·  Curve Sketching 


                  ·  Maximums and Minimums 


                  ·  Applied Maximum and Minimum Problems 


                  ·  Distance, Velocity, Acceleration, and Rectilinear Motion 


                  ·  Related Rates 


                  ·  The Mean-Value Theorem and L’Hopital’s Ryler 


                  ·  Linearization 


Module 05: Integrations

                  ·  Area Approximation and Riemann Sums 


                  ·  Introduction to the Definite Integral 


                  ·  The Fundamental Theorem of Calculus 


                  ·  Integrals and Anti-derivatives 


                  ·  Integration by Substitution 


                  ·  The Definite Integral 


Module 06: Applications of Integrals

                  ·  Finding the Area Under and Between Curves 


                  ·  Volume by Discs (Slicing) 


                  ·  Average Value of a Function and Rectilinear Motion Revisited 


Module 07: Differential Equations

                  ·  Introduction to Differential Equations 


                  ·  Initial Value Problems and Slope Fields 


                  · Numerical Approximation Methods with Integrals

Module 08: Supplemental Topics

                  ·  Exploring the graphs of f, f Prime, and f Double Prime 


                  ·  Relative Rates of Growth 


                  ·  Using Calculus with Data in a Table 


                  ·  Functions Defined by Integral 


 

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Sylabus kurzu

Syllabus Calculus Honors

• Syllabus Calculus Honors

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Materiály

K vašemu kurzu potřebujete tyto učebnice a studijní pomůcky (pokud ke kurzu potřebujete laboratorní sadu, zkuste si nejdříve dohodnout možnost využívání školní laboratoře):

Description	Number	Type	Source
Graphing Calculator		Tool	NOT included in the price of the course
Graphing Calculator			NOT included in the price of the course
Study Forge		e-Book	included in the price of the course

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Cena

cena kurzu: 13 550,- Kč / 569,- EUR

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Zkušenosti studentů

Great course, especially the exercises.

Jan K., 2021

The Calculus Honors course is the third and the hardest math course I ever took. However, I enjoyed it thoroughly. I like how every lesson had numerous practice questions (much more than in my previous courses), so I had enough practice to be prepared for the tests. One great thing I'd like to point out were the links to various Geogebra stuff, in which I could explore the graphs. This was really helpful.

I enjoyed learning about both the derivatives and the integrals and I believe I understood most of the lessons. I'm excited for when we'll be learning this stuff at school, although I don't know if we'll go deeper than this course did. Overall, I found this course to be not only the most challenging, but also the most interesting math course I ever took.

Barbora L., 2022