Description

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

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

Course Structure

Study Scope and Sequence

Segment One

Module 01 - Functions

• Course Introduction
• Introduction to Calculus
• Review of Function Terminology and More
• Graphing Calculators
• Compositions and Transformations of Functions
• Some Common Functions

Module 02 - Limits and Continuity

• Introduction to Limits
• Properties of Limits
• Limits Involving Infinity
• Continuity
• Application of Limits

Module 03 - Differentitiation

• The Derivative
• Rules of Differentitiation
• Trigonometric Derivatives and the Chain Rule
• Inverse Functions
• Exponential and Logarithmic Functions
• Dirivatives of Exponential, Logarithmic, and Inverse Trig Functions
• Implicit Differentitiation

Module 04 - Applications of Dervivatives

• Analyzing Functions Part I: Curve Sketching
• Analyzing Functions Part II: Maximums and Minimums
• Maximum and Minimum Problems
• Distance, Velocity, Acceleration, and Rectilinear Motion
• Related Rates
• The Mean-Value Theorem and L\'Hopital\'s Rule
• Linearization

Segment 02

Module 05 -Integration

• Area Approximation and Riemann Sums
• Introduction to the Definite Integral
• The Fundemental Theorem of Calculus
• Integrals and Antiderivatives
• Integration by Substitution
• The Definite Integral

Module 06 - Applications of Integrals

• Finding the Area Under and Between Curves
• Volume by Disks (Slicing)
• Average Value of a Function and Rectilinear Motion Revisited

Module 07 - Differential Equations and More Riemann Sums

• Differential Equations--An Introduction
• Initial Value Problems and Slow Fields
• Numerical Approximation Methods and Integrals

Module 08 - Supplemental Topics

• Exlporing the Graphs of f, Prime, and f Double Prime
• Relative Rates of Growth
• Using Calculus with Data in a Table
• Functions Defined by Integral

Course syllabus

Syllabus Calculus Honors

• Syllabus Calculus Honors

Materials required

For this course you need to secure the following textbook and materials (if lab kit is listed, check first the possibility of using your school lab prior to buying the lab kit):

Price

course fee: 567,- EUR / 13 500,- Kč

Student’s Experience

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