Calculus (University & High School Level) Inspired by IB MATH AAHL & TU/e's Calculus Variant 2 Course (2WBB0)

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From 33 € /h

This course offers a comprehensive introduction to calculus, emphasizing the foundational mathematical concepts and tools essential for further studies in mathematics and related fields. Topics include limits, differentiation, and integration, approached with clarity and structure. The course is designed to begin from the absolute fundamentals—starting with numbers and functions—and progressively build up to advanced topics such as optimization, related rates, and linear differential equations.

Course Outline:
1.1 Numbers, Functions, (In-)equalities, Polynomials, Rational Functions
1.2 Trigonometric Functions, Vectors in Two and Three Dimensions
1.3 Limits, Continuity, Introduction to Differentiation
1.4 Differentiation Rules and Theorems: Power Rule, Product Rule, Chain Rule
1.5 Derivatives of Exponential, Logarithmic, and Trigonometric Functions, Taylor Series
1.6 Implicit Differentiation and Derivatives of Inverse Functions
1.7 Intermediate Value Theorem, Critical Points, Maxima and Minima
1.8 First and Second Derivative Tests, Inflection Points
1.9 Antiderivatives, Indefinite Integrals, Integration by Substitution and by Parts
1.10 Definite Integrals and Their Applications (e.g., Area Between Curves, Related Rates)
1.11 Optimization, Related Rates, and Linear Differential Equations

This syllabus is inspired by the IB Mathematics: Analysis and Approaches HL curriculum and incorporates elements from the Technical University of Eindhoven’s Calculus Variant 2 Course (2WBBO).

Extra information

Flexibility and Personalization:
This course is designed with adaptability in mind, ensuring it meets the unique needs of each student. Topics can be explored in greater depth where needed, and the style of instruction can be tailored to align with the student’s preferred pace and learning approach. The ultimate goal is to create a supportive, engaging, and effective learning environment.

The first session will be dedicated to setting clear goals and understanding what the student hopes to achieve through these tutoring sessions. Together, we will develop a personalized study plan that systematically addresses all key areas of calculus—placing additional focus on topics where the student may feel less confident—while maintaining a strong emphasis on clarity, efficiency, and progress.

Location

Online from Netherlands

Age

Teenagers (13-17 years old)

Adults (18-64 years old)

Seniors (65+ years old)

Student level

Beginner

Intermediate

Advanced

Duration

60 minutes

The class is taught in

Dutch

English

Skills

Calculus

Math

High school entrance prep

Availability of a typical week

(GMT -05:00)

New York

Online via webcam

Mon

Tue

Wed

Thu

Fri

Sat

Sun

00-04

04-08

08-12

12-16

16-20

20-24

Mathematics for Pre-School/ Mathematics for Middle School/IB MYP/ Mathematics for IB (AASL or AAHL)

26 € /h

Hey There!

About Me:
I am Shrika, a former IB student who has recently passed IB in 2024. Of the 6 subjects I have taken, I am most profound in mathematics followed by geography at higher level. Currently I am a university student at the Technical University of Eindhoven pursuing Data Science at a bachelor's level.

What I offer:
Considering the challenging math I have encountered during my IB years along with my current university course, I am quite comfortable with mathematics and am looking to provide mathematics lessons for individuals who are especially in the IB curriculum. I can provide classes for Math AISL , AASL and AAHL students. Of course, due to the nature of the course, I am proficient to teach students who are younger such as in primary or secondary school as IB is a course for high school students.

What the course offers:
As I have hinted out in the previous section, the course is tailored to the student itself. IB students don't need to worry as I have materials and classes already prepared. If you are a student not following the IB curriculum but can provide a textbook in mathematics for me to teach from, that is possible too! Feel free to contact me to discuss further details!

Benoit

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This class aims to provide an overview of calculus and linear algebra and focuses on the fundamental mathematical tools and concepts, such as limits, differentiation, and integration. Building on these basic concepts, we will review methods for solving problems related to optimization, linear differential equations, and matrix algebra.

Outline of the course:
1. Calculus:
1.1 Limits of functions
1.2 Continuity, types of discontinuities, intermediate value theorem
1.3 Differentiation (or derivative), slope, secant, tangent
1.4 Rules and theorems for differentiation, power rule, product rule, chain rule
1.5 Derivatives of exp, log, and trigonometric functions
1.6 Implicit differentiation and derivative of inverse functions
1.7 Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function
1.8 First and second derivative tests, inflection points
1.9 Anti-derivative, indefinite integral, integration by substitution, integration by parts
1.10 Definite integral and its application (area between curves, application in physics)\
1.11 Optimization and linear differential equations

2. Linear Algebra:
2.1 Vectors and scalars in Euclidean space, vector arithmetic, scalar product, cross product
2.2 Equations for lines and planes, vector spaces, linear independence, span, basis, dimension
2.3 Linear transformations, coordinates, and representation of linear transformations by matrices
2.4 Matrix operations: matrix multiplication, transpose, determinant, inverse, and Hermitian conjugate
2.5 Systems of linear equations, Gaussian elimination
2.6 Eigenvalues and eigenvectors
2.7 Range, kernel, and rank-nullity theorem

and many more...

*Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).

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Mmh

5.0

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Differentiation: First, find the domain of the functions, whether they are polynomial, radical, rational, intrinsic, logarithmic, or exponential functions.
Second: Studying the limits of the previously mentioned functions
Third: Function connection
Fourth: Derivation (first and second derivatives)
Fourth: Critical points and the study of function variations

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