Introduction to Calculus & Functions

Course Overview

This course offers a comprehensive introduction to the key concepts of calculus and functions.
Designed for students looking to build a strong mathematical foundation, it covers function transformations, limits, derivatives, and integrals. Tailored for students eager to build a strong mathematical foundation.

Course Content

Function
Transformations
Limits
Derivatives, and
Integrals.

Course Details:

Start Date: 16th January 2025
Duration: 8 Weeks
Classes per Week: 2 (Each 90 minutes)
Course Fee: 660 CHF
Delivery: 100% Online
Language: English
Internet access and an email address are required.

Weeks 1 & 2: Functions Review

Class 1: Function Notation & Graphing

Function notation and graphing techniques
Types of functions: linear, quadratic, cubic, polynomials, logarithmic, exponential, trigonometric
Intercepts and function intersections
Examples & Exercises

Class 2: Function Transformations

Function transformations: displacement, symmetries, scaling
Absolute value transformations
Using technology to model functions
Examples & Exercises

Weeks 3 & 4: Introduction to Calculus – Asymptotes, Limits, and Derivatives

Class 3: Conceptual Introduction to Limits

Limits and their role in calculus
Understanding asymptotes
Derivative as the instantaneous rate of change
Interpreting the sign of the derivative: growth and decrease
Examples & Exercises

Class 4: Tangent Lines and Derivatives

Deriving the tangent line equation
Understanding second derivatives and their role in analyzing maxima, minima, and inflection points
Basic differentiation rules
Examples & Exercises

Weeks 5 & 6: Differential Calculus and Introduction to Integral Calculus

Class 5: Advanced Differentiation Techniques

Product rule, quotient rule, chain rule
Implicit differentiation
Taylor and McLaurin's theorems
Examples & Exercises

Class 6: Introduction to Integrals

Geometric interpretation: area under a curve
Fundamental Theorem of Calculus: integration as anti-differentiation
Direct integration techniques for basic functions
Examples & Exercises

Weeks 7 & 8: Integral Calculus

Class 7: Integration Techniques

Substitution, integration by parts, reverse chain rule
Cyclic integrals and applications
Examples & Exercises

Class 8: Applications of Integration and Differentiation

Physics applications: solving SUVAT equations and kinematics problems
Volumes of solids of revolution (x and y axes)
Examples & Exercises

Why Choose This Course?

✔ Comprehensive curriculum covering key calculus topics.
✔ Blends theoretical understanding with practical exercises.
✔ Suitable for students aiming to strengthen their mathematical foundation.
✔ Learn at Your Own Pace: Flexible, 100% online learning, accessible anytime, anywhere.

Ready to Strengthen Your Math Skills?

💻 Enroll Today and unlock the key to mastering mathematics for real-world success!

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Accreditation & Certification

Lecturer: Carlos Morales López

Carlos Morales López holds a degree in Physics, a degree in Mathematics, and a Master’s in Education, all from the Complutense University of Madrid. He has contributed to research as part of the interdisciplinary Complex Systems Group (GISC) at the same university and has taught in various international schools across Turkey, Switzerland, and Spain.

Carlos is also the founder and former director of the Inspiring Science Association, where he organized four editions of an international science summer camp. Currently, he is pursuing another Master’s degree and conducting research on giftedness and talented education.

Graduate Benefits

Completing a mathematics course offers key benefits, including enhanced critical thinking, problem-solving, and analytical skills. It strengthens logical reasoning, which is valuable across fields like science, engineering, finance, and technology. For students, it prepares for advanced studies, while for professionals, it sharpens quantitative and data interpretation skills essential in modern workplaces.

Professional Development

Our programs are designed to give you the edge to excel on your profession with advanced knowledge.

Quality Education

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Alumni

We have a global pool of alumni from all eh parts of the world who are excelling on their leadership journey.