A Rapid Introduction To Calculus
Master the Fundamentals of Calculus in No Time!
Updated on Mar, 2026
Language - English
Teaching and Academics ,Math,Calculus
Lectures -63
Resources -61
Duration -8 hours
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Course Description
Below is the breakdown of the course curriculum:
1. Mathematical Preliminaries
- Review of elementary algebraic concepts and techniques
- Introduction to mathematical notation and terminology
- Definition and properties of functions
- Types of functions: linear, quadratic, exponential, trigonometric, and others
- Notation for functions and basic operations with functions
- Introduction to the concept of a limit
- Finding limits of functions algebraically and graphically
- Intuitive definition of a limit
- Definition of continuity
- Detective work to find points of discontinuity
- Intermediate Value Theorem
- Introduction to the derivative of a function
- Rules for differentiating mathematical expressions
- Concept of instantaneous rate of change
- Rolle's Theorem and the Mean Value Theorem
- Applications of the Mean Value Theorem
- Relationship between the derivative and what functions look like
- What functions look like in terms of their first and second derivatives
- Graphs of functions
- Local extrema and inflection points
- Introduction to the concept of integration
- Calculation of definite and indefinite integrals
- Basic techniques of integration, including substitution and integration by parts
Goals
The following are the course goals:
Learn fundamental concepts of Pre-Calculus and Calculus: Build a strong foundation by mastering essential topics that lead to a clear understanding of calculus concepts.
Gain an intuitive and formal understanding of limits, continuous functions, derivatives, and integrals: Explore both the intuitive and technical aspects of key calculus ideas, such as how functions behave, how rates of change are measured, and how areas and accumulations are calculated.
Understand why Calculus is important: Appreciate the role of calculus in various fields of science, engineering, economics, and more, and how it forms the backbone of modern mathematical applications.
Gain an intuitive and formal understanding of limits, continuous functions, derivatives, and integrals: Explore both the intuitive and technical aspects of key calculus ideas, such as how functions behave, how rates of change are measured, and how areas and accumulations are calculated.
Prerequisites
To enroll in this course, you should feel confident in solving basic equations, such as 2x + 3 = 0, and have a basic understanding of arithmetic. All other concepts will be introduced from the basics.
Curriculum
Check out the detailed breakdown of what’s inside the course
Introduction
2 Lectures
-
Introduction
01:35
01:35
-
History and Motivation
09:33
09:33
Mathematical Preliminaries
8 Lectures
Functions
16 Lectures
Limits
5 Lectures
Continuous Functions
3 Lectures
Differentiable Functions
14 Lectures
Main Theorems of the Derivative
4 Lectures
Integration
11 Lectures
Instructor Details
Ron Erez
Dr. Ron Erez has been programming for over 30 years and has always been amazed by the creativity and satisfaction of writing computer programs. Ron is also an experienced teacher having taught mathematics, computer science and English literature from middle school to university level courses.
In Ron's free time he is out cooking, cleaning, skateboarding and just living life.
I hope you enjoy taking my course as much as I enjoyed teaching it.
Good luck on your journey to learn something new and exciting.
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