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Who this course is for:
- Anyone eager to learn Calculus.
- Individuals looking for a rapid, comprehensive overview of core Calculus concepts.
- Learners with minimal mathematical background interested in building their Calculus knowledge.
What you’ll learn:
- Master the essential concepts in Pre-Calculus and Calculus.
- Develop skills in presenting formal mathematical proofs.
- Build both intuitive and rigorous understanding of limits, continuity, derivatives, and integrals.
- Appreciate the real-world significance and applications of Calculus.
Requirements:
- Basic algebra skills: You should be able to solve equations like 2x + 3 = 0 before starting this online calculus course.
- Curiosity and engagement
“A Rapid Introduction To Calculus” is an expertly designed online calculus course that provides students with a foundational understanding of the key concepts and techniques in Calculus. This course is ideal for those who need a solid introduction to how to learn Calculus efficiently without an exhaustive dive into every detail of the subject.
Course Curriculum:
- Mathematical Preliminaries
- Review essential algebraic concepts and techniques.
- Learn mathematical notation and terminology for Calculus.
- Functions
- Define and understand core properties of functions.
- Explore key function types, including linear, quadratic, exponential, and trigonometric.
- Master function notation and basic operations with functions.
- Limits
- Understand the foundational concept of limits in Calculus.
- Practice calculating limits algebraically and graphically.
- Gain an intuitive grasp of the idea of limits.
- Continuous Functions
- Define and explore continuity in functions.
- Learn to identify and analyze points of discontinuity.
- Apply the Intermediate Value Theorem.
- Differentiable Functions
- Introduction to the derivative and its significance.
- Calculate derivatives using fundamental rules.
- Understand the concept of instantaneous rate of change.
- Core Theorems in Differential Calculus
- Discover Rolle’s Theorem and the Mean Value Theorem.
- Learn applications of the Mean Value Theorem.
- Examine the connection between derivatives and function behavior.
- Graphing Functions
- Analyze functions using first and second derivatives.
- Develop skills for sketching graphs of functions.
- Identify critical points and inflection points for better graph interpretation.
- Integration
- Introduction to integration as a fundamental concept.
- Calculate both definite and indefinite integrals.
- Practice basic techniques of integration, including substitution and integration by parts.
This online calculus course is structured to help students understand how to learn Calculus through clear explanations, proven learning methods, and real-world examples. It’s perfect for those who need to quickly grasp the fundamentals for academic or professional use.
Ready to become a lifelong learner? My courses are designed to inspire and educate.
Our Promise to You
By the end of this course, you will have learned essential calculus concepts and techniques to confidently solve foundational problems.
10 Day Money Back Guarantee. If you are unsatisfied for any reason, simply contact us and we’ll give you a full refund. No questions asked.
Get started today!
Course Curriculum
| Section 1 - Introduction | |||
| Introduction | 00:00:00 | ||
| History And Motivation | 00:00:00 | ||
| Section 2 - Mathematical Preliminaries | |||
| Set Theory Part 1 | 00:00:00 | ||
| Set Theory Part 2 | 00:00:00 | ||
| Linear Functions And Linear Equations | 00:00:00 | ||
| Quadratic Functions And Quadratic Equations | 00:00:00 | ||
| Important Algebraic Identities | 00:00:00 | ||
| Factoring Trinomials | 00:00:00 | ||
| Inequalities | 00:00:00 | ||
| Absolute Value And Distance | 00:00:00 | ||
| Section 3 - Functions | |||
| What Is A Function? | 00:00:00 | ||
| Domain And Range Of A Function + Examples | 00:00:00 | ||
| Domain Solution To Homework | 00:00:00 | ||
| Monotone Functions | 00:00:00 | ||
| Monotone Functions Exercise | 00:00:00 | ||
| Injections (One-To-One Functions) | 00:00:00 | ||
| Image Of A Function | 00:00:00 | ||
| Surjections (Onto Function) | 00:00:00 | ||
| Function Composition | 00:00:00 | ||
| Inverse Functions | 00:00:00 | ||
| Bounded Functions | 00:00:00 | ||
| Even And Odd Functions | 00:00:00 | ||
| Polynomials And Rational Functions | 00:00:00 | ||
| Exponents And Logarithms | 00:00:00 | ||
| Trigonometric Functions | 00:00:00 | ||
| Elementary Functions | 00:00:00 | ||
| Section 4 - Limits | |||
| What Is A Limit? | 00:00:00 | ||
| Examples Of Limits | 00:00:00 | ||
| One Sided Limits | 00:00:00 | ||
| Infinite Limits | 00:00:00 | ||
| Limit Arithmetic | 00:00:00 | ||
| Section 5 - Continuous Functions | |||
| Continuous Functions | 00:00:00 | ||
| Intermediate Value Theorem | 00:00:00 | ||
| Roots Of Polynomials Of Odd Degree | 00:00:00 | ||
| Section 6 - Differentiable Functions | |||
| Intuition And Motivations For The Notion Of Differentiable Functions | 00:00:00 | ||
| Definition Of Differentiable Functions And Examples | 00:00:00 | ||
| An Example Of A Continuous Non-differentiable Function | 00:00:00 | ||
| An Example Of A Continuous Non-differentiable Function (Continued) | 00:00:00 | ||
| Not Every Elementary Function Is Differentiable | 00:00:00 | ||
| Every Differentiable Function Is Continuous | 00:00:00 | ||
| Derivative Notations | 00:00:00 | ||
| Standard Derivatives | 00:00:00 | ||
| Rules Of Differentiation | 00:00:00 | ||
| Derivative Of An Inverse Function | 00:00:00 | ||
| Derivation Of The Derivative Of logₐx | 00:00:00 | ||
| Derivative Of Inverse Of xⁿ | 00:00:00 | ||
| Differentiable Functions And Monotonicity | 00:00:00 | ||
| Proving Inequalities Using The Derivative Of A Function | 00:00:00 | ||
| Section 7 - Main Theorems of Derivative | |||
| Fermat’s Theorem | 00:00:00 | ||
| Rolle’s Theorem | 00:00:00 | ||
| Lagrange’s Theorem | 00:00:00 | ||
| Rolle’s Theorem As A Special Case Of Lagrange’s Theorem | 00:00:00 | ||
| Section 8 - Integration | |||
| Motivation Of Definite And Indefinite Integrals | 00:00:00 | ||
| Anti-derivative | 00:00:00 | ||
| Indefinite Integral | 00:00:00 | ||
| Integration Examples | 00:00:00 | ||
| Solution To Integral Homework | 00:00:00 | ||
| Integration By Substitution | 00:00:00 | ||
| Integration By Parts | 00:00:00 | ||
| INTEGRATION EXERCISE 1 | 00:00:00 | ||
| INTEGRATION EXERCISE 2 | 00:00:00 | ||
| INTEGRATION EXERCISE 3 | 00:00:00 | ||
| INTEGRATION EXERCISE 4 – Part 1 | 00:00:00 | ||
| INTEGRATION EXERCISE 4 – Part 2 | 00:00:00 | ||
About This Course
Who this course is for:
- Anyone eager to learn Calculus.
- Individuals looking for a rapid, comprehensive overview of core Calculus concepts.
- Learners with minimal mathematical background interested in building their Calculus knowledge.
What you’ll learn:
- Master the essential concepts in Pre-Calculus and Calculus.
- Develop skills in presenting formal mathematical proofs.
- Build both intuitive and rigorous understanding of limits, continuity, derivatives, and integrals.
- Appreciate the real-world significance and applications of Calculus.
Requirements:
- Basic algebra skills: You should be able to solve equations like 2x + 3 = 0 before starting this online calculus course.
- Curiosity and engagement
“A Rapid Introduction To Calculus” is an expertly designed online calculus course that provides students with a foundational understanding of the key concepts and techniques in Calculus. This course is ideal for those who need a solid introduction to how to learn Calculus efficiently without an exhaustive dive into every detail of the subject.
Course Curriculum:
- Mathematical Preliminaries
- Review essential algebraic concepts and techniques.
- Learn mathematical notation and terminology for Calculus.
- Functions
- Define and understand core properties of functions.
- Explore key function types, including linear, quadratic, exponential, and trigonometric.
- Master function notation and basic operations with functions.
- Limits
- Understand the foundational concept of limits in Calculus.
- Practice calculating limits algebraically and graphically.
- Gain an intuitive grasp of the idea of limits.
- Continuous Functions
- Define and explore continuity in functions.
- Learn to identify and analyze points of discontinuity.
- Apply the Intermediate Value Theorem.
- Differentiable Functions
- Introduction to the derivative and its significance.
- Calculate derivatives using fundamental rules.
- Understand the concept of instantaneous rate of change.
- Core Theorems in Differential Calculus
- Discover Rolle’s Theorem and the Mean Value Theorem.
- Learn applications of the Mean Value Theorem.
- Examine the connection between derivatives and function behavior.
- Graphing Functions
- Analyze functions using first and second derivatives.
- Develop skills for sketching graphs of functions.
- Identify critical points and inflection points for better graph interpretation.
- Integration
- Introduction to integration as a fundamental concept.
- Calculate both definite and indefinite integrals.
- Practice basic techniques of integration, including substitution and integration by parts.
This online calculus course is structured to help students understand how to learn Calculus through clear explanations, proven learning methods, and real-world examples. It’s perfect for those who need to quickly grasp the fundamentals for academic or professional use.
Ready to become a lifelong learner? My courses are designed to inspire and educate.
Our Promise to You
By the end of this course, you will have learned essential calculus concepts and techniques to confidently solve foundational problems.
10 Day Money Back Guarantee. If you are unsatisfied for any reason, simply contact us and we’ll give you a full refund. No questions asked.
Get started today!
Course Curriculum
| Section 1 - Introduction | |||
| Introduction | 00:00:00 | ||
| History And Motivation | 00:00:00 | ||
| Section 2 - Mathematical Preliminaries | |||
| Set Theory Part 1 | 00:00:00 | ||
| Set Theory Part 2 | 00:00:00 | ||
| Linear Functions And Linear Equations | 00:00:00 | ||
| Quadratic Functions And Quadratic Equations | 00:00:00 | ||
| Important Algebraic Identities | 00:00:00 | ||
| Factoring Trinomials | 00:00:00 | ||
| Inequalities | 00:00:00 | ||
| Absolute Value And Distance | 00:00:00 | ||
| Section 3 - Functions | |||
| What Is A Function? | 00:00:00 | ||
| Domain And Range Of A Function + Examples | 00:00:00 | ||
| Domain Solution To Homework | 00:00:00 | ||
| Monotone Functions | 00:00:00 | ||
| Monotone Functions Exercise | 00:00:00 | ||
| Injections (One-To-One Functions) | 00:00:00 | ||
| Image Of A Function | 00:00:00 | ||
| Surjections (Onto Function) | 00:00:00 | ||
| Function Composition | 00:00:00 | ||
| Inverse Functions | 00:00:00 | ||
| Bounded Functions | 00:00:00 | ||
| Even And Odd Functions | 00:00:00 | ||
| Polynomials And Rational Functions | 00:00:00 | ||
| Exponents And Logarithms | 00:00:00 | ||
| Trigonometric Functions | 00:00:00 | ||
| Elementary Functions | 00:00:00 | ||
| Section 4 - Limits | |||
| What Is A Limit? | 00:00:00 | ||
| Examples Of Limits | 00:00:00 | ||
| One Sided Limits | 00:00:00 | ||
| Infinite Limits | 00:00:00 | ||
| Limit Arithmetic | 00:00:00 | ||
| Section 5 - Continuous Functions | |||
| Continuous Functions | 00:00:00 | ||
| Intermediate Value Theorem | 00:00:00 | ||
| Roots Of Polynomials Of Odd Degree | 00:00:00 | ||
| Section 6 - Differentiable Functions | |||
| Intuition And Motivations For The Notion Of Differentiable Functions | 00:00:00 | ||
| Definition Of Differentiable Functions And Examples | 00:00:00 | ||
| An Example Of A Continuous Non-differentiable Function | 00:00:00 | ||
| An Example Of A Continuous Non-differentiable Function (Continued) | 00:00:00 | ||
| Not Every Elementary Function Is Differentiable | 00:00:00 | ||
| Every Differentiable Function Is Continuous | 00:00:00 | ||
| Derivative Notations | 00:00:00 | ||
| Standard Derivatives | 00:00:00 | ||
| Rules Of Differentiation | 00:00:00 | ||
| Derivative Of An Inverse Function | 00:00:00 | ||
| Derivation Of The Derivative Of logₐx | 00:00:00 | ||
| Derivative Of Inverse Of xⁿ | 00:00:00 | ||
| Differentiable Functions And Monotonicity | 00:00:00 | ||
| Proving Inequalities Using The Derivative Of A Function | 00:00:00 | ||
| Section 7 - Main Theorems of Derivative | |||
| Fermat’s Theorem | 00:00:00 | ||
| Rolle’s Theorem | 00:00:00 | ||
| Lagrange’s Theorem | 00:00:00 | ||
| Rolle’s Theorem As A Special Case Of Lagrange’s Theorem | 00:00:00 | ||
| Section 8 - Integration | |||
| Motivation Of Definite And Indefinite Integrals | 00:00:00 | ||
| Anti-derivative | 00:00:00 | ||
| Indefinite Integral | 00:00:00 | ||
| Integration Examples | 00:00:00 | ||
| Solution To Integral Homework | 00:00:00 | ||
| Integration By Substitution | 00:00:00 | ||
| Integration By Parts | 00:00:00 | ||
| INTEGRATION EXERCISE 1 | 00:00:00 | ||
| INTEGRATION EXERCISE 2 | 00:00:00 | ||
| INTEGRATION EXERCISE 3 | 00:00:00 | ||
| INTEGRATION EXERCISE 4 – Part 1 | 00:00:00 | ||
| INTEGRATION EXERCISE 4 – Part 2 | 00:00:00 | ||
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