Calculus Fundamentals
Introduces the foundational concepts of limits, derivatives, and integrals.
Description : Students gain a solid grounding in calculus by studying limits, continuity, differentiation, and basic integration. Through theoretical exploration and practical problem solving, the course builds an essential framework for further study in calculus.
Category : Math
Age : 12+
Difficulty Level : Normal
Curriculum :
Module 1: Calculus Foundations
Section 1: Revisiting Algebra and Functions
- Lesson 1: Algebra Refresher
- Module 1, Section 1, Lesson 1: Algebra Refresher
- Lesson 2: Functions and Graphs
- Module 1, Section 1, Lesson 2: Functions and Graphs
Section 2: Introduction to Calculus Concepts
- Lesson 1: What is Calculus?
- Module 1, Section 2, Lesson 1: What is Calculus?
- Lesson 2: The Language of Change
- Module 1, Section 2, Lesson 2: The Language of Change
Section 3: Understanding Mathematical Notations
- Lesson 1: Symbols and Terminology
- Module 1, Section 3, Lesson 1: Symbols and Terminology
- Lesson 2: Notation in Calculus
- Module 1, Section 3, Lesson 2: Notation in Calculus
Section 4: Problem-Solving Strategies in Math
- Lesson 1: Basic Problem-Solving Techniques
- Module 1, Section 4, Lesson 1: Basic Problem-Solving Techniques
- Lesson 2: Analyzing Mathematical Problems
- Module 1, Section 4, Lesson 2: Analyzing Mathematical Problems
Section 5: Preparing for Calculus
- Lesson 1: Developing Mathematical Thinking
- Module 1, Section 5, Lesson 1: Developing Mathematical Thinking
- Lesson 2: Building a Calculus Mindset
- Module 1, Section 5, Lesson 2: Building a Calculus Mindset
Module 2: Limits and Continuity
Section 1: Introduction to Limits
- Lesson 1: Concept of a Limit
- Module 2, Section 1, Lesson 1: Concept of a Limit
- Lesson 2: Approaching a Limit
- Module 2, Section 1, Lesson 2: Approaching a Limit
Section 2: Hands-on with Limits
- Lesson 1: Evaluating Simple Limits
- Module 2, Section 2, Lesson 1: Evaluating Simple Limits
- Lesson 2: Exploring Limits Graphically
- Module 2, Section 2, Lesson 2: Exploring Limits Graphically
Section 3: One-Sided Limits
- Lesson 1: Understanding Left-Hand Limits
- Module 2, Section 3, Lesson 1: Understanding Left-Hand Limits
- Lesson 2: Understanding Right-Hand Limits
- Module 2, Section 3, Lesson 2: Understanding Right-Hand Limits
Section 4: Continuity Basics
- Lesson 1: Defining Continuity
- Module 2, Section 4, Lesson 1: Defining Continuity
- Lesson 2: Types of Discontinuities
- Module 2, Section 4, Lesson 2: Types of Discontinuities
Section 5: Real-World Applications of Continuity
- Lesson 1: Continuity in Everyday Functions
- Module 2, Section 5, Lesson 1: Continuity in Everyday Functions
- Lesson 2: Practical Examples of Continuity
- Module 2, Section 5, Lesson 2: Practical Examples of Continuity
Module 3: Differentiation Concepts
Section 1: Derivatives as Rates of Change
- Lesson 1: Understanding Derivatives
- Module 3, Section 1, Lesson 1: Understanding Derivatives
- Lesson 2: Slope and Rate of Change
- Module 3, Section 1, Lesson 2: Slope and Rate of Change
Section 2: Rules of Differentiation Part 1
- Lesson 1: The Power Rule
- Module 3, Section 2, Lesson 1: The Power Rule
- Lesson 2: Sum and Difference Rules
- Module 3, Section 2, Lesson 2: Sum and Difference Rules
Section 3: Rules of Differentiation Part 2
- Lesson 1: The Product Rule
- Module 3, Section 3, Lesson 1: The Product Rule
- Lesson 2: The Quotient Rule Basics
- Module 3, Section 3, Lesson 2: The Quotient Rule Basics
Section 4: Derivatives of Common Functions
- Lesson 1: Differentiating Polynomials
- Module 3, Section 4, Lesson 1: Differentiating Polynomials
- Lesson 2: Differentiating Exponential and Logarithmic Functions
- Module 3, Section 4, Lesson 2: Differentiating Exponential and Logarithmic Functions
Section 5: Graphical Interpretation of Derivatives
- Lesson 1: Tangent Lines and Slopes
- Module 3, Section 5, Lesson 1: Tangent Lines and Slopes
- Lesson 2: Instantaneous Rate of Change
- Module 3, Section 5, Lesson 2: Instantaneous Rate of Change
Module 4: Techniques of Differentiation
Section 1: Implicit Differentiation Introduction
- Lesson 1: Understanding Implicit Functions
- Module 4, Section 1, Lesson 1: Understanding Implicit Functions
- Lesson 2: Differentiating Implicitly
- Module 4, Section 1, Lesson 2: Differentiating Implicitly
Section 2: Differentiation with Trigonometric Functions
- Lesson 1: Derivatives of Sine and Cosine
- Module 4, Section 2, Lesson 1: Derivatives of Sine and Cosine
- Lesson 2: Derivatives of Basic Trigonometric Functions
- Module 4, Section 2, Lesson 2: Derivatives of Basic Trigonometric Functions
Section 3: Chain Rule Essentials
- Lesson 1: Introducing the Chain Rule
- Module 4, Section 3, Lesson 1: Introducing the Chain Rule
- Lesson 2: Applying the Chain Rule
- Module 4, Section 3, Lesson 2: Applying the Chain Rule
Section 4: Higher Order Derivatives
- Lesson 1: Understanding Second Derivatives
- Module 4, Section 4, Lesson 1: Understanding Second Derivatives
- Lesson 2: Interpreting Concavity and Inflection Points
- Module 4, Section 4, Lesson 2: Interpreting Concavity and Inflection Points
Section 5: Connection with Graphing Techniques
- Lesson 1: Using Derivatives for Graph Sketching
- Module 4, Section 5, Lesson 1: Using Derivatives for Graph Sketching
- Lesson 2: Finding Critical Points and Analyzing Behavior
- Module 4, Section 5, Lesson 2: Finding Critical Points and Analyzing Behavior
Module 5: Introduction to Integration
Section 1: Understanding Integration
- Lesson 1: The Concept of an Integral
- Module 5, Section 1, Lesson 1: The Concept of an Integral
- Lesson 2: Basic Integral Notation and Terminology
- Module 5, Section 1, Lesson 2: Basic Integral Notation and Terminology
Section 2: Antiderivatives
- Lesson 1: Finding Antiderivatives
- Module 5, Section 2, Lesson 1: Finding Antiderivatives
- Lesson 2: Basic Techniques in Integration
- Module 5, Section 2, Lesson 2: Basic Techniques in Integration
Section 3: The Fundamental Theorem of Calculus
- Lesson 1: Statement of the Fundamental Theorem
- Module 5, Section 3, Lesson 1: Statement of the Fundamental Theorem
- Lesson 2: Connecting Differentiation and Integration
- Module 5, Section 3, Lesson 2: Connecting Differentiation and Integration
Section 4: Applications of Integration
- Lesson 1: Understanding Area Under a Curve
- Module 5, Section 4, Lesson 1: Understanding Area Under a Curve
- Lesson 2: Practical Examples of Integration Applications
- Module 5, Section 4, Lesson 2: Practical Examples of Integration Applications
Section 5: Techniques for Evaluating Integrals
- Lesson 1: Introduction to the Substitution Method
- Module 5, Section 5, Lesson 1: Introduction to the Substitution Method
- Lesson 2: Evaluating Definite Integrals
- Module 5, Section 5, Lesson 2: Evaluating Definite Integrals