How this course works
The chapters and lessons below are the fixed course structure. When you start, LearnLive teaches each lesson interactively and adapts examples, pacing, and questions to you.
Complete syllabus
Every chapter and lesson
- 01
Chapter 1 · 3 lessons
Limits & Continuity
- 1.1
The idea of a limit
9 min · Quick check
Lesson goal: By the end you can understand the concept of a limit and its significance in calculus.
- Define a limit and its notation.
- Explain the importance of limits in calculus.
- Introduce the concept of approaching values.
- 1.2
Computing limits
9 min · Quick check
Lesson goal: By the end you can compute limits using various techniques.
- Identify different methods for computing limits.
- Apply algebraic techniques to find limits.
- Use the Squeeze Theorem for limits.
- 1.3
Continuity & the IVT
8 min · Quick check
Lesson goal: By the end you can explain continuity and apply the Intermediate Value Theorem (IVT).
- Define continuity at a point and on an interval.
- Discuss the conditions for a function to be continuous.
- Explain the Intermediate Value Theorem and its implications.
- 1.1
- 02
Chapter 2 · 3 lessons
The Derivative
- 2.1
Rates of change & the derivative
9 min · Quick check
Lesson goal: By the end you can explain the concept of rates of change and how it relates to the derivative.
- Define the concept of a rate of change.
- Explain how the derivative represents the instantaneous rate of change.
- Discuss the relationship between average rate of change and instantaneous rate of change.
- 2.2
Differentiation rules
9 min · Quick check
Lesson goal: By the end you can apply differentiation rules to find derivatives of various functions.
- Identify and apply the power rule for differentiation.
- Use the product rule and quotient rule for finding derivatives.
- Differentiate basic trigonometric, exponential, and logarithmic functions.
- 2.3
The chain rule
8 min · Quick check
Lesson goal: By the end you can utilize the chain rule to differentiate composite functions.
- Define the chain rule and its significance in differentiation.
- Apply the chain rule to find the derivative of composite functions.
- Practice using the chain rule in various examples.
- 2.1
- 03
Chapter 3 · 3 lessons
Applying Derivatives
- 3.1
Related rates
9 min · Quick check
Lesson goal: By the end you can understand and apply the concept of related rates in calculus.
- Define related rates and their significance in calculus.
- Identify scenarios where related rates can be applied.
- Set up equations relating different quantities.
- Differentiate with respect to time to find rates of change.
- Solve related rates problems step-by-step.
- 3.2
Extrema & curve analysis
9 min · Quick check
Lesson goal: By the end you can analyze functions to find extrema and understand curve behavior.
- Define extrema and their importance in calculus.
- Learn how to find critical points of a function.
- Apply the first derivative test to determine increasing and decreasing intervals.
- Use the second derivative test to identify concavity and points of inflection.
- Analyze the overall behavior of a function using its derivatives.
- 3.3
Optimization
8 min · Quick check
Lesson goal: By the end you can apply optimization techniques to solve real-world problems.
- Define optimization and its relevance in various fields.
- Identify the objective function and constraints in a problem.
- Use derivatives to find maximum and minimum values.
- Set up and solve optimization problems step-by-step.
- Interpret the results in the context of the original problem.
- 3.1
- 04
Chapter 4 · 3 lessons
The Integral
- 4.1
Antiderivatives
8 min · Quick check
Lesson goal: By the end you can identify and compute antiderivatives of basic functions.
- Understand the definition of an antiderivative.
- Learn common antiderivatives of polynomial, exponential, and trigonometric functions.
- Apply the concept of antiderivatives to solve simple differential equations.
- 4.2
The definite integral
9 min · Quick check
Lesson goal: By the end you can evaluate definite integrals using various techniques.
- Define the definite integral and its properties.
- Learn the relationship between the definite integral and the area under a curve.
- Apply the Fundamental Theorem of Calculus to evaluate definite integrals.
- 4.3
The Fundamental Theorem
9 min · Quick check
Lesson goal: By the end you can explain and apply the Fundamental Theorem of Calculus.
- Understand the two parts of the Fundamental Theorem of Calculus.
- Learn how to connect differentiation and integration through the theorem.
- Apply the theorem to solve problems involving definite integrals.
- 4.1
- 05
Chapter 5 · 3 lessons
Applying Integration
- 5.1
Substitution
9 min · Quick check
Lesson goal: By the end you can apply the substitution method to evaluate integrals.
- Understand the concept of substitution in integration.
- Identify appropriate substitutions for integrals.
- Perform the substitution and simplify the integral.
- 5.2
Area between curves
8 min · Quick check
Lesson goal: By the end you can calculate the area between two curves using integration.
- Define the area between curves and its significance.
- Set up the integral for the area between two curves.
- Evaluate the integral to find the area.
- 5.3
Average value & applications
8 min · Quick check
Lesson goal: By the end you can determine the average value of a function and apply it to real-world scenarios.
- Define the average value of a function over an interval.
- Set up the integral to calculate the average value.
- Apply the average value concept to practical problems.
- 5.1