Calculus Essentials
Review the core ideas of single-variable calculus: limits, derivatives, graph interpretation, antiderivatives, integrals, and the common mistakes that trip learners up.
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Activities
Quiz52 Questions
Flashcards52 Cards
Study Notes6 Notes
Mind Map3 Maps
Modules
Learn in sequence
Start with the earlier modules and work forward. Each one builds on the last, so the course gets more advanced as you go.
1
Functions and Limits
Calculus is built on the idea of functions and the notion of a limit. This module lays the groundwork by reviewing function notation, domain and range, and then introduces the formal concept of a limit as the foundation for all that follows.
Foundations: Function Notation, Domain, and the Limit Concept
4 min • Background
Identifying Domain, Range, and Limits from Graphs
Quiz • 14 Questions
Key Terms: Domain, Range, Limit, Continuity
Flashcards • 21 Cards
Functions and Limits - Mind Map
Mind Map
2
Derivative Rules
The derivative measures instantaneous rates of change and is the central tool of differential calculus. This module covers the definition of the derivative as a limit, the power rule, product, quotient and chain rules, and derivatives of trigonometric functions.
Differentiation Toolkit: Power, Product, Quotient, and Chain Rules
3 min • Cheatsheet
Worked Examples: Finding the Next Step in Differentiation
Quiz • 9 Questions
Derivative Formulas for Polynomials and Trigonometric Functions
Flashcards • 19 Cards
3
Derivative Applications
Derivatives describe how quantities change, making them powerful tools for solving real-world problems. This module explores related rates, finding maxima and minima, and using the first and second derivative to understand the shape of a graph.
Practical Calculus: Related Rates, Optimization, and Graph Sketching
3 min • Mental Models And Frameworks
Connecting f, f_prime, and f_double_prime: Graph Interpretation Quiz
Quiz • 5 Questions
Related Rates and Optimization: Choose the Correct Setup
Quiz • 4 Questions
Derivative Applications - Mind Map
Mind Map
4
The Integral
Integration reverses differentiation and measures the accumulation of quantities, such as area under a curve. This module introduces the antiderivative, the definite integral as a limit of Riemann sums, and the Fundamental Theorem of Calculus that links the two branches of calculus.
From Antiderivatives to Area: The Fundamental Theorem of Calculus
3 min • Theory
Identifying the Correct Antiderivative and Applying the FTC
Quiz • 10 Questions
Integral Notation and the Fundamental Theorem
Flashcards • 12 Cards
5
Mastering Mistakes
Even the best calculus students slip on notation, algebra, and the chain rule. This final module synthesizes the key concepts from all previous modules by focusing on common errors and how to avoid them, from limit notation mistakes to misapplying the Fundamental Theorem.
Common Calculus Errors: Notation, Algebra, and Misapplied Rules
3 min • Summary
Spot the Error: Limits, Derivatives, and Integrals
Quiz • 10 Questions
Synthesis: A Case Study Connecting Limits, Derivatives, and Integrals
4 min • Case Study
Mastering Mistakes - Mind Map
Mind Map
Materials
List of Flashcards52 flashcards
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