Math Subjects
Calculus
Learn calculus through structured practice, worked examples, study guides, and step-by-step solutions covering limits, derivatives, integrals, series, and multivariable calculus.
Browse Calculus by Course
Explore calculus resources organized by course. Choose the level that best matches your current studies.
Introductory Calculus
Build the foundations needed for calculus through functions, limits, continuity, introductory derivatives, and basic integrals.
Explore Introductory Calculus →Calculus I
Limits, continuity, derivatives, applications of derivatives, definite and indefinite integrals, and the Fundamental Theorem of Calculus.
Explore Calculus I →Calculus II
Applications of integration, advanced integration techniques, improper integrals, sequences, infinite series, and parametric and polar topics.
Explore Calculus II →Calculus III / Multivariable Calculus
Vectors, multivariable functions, partial derivatives, multiple integrals, vector fields, and vector calculus.
Explore Calculus III →Introductory Calculus
Build the conceptual and algebraic foundations needed for a first calculus course, with emphasis on functions, limits, rates of change, and introductory integration.
Function Review
Domain, range, graphs, transformations, composition, and inverse functions.
Understanding Limits
Numerical, graphical, and algebraic approaches to the concept of a limit.
Limit Laws
Evaluating limits using algebraic properties, factoring, rationalization, and simplification.
Continuity
Continuous functions, discontinuities, and connections between limits and continuity.
Average & Instantaneous Rate of Change
Secant lines, tangent lines, and the motivation for derivatives.
Introduction to Derivatives
Derivatives as limits, slopes, and instantaneous rates of change.
Basic Differentiation
Constant, power, sum, difference, and elementary derivative rules.
Antiderivatives
Basic antiderivatives and the relationship between differentiation and integration.
Introduction to Definite Integrals
Accumulated change, area, and basic interpretations of definite integrals.
Free Introductory Calculus Resources
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Introductory Calculus Practice Packs
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Calculus I
Study limits, derivatives, applications of differentiation, definite and indefinite integrals, and the Fundamental Theorem of Calculus.
Limits
Algebraic, graphical, and numerical limits, one-sided limits, and limits at infinity.
Continuity
Continuity, discontinuities, and the Intermediate Value Theorem.
Derivative Definition
Difference quotients, tangent lines, and derivatives defined by limits.
Differentiation Rules
Power, product, quotient, and chain rules.
Implicit Differentiation
Differentiating implicitly defined relationships and finding tangent slopes.
Related Rates
Modeling relationships between changing quantities using derivatives.
Optimization
Maximum and minimum problems using derivative methods.
Curve Analysis
Critical points, monotonicity, concavity, extrema, and graph sketching.
Antiderivatives
Indefinite integrals, initial-value problems, and basic techniques.
Definite Integrals
Riemann sums, signed area, properties, and interpretation.
Fundamental Theorem of Calculus
Connecting derivatives and integrals through the Fundamental Theorem.
Substitution
Basic u-substitution for evaluating indefinite and definite integrals.
Free Calculus I Resources
Free worksheets, review exercises, and study materials will appear here as they are published.
Calculus I Practice Packs & Study Guides
Practice packs, worked solutions, review materials, and study guides will appear here when available.
Calculus II
Extend your understanding of integration through advanced techniques and applications, and study improper integrals, sequences, infinite series, parametric equations, and polar curves.
Applications of Integration
Area between curves, accumulated change, and geometric applications of definite integrals.
Volumes of Solids
Disk, washer, and shell methods for computing volumes of solids of revolution.
Integration by Parts
Applying the integration-by-parts formula to products of functions.
Trigonometric Integrals
Integrals involving powers and products of trigonometric functions.
Trigonometric Substitution
Using trigonometric substitutions to evaluate integrals involving radicals.
Partial Fractions
Decomposing rational functions and integrating the resulting expressions.
Improper Integrals
Infinite intervals, unbounded integrands, convergence, and divergence.
Sequences
Limits of sequences, monotonicity, boundedness, and convergence.
Infinite Series
Geometric series, telescoping series, convergence, and divergence.
Convergence Tests
Integral, comparison, ratio, root, and alternating-series tests.
Power & Taylor Series
Power series, intervals of convergence, Taylor series, and Maclaurin series.
Parametric & Polar Calculus
Parametric curves, polar coordinates, derivatives, arc length, and areas.
Free Calculus II Resources
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Calculus II Practice Packs & Study Guides
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Calculus III / Multivariable Calculus
Study functions of several variables, vectors, partial derivatives, multiple integrals, vector fields, and the fundamental ideas of vector calculus.
Vectors & Three-Dimensional Space
Vectors, dot products, cross products, lines, planes, and geometric representations in space.
Vector-Valued Functions
Curves in space, derivatives, integrals, velocity, acceleration, and arc length.
Functions of Several Variables
Domains, graphs, level curves, level surfaces, and multivariable limits.
Partial Derivatives
First- and higher-order partial derivatives and their interpretation.
Tangent Planes & Linear Approximation
Tangent planes, differentials, linearization, and local approximation.
Chain Rule
Multivariable chain rules, implicit differentiation, and related applications.
Directional Derivatives & Gradient
Directional change, gradient vectors, tangent directions, and level sets.
Optimization
Local extrema, critical points, second derivative tests, and constrained optimization.
Lagrange Multipliers
Optimization of multivariable functions subject to equality constraints.
Double Integrals
Iterated integrals, rectangular regions, general regions, and applications.
Triple Integrals
Integration over three-dimensional regions and applications to volume and mass.
Change of Coordinates
Polar, cylindrical, and spherical coordinates, including Jacobian factors.
Vector Fields
Vector fields, conservative fields, potentials, and geometric interpretation.
Line Integrals
Scalar and vector line integrals, work, circulation, and path independence.
Surface Integrals
Parametric surfaces, surface area, flux, and vector surface integrals.
Green’s, Stokes’ & Divergence Theorems
Fundamental integral theorems connecting derivatives, circulation, flux, and boundaries.
Free Calculus III Resources
Free worksheets, review exercises, examples, and study materials will appear here as they are published.
Calculus III Practice Packs & Study Guides
Practice packs, worked problem sets, review materials, and study guides will appear here when available.