Standard syllabus
Calculus III · Undergraduate · Math
Learning objectives from the Calculus III syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Calculus III — scope drawn from OpenStax Calculus Volume 3 (vectors, multivariable calculus, multiple integration, vector calculus).
Vectors and vector functions
- Vectors in two and three dimensions — Vectors in two and three dimensions; dot product, projections, and work
- Cross product, lines and planes in space, and vector-valued functions — Cross product, lines and planes in space, and vector-valued functions
Partial derivatives and optimization
- Functions of several variables — Functions of several variables
- Continuity in R^n — Continuity in R^n
- Partial derivatives and gradients — Partial derivatives and gradients
- Directional derivatives — Directional derivatives
- Tangent planes and linearization — Tangent planes and linearization
- The multivariable chain rule — The multivariable chain rule
- Lagrange multipliers — Lagrange multipliers
- Constrained optimization — Constrained optimization
Multiple integrals
- Double integrals over rectangles — Double integrals over rectangles
- General regions in the plane — General regions in the plane
- Double integrals in polar coordinates — Double integrals in polar coordinates; changing the order of integration
- Triple integrals in rectangular and cylindrical coordinates — Triple integrals in rectangular and cylindrical coordinates
- Spherical coordinates — Spherical coordinates
- Change of variables in multiple integrals — Change of variables in multiple integrals
- The Jacobian determinant — The Jacobian determinant
Vector calculus
- Vector fields and line integrals — Vector fields and line integrals
- Circulation — Circulation
- Fundamental theorem for line integrals — Fundamental theorem for line integrals
- Potential functions — Potential functions
- Green's theorem in the plane — Green's theorem in the plane
- Divergence (introduction) — Divergence (introduction)
- Surface integrals — Surface integrals
- The divergence theorem (introduction) — The divergence theorem (introduction)
- Stokes' theorem (introduction) — Stokes' theorem (introduction)
- Connections among the major theorems — Connections among the major theorems
Learning objectives
Click an objective for study materials.
Vectors and vector functions
- Vectors in two and three dimensions — Vectors in two and three dimensions; dot product, projections, and work
- Cross product, lines and planes in space, and vector-valued functions — Cross product, lines and planes in space, and vector-valued functions
Partial derivatives and optimization
- Functions of several variables — Functions of several variables
- Continuity in R^n — Continuity in R^n
- Partial derivatives and gradients — Partial derivatives and gradients
- Directional derivatives — Directional derivatives
- Tangent planes and linearization — Tangent planes and linearization
- The multivariable chain rule — The multivariable chain rule
- Lagrange multipliers — Lagrange multipliers
- Constrained optimization — Constrained optimization
Multiple integrals
- Double integrals over rectangles — Double integrals over rectangles
- General regions in the plane — General regions in the plane
- Double integrals in polar coordinates — Double integrals in polar coordinates; changing the order of integration
- Triple integrals in rectangular and cylindrical coordinates — Triple integrals in rectangular and cylindrical coordinates
- Spherical coordinates — Spherical coordinates
- Change of variables in multiple integrals — Change of variables in multiple integrals
- The Jacobian determinant — The Jacobian determinant
Vector calculus
- Vector fields and line integrals — Vector fields and line integrals
- Circulation — Circulation
- Fundamental theorem for line integrals — Fundamental theorem for line integrals
- Potential functions — Potential functions
- Green's theorem in the plane — Green's theorem in the plane
- Divergence (introduction) — Divergence (introduction)
- Surface integrals — Surface integrals
- The divergence theorem (introduction) — The divergence theorem (introduction)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Vectors and vector functions
Vectors in two and three dimensions; dot product, projections, and work
Coming soon - Partial derivatives and optimization
Functions of several variables
Coming soon - Multiple integrals
Double integrals over rectangles
Coming soon - Vector calculus
Vector fields and line integrals
Coming soon
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