Standard syllabus
Calculus II · Undergraduate · Math
Learning objectives from the Calculus II 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 II — scope drawn from OpenStax Calculus Volume 2 (techniques of integration, sequences and series, polar/parametric intro).
Integration techniques
- Integration by parts (classic LIATE method) — Use LIATE to choose u and dv; apply ∫u dv = uv − ∫v du for products of algebraic, exponential, log, and trig factors.
- Integration by parts (DI / tabular method) — Organize repeated differentiation and integration in a DI table; apply sign pattern for products that need multiple IBP steps.
- Trigonometric integrals — Integrate powers of sine and cosine, and products of sin/cos using identities and reduction.
- Trigonometric substitution — Trigonometric substitution
- Partial fraction decomposition — Partial fraction decomposition
- Integration of rational functions — Integration of rational functions
- General substitution strategies — General substitution strategies
- Improper integrals — Improper integrals
- Tests for convergence — Tests for convergence
Applications of integration
- Applications of integration — Applications of integration
- Center of mass — Center of mass
Parametric and polar calculus
- Parametric equations — Parametric equations
- Calculus with parametric curves — Calculus with parametric curves
- Polar coordinates — Polar coordinates
- Slope in polar form — Slope in polar form
Sequences and series
- Sequences and limits of sequences — Define sequences, find limits, and classify bounded/monotonic behavior.
- Introduction to infinite series — Define partial sums and convergence of infinite series; geometric and telescoping examples.
- Integral and comparison tests — Apply the integral test and direct comparison test for positive-term series.
- Limit comparison, ratio, and root tests — Use limit comparison, ratio, and root tests to decide absolute convergence.
- Alternating series test — Apply the alternating series (Leibniz) test and estimate remainder.
- Power series, radius and interval of convergence — Power series, radius and interval of convergence
- Taylor and Maclaurin series — Taylor and Maclaurin series; Taylor polynomial approximation and error
Introductory differential equations
- Introduction to differential equations: direction fields and modeling — Introduction to differential equations: direction fields and modeling
- Separable differential equations — Separable differential equations
- First-order linear differential equations — First-order linear differential equations
Learning objectives
Click an objective for study materials.
Integration techniques
- Use LIATE to choose u and dv — Use LIATE to choose u and dv; apply ∫u dv = uv − ∫v du for products of algebraic, exponential, log, and trig factors.
- Organize repeated differentiation and integration in a DI table — Organize repeated differentiation and integration in a DI table; apply sign pattern for products that need multiple IBP steps.
- Integrate powers of sine and cosine, and products of sin/cos using id... — Integrate powers of sine and cosine, and products of sin/cos using identities and reduction.
- Trigonometric substitution — Trigonometric substitution
- Partial fraction decomposition — Partial fraction decomposition
- Integration of rational functions — Integration of rational functions
- General substitution strategies — General substitution strategies
- Improper integrals — Improper integrals
Applications of integration
- Applications of integration — Applications of integration
- Center of mass — Center of mass
Parametric and polar calculus
- Parametric equations — Parametric equations
- Calculus with parametric curves — Calculus with parametric curves
- Polar coordinates — Polar coordinates
- Slope in polar form — Slope in polar form
Sequences and series
- Define sequences, find limits, and classify bounded/monotonic behavior. — Define sequences, find limits, and classify bounded/monotonic behavior.
- Define partial sums and convergence of infinite series — Define partial sums and convergence of infinite series; geometric and telescoping examples.
- Apply the integral test and direct comparison test for positive-term... — Apply the integral test and direct comparison test for positive-term series.
- Use limit comparison, ratio, and root tests to decide absolute conver... — Use limit comparison, ratio, and root tests to decide absolute convergence.
- Apply the alternating series (Leibniz) test and estimate remainder. — Apply the alternating series (Leibniz) test and estimate remainder.
- Power series, radius and interval of convergence — Power series, radius and interval of convergence
- Taylor and Maclaurin series — Taylor and Maclaurin series; Taylor polynomial approximation and error
Introductory differential equations
- Introduction to differential equations: direction fields and modeling — Introduction to differential equations: direction fields and modeling
- Separable differential equations — Separable differential equations
- First-order linear differential equations — First-order linear differential equations
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.
- Integration techniques
Use LIATE to choose u and dv; apply ∫u dv = uv − ∫v du for products of algebraic, exponential, log, and trig factors.
Coming soon - Applications of integration
Applications of integration
Coming soon - Parametric and polar calculus
Parametric equations
Coming soon - Sequences and series
Define sequences, find limits, and classify bounded/monotonic behavior.
Coming soon - Introductory differential equations
Introduction to differential equations: direction fields and modeling
Coming soon
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$1,162 · Calculus II · 18 tutoring hrs
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