Standard syllabus
Calculus II · Undergraduate · Math
Topics
Integration techniques
- Integration by parts and trigonometric integrals
- Trigonometric substitution and partial fraction decomposition
- Integration of rational functions and general substitution strategies
- Improper integrals and tests for convergence
Applications of integration
- Applications of integration: arc length, work, fluid force, and center of mass
Parametric and polar calculus
- Parametric equations and calculus with parametric curves
- Polar coordinates; area, arc length, and slope in polar form
Sequences and series
- Sequences, limits of sequences, and introduction to infinite series
- Convergence tests: integral, comparison, limit comparison, ratio, root, and alternating series
- Power series, radius and interval of convergence
- Taylor and Maclaurin series; Taylor polynomial approximation and error
Introductory differential equations
- Introduction to differential equations: direction fields and modeling
- Separable differential equations and first-order linear differential equations
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$1,162 · Calculus II · 18 tutoring hrs
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