MATH 212 - Calculus II

1. Evaluate integrals by the method of substitution.
2. Approximate integrals by Simpson’s rule and by other elementary numerical quadrature methods.
3. Evaluate integrals using integration by parts.
4. Evaluate trigonometric integrals.
5. Evaluate integrals of rational functions by the partial fractions method.
6. Evaluate integrals using trigonometric substitution.
7. Apply the integral calculus to find arc length and the area of a surface of revolution.
8. Apply the integral calculus to solve force and work problems.
9. Sketch solution curves of differential equations using the direction field method.
10. Find numerical solutions of initial value problems using Euler’s method.
11. Solve separable differential equation
12. Determine whether a sequence converges by using the limit laws, the substitution. law, the squeeze law, L’Hôpital’s rule or the bounded monotone convergence property.
13. Determine whether a series converges by approximating the partial sums, or by using comparison tests, the integral test, the alternating series test, the ratio test or the root test.
14. Determine whether a series is absolutely convergent, conditionally convergent or divergent.
15. Find the Taylor polynomial with remainder, the Maclaurin series and the Taylor series of a function.
16. Apply the ratio test to determine the interval of convergence of a power series.
17. Use termwise differentiation and integration to find the power series representation of a function.

Graphical solution of differential equations

Integration by parts

Approximate solution of differential equations

Trigonometric integrals

Separable differential equations

Integration of rational functions

Convergence of sequences

Approximating integrals

Convergence of series

Arc length

Taylor and Maclaurin series

Area of a surface of revolution

Representation by power series

Work and force problems
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