In Calculus Part 2, notation for antiderivatives and indefinite integrals will be explored and the basics of integration are introduced. Students will also investigate trigonometric functions, probability, series, and Taylor polynomials.
It is recommended that students successfully complete Calculus Part 1 or equivalent course work before enrolling in this course. The material presented in Calculus Part 1 forms the basis for integral calculus.
Unit 1: Essential Content and Skills
- Use basic integration rules to find antiderivatives.
- Apply substitution to find indefinite integrals.
- Analyze the Fundamental Theorem of Calculus.
- Find the areas of regions bound by two graphs.
- Employ integration by parts to find indefinite and definite integrals.
- Use partial fractions to find indefinite integrals.
- Employ the Trapezoidal Rule to approximate definite integrals.
Unit 2: Essential Content and Skills
- Evaluate improper integrals with infinite limits of integration.
- Appraise improper integrals with infinite integrands.
- Draw planes in space with different numbers of intercepts.
- Examine partial derivatives.
- Explore Lagrange multipliers.
- Evaluate double integrals.
Unit 3: Essential Content and Skills
- Examine trigonometric functions and identities.
- Analyze the derivatives of the sine and cosine functions.
- Question the derivatives of the tangent, cotangent, secant, and cosecant functions.
- Explore integrals of trigonometric functions.
- Discover integrals of other trigonometric functions
Unit 4: Essential Content and Skills
- Find the expected values of continuous probability density functions.
- Discover the variances and standard deviations of continuous probability density functions.
- Determine the convergence or divergence of sequences and find the limits of convergent sequences.
- Examine convergence or divergence of infinite series.
- Determine the convergence or divergence of p-series.
- Discover Taylor polynomials.
- Test Newton’s Method.
- Calculus: An Applied Approach (textbook)
*Available as an iText course