he student will apply the basic integration formulas, and their associated antiderivative formulas, by evaluating both definite and indefinite integrals in classical and practical problems, including calculating area, volumes of solids of revolution, arc length, areas of surfaces of revolution, total work by a variable force, centroids and centers of mass, and total fluid force.
he student will apply the following integration techniques, and determine when it is appropriate to use a specific technique: (a) integration by parts, (b) integrands of trigonometric products and power, (c) trigonometric substitutions, (d) rationalization substitutions and (e) partial fractions, (f) numerical integration, and using (g) a table of integrals, and the student will evaluate improper integrals.
he student will apply the following integration techniques, and determine when it is appropriate to use a specific technique: (a) integration by parts, (b) integrands of trigonometric products and power, (c) trigonometric substitutions, (d) rationalization substitutions and (e) partial fractions, (f) numerical integration, and using (g) a table of integrals, and the student will evaluate improper integrals.
he student will define sequences and evaluate limits of sequences
The student will determine convergence of infinite series by calculating the limit of its sequence of partial sums, applying the formula for an infinite geometric series, the Integral Test, the Direct and Limit- Comparison Tests, the Alternating Series Test, and the Ratio and Root Tests
The student will construct Taylor Polynomials using the definition and apply Taylor’s Theorem
he student will calculate the interval of convergence of power series, represent functions by power series, and construct Taylor and Maclaurin Series from existing power series by applying the processes of differentiation, integration, multiplication, division, and substitution.
The student will apply calculus techniques to parametric equations, conic sections, polar equations to find derivatives, arc length, area, and surface area of revolution.