Calculus II

Catalogue Description: This is the second course in calculus and analytic geometry. It covers techniques and applications of integration, polar coordinates, and infinite series. Technology and writing as appropriate to the discipline will be emphasized throughout the course. The course is broken up into 6 units.

Students the Course is Expected to Serve: This course is intended for students who plan to major in business, mathematics, engineering, and science and those students who require at least two courses in calculus.

Course Objectives:

1. Differentiate inverse trigonometric, exponential, and logarithmic functions.
2. Differentiate and integrate in polar coordinates.
3. Apply the concepts of integral calculus to contextual (real-world) scenarios.
4. Apply various convergence tests to an infinite series.
5. Derive and apply the Taylor series of a function.
6. Apply various integration techniques, calculate improper integrals and numerically estimate definite integrals.

Student Learning Outcomes: Upon satisfactory completion of the course, students will be able to:

A. Apply integration techniques such as partial fractions, trigonometric substitution, or use of integration tables.
B. Estimate definite integrals using the Midpoint Rule, Trapezoidal Rule and Simpson’s Rule.
C. Apply L’Hospital’s Rule to calculate limits of functions.
P. Evaluate improper integrals.
Q. Apply integration to computing the area between two curves and the volume of a solid.
R. Graph a curve, including the conics, using polar coordinates.
S. Differentiate equations in parametric and polar form.
T. Calculate the area of regions in polar form using integrals.
U. Determine the limit of a sequence.
V. Calculate the sum of a geometric series.
W. Determine the convergence or divergence of a series using the Integral Test, comparison tests, Alternate Series Test, and Ratio Test.
X. Determine the interval of convergence for a power series.
Y. Determine the McLaurin and Taylor series representation of a function at a point.
Z. Apply Taylor series to estimate function values and definite integrals.
AA. Calculate integrals using substitution and integration by parts methods.

Topical Outline: The course will cover the following topics:

1. Application of Definite Integral
2. Introduction to Differential Equations
3. Inverse Trigonometric Functions
4. Integral Techniques and Improper Integrals
5. Polar and Parametric Coordinates
6. Sequences and Series

A more detailed breakdown of topics and curriculum outline can be found here.