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Single Variable Calculus I Late Transcendentals (Math 211, CAN 18).

1. Derivatives and integrals of inverse functions and transcendental functions such as trigonometric, exponential or logarithmic;
2. Indeterminate forms and L'Hopital's Rule;
3. Additional techniques of integration including integration by parts and trigonometric substitution;
4. Numerical integration; trapezoidal and Simpson's rule;
5. Improper integrals;
6. Additional applications such as work, volumes, arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay;
7. Introduction to sequences and series;
8. Multiple tests for convergence of sequences and series;
9. Power series, radius of convergence, interval of convergence;
10. Differentiation and integration of power series;
11. Taylor series expansion of functions;
12. Parametric equations and calculus with parametric curves; and
13. Polar curves and calculus in polar coordinates.

Upon successful completion of the course, students will be able to:

1. Evaluate indeterminate forms using L'Hopital's Rule;
2. Find derivatives of transcendental functions;
3. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques;
4. Use integration to solve applications such as work or length of a curve;
5. Evaluate improper integrals;
6. Apply convergence tests to sequences and series;
7. Represent functions as power series; an
8. Graph, differentiate and integrate functions in polar and parametric form.

Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.

A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.