Calculus II: Techniques of Integration

A detailed study of methods of integration, applications of the integrals, improper integrals, sequences, series and power series, polar coordinates and parametric curves. 

Prerequisites

Calculus I with a grade of C or better.

Textbook

Calculus with Early Transcendentals by Stewart, any edition is fine.

For those who can read Albanian, I have my own Calculus book which can be downloaded for free here. 

Syllabus

For detailed syllabus click here

Course Materials

Old exams, sample tests, and other materials will be posted here.

• Sample Midterm I

• Sample Midterm II

• Sample Midterm III

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• Areas Between Curves 

• Volumes

• Volumes by Cylindrical Shells 

• Work

• Average Value of a Function

• Integration by Parts 

• Trigonometric Integrals

• Trigonometric Substitution

• Integration of Rational Functions by Partial Fractions 

• Strategy for Integration 

• Integration Using Tables 

• Approximate Integration 

• Improper Integrals 

• Arc Length 

• Area of a Surface of Revolution 

• Applications to Physics and Engineering 

• Curves Defined by Parametric Equations 

• Calculus with Parametric Curves 

• Polar Coordinates

• Areas and Lengths in Polar Coordinates

• Conic Sections

• Conic Sections in Polar Coordinates

• Sequences

• Series

• The Integral Test and Estimates of Sums

• The Comparison Tests 

• Alternating Series 

• Absolute Convergence and the Ratio and Root Tests 

• Strategy for Testing Series

• Power Series 

• Representations of Functions as Power Series

• Taylor and Maclaurin Series 

• Applications of Taylor Polynomials