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UCI OpenCourseWare

Calculus

This course focuses on integral calculus and its applications, and infinite sequences and series. Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations. Course Textbook - Calculus: Early Transcendentals by James Stewart, 7th Edition.

Instructor

Professor Natalia L. Komarova.

Mathematics

2013

Lecture 05 - Indefinite Integral & The Net Change Theorem

Lecture 06 - The Substitution Rule

Lecture 07 - Areas Between Curves

Lecture 08 - Calculating The Volume of Solids

Lecture 09 - Midterm Review

Lecture 10 - Integration by Parts

Lecture 11 - Trigonometric Integrals

Lecture 12 - Trigonometric Substitution

Lecture 13 - Integration by Partial Fractions

Lecture 14 - Strategy for Integration

Lecture 15 - Indeterminate Forms and L'Hospital Rule

Lecture 16 - Improper Integrals

Lecture 17 - Arc Length, Review Integration Techniques

Lecture 18 - Midterm II Review

Lecture 19 - Sequences

Lecture 20 - Series

Lecture 21 - Integral Test and Estimates of Sums

Lecture 22 - The Comparison Test

Lecture 23 - The Comparison Test/ Alternating Series Test, Part II

Lecture 24 - Strategies for Testing Series

Lecture 25 - Power Series

Lecture 26 - Representing Functions as Power Series

Lecture 27 - Taylor Series and Maclaurin Series

Lecture 28 - Final Review