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Math 2B: Calculus

Math 2B: Calculus (Fall 2013, UC Irvine). Instructor: Professor Natalia L. Komarova. 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.

Introduction


Lecture 01 - Course Introduction & Antiderivative
Lecture 02
Lecture 03 - Definite Integral
Lecture 04 - The Fundamental Theorem of Calculus
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

References
MATH 2A LEC B: Calculus
Instructor: Natalia Komarova. Video recording of the lectures. Textbook - Calculus: Early Transcendentals by James Stewart, 7th Edition.