Math 2B. Calculus. Lecture 01. Course Introduction & Antiderivative.

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 03. Single-Variable Calculus -- Definite Integral --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on October 2, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

UCI Math 2A: Single-Variable Calculus (Fall 2013)
Lec 01. Single-Variable Calculus -- Functions --
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Instructor: German A. Enciso, Ph.D.

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Description: UCI Math 2A is the first quarter in Single-Variable Calculus and covers the following topics: Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.

Recorded on September 27, 2013

Required attribution: Enciso, German A. Math 2A (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 12. Single-Variable Calculus -- Trigonometric Substitution --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on October 25, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

Course Description:
Math 31A is a course that provides insight into differential calculus and applications as well as an introduction to integration.

About the Professor:
Steve Butler is a NSF Postdoctoral Scholar and Assistant Adjunct Professor of the UCLA Department of Mathematics. He received his Ph. D. from UCSD in June of 2008 and has been at UCLA since the Fall of 2008 (where he will be staying for a total of three years). His area of research consists of Combinatorics as well as particular spectral graph theory, combinatorial geometry, and recreational mathematics (i.e., juggling).

Course Webpage:
Professors Webpage: math.ucla.edu/~butler

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* See all the UCLA Math 31A: Differential & Integral Calculus classes in this series:
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Calculus 1 Lecture 1.1: An Introduction to Limits

This video shows how calculus is both interesting and useful. Its history, practical uses, place in mathematics and wide use are all covered. If you are wondering why you might want to learn calculus, start here!

A documentary on Leibniz and the calculus.

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 19. Single-Variable Calculus -- Sequences --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on November 13, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

Computing Antiderivatives
Instructor: Joel Lewis
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Some introductory examples of antidifferentiation.

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 13. Single-Variable Calculus -- Integration by Partial Fractions --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on October 28, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 05. Single-Variable Calculus -- Indefinite Integral & The Net Change Theorem --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on October 7, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 25. Single-Variable Calculus -- Power Series --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on November 27, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

This talk describes the motivation for developing mathematical models, including models that are developed to avoid ethically difficult experiments.  Three different examples from the field of human health are presented.

Jeffrey J. Heys is an assistant professor of chemical engineering at Montana State University. He received his B.S. in chemical engineering in 1996 from Montana State University, and his M.S. and Ph.D. from the University of Colorado at Boulder in 1998 and 2001,respectively.  His research area is computational transport and computational fluid dynamics in biological systems with an emphasis on fluid-structure interaction and multiphase flows.

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In the spirit of ideas worth spreading, TEDx is a program of local, self-organized events that bring people together to share a TED-like experience. At a TEDx event, TEDTalks video and live speakers combine to spark deep discussion and connection in a small group. These local, self-organized events are branded TEDx, where x = independently organized TED event. The TED Conference provides general guidance for the TEDx program, but individual TEDx events are self-organized.*

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UCI Math 176: Math of Finance (Fall 2014)
Lec 01. Math of Finance
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Instructor: Donald Saari, Ph.D.

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Description: UCI Math 176 covers the following topics: reviewing of tools from probability, statistics, and elementary differential and partial differential equations, concepts such as hedging, arbitrage, Puts, Calls, the design of portfolios, the derivation and solution of the Blac-Scholes, and other equations.

Recorded on January 7, 2014

Required attribution: Saari, Donald. Math 176 (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 4.0 United States License. (

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Basic Integration of Indefinite Integrals. For more free math videos, visit

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 28. Single-Variable Calculus -- Final Review --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on December 6, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 27. Single-Variable Calculus -- Taylor Series and Maclaurin Series --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on December 4, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

UCI Math 2A: Single-Variable Calculus (Fall 2013)
Lec 09. Single-Variable Calculus -- Derivatives --
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Instructor: German A. Enciso, Ph.D.

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Description: UCI Math 2A is the first quarter in Single-Variable Calculus and covers the following topics: Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.

Recorded on October 16, 2013

Required attribution: Enciso, German A. Math 2A (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

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Using the power rule to find an antiderivative.

An introduction to indefinite integration of polynomials.

UCI BioSci M121: Immunology with Hematology (Fall 2013)
Lec 02. Immunology with Hematology -- The Immune System & Host Defense --
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Instructor: David A. Fruman, Ph.D.

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Description: UCI BioSci M121 covers the following topics: Antibodies, antigens, antigen-antibody reactions, cells and tissues of lymphoreticular and hematopoietic systems, and individual and collective components of cell-mediated and humoral immune response.

Recorded on September 30, 2013

Required attribution: Fruman, David. Immunology with Hematology M121 (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 4.0 United States License. (

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Understand the definition of the integral and learn how to find the area underneath the curve.

Review a basic indefinite integral example using a polynomial function.

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How to solve Antiderivatives? - Calculus Tips. Watch and learn now! Then take an online Calculus course at StraighterLine for college credit:

(October 22, 2012) Professor Keith Devlin discusses how calculus is truly one of the most useful discoveries of all time.

Originally presented in the Stanford Continuing Studies Program.

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This video has a few examples of finding indefinite integrals.




and click on the 'Free Video Lessons' tab on the left!

Just Math Tutoring

Easy to understand explanation of integrals and derivatives using 3D animations.

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 26. Single-Variable Calculus -- Representing Functions as Power Series --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on December 2, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

I introduce the concept of finding the general Antiderivative through the process of Indefinite Integration. I finish by working through many examples. NOTE: I miscopied the Power Rule writing that n can't equal 1, there is an annotation correction, n cannot equal -1.

NOTE: At min 9:00 I verbal say the derivative of 3x is 3x^2 which is incorrect. It is 3. You will not see the annotation correction if viewing on an iPad or iPhone.
Please help Close Caption this lesson


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Antiderivatives of trigonometric functions

Lecture 1: The Geometry of Linear Equations.
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UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 06. Single-Variable Calculus -- The Substitution Rule --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on October 9, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

Derivatives, slope, velocity, rate of change
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UCI BioSci M121: Immunology with Hematology (Fall 2013)
Lec 01. Immunology with Hematology -- Course Introduction --
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Instructor: David A. Fruman, Ph.D.

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Description: UCI BioSci M121 covers the following topics: Antibodies, antigens, antigen-antibody reactions, cells and tissues of lymphoreticular and hematopoietic systems, and individual and collective components of cell-mediated and humoral immune response.

Recorded on September 23, 2013

Required attribution: Fruman, David. Immunology with Hematology M121 (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 4.0 United States License. (

Anti Derivative (Indefinite Integration or Primitive) is the opposite of Derivative. It is commonly known as integration. We have two types of integration one is Indefinite Integration and other is definite integration. In this anti derivative - calculus video lesson, we are discussing the primitives, anti derivative or indefinite integration.

Whenever we are differentiating a function, it always gives you a derivative, but the process of integration of a derivative tries to give you the function, whose derivative you have. But its not sure that one function have only one derivative. Many function can have same derivative, therefore, we say indefinite integration,

I have tried to clear very nicely the concept hidden behind the calculus math chapter Anti Derivative or Indefinite Integration or Primitive, once we learn this, we will jump to definite integration.

All the fundamental concepts and basics of integration is tried to explain in this calculus lecture.

We have tried to explain geometrical meaning of anti derivative as well. Geometrically, how should we learn anti derivative, indefinite integration, its very well explained.

I believe this , conceptual calculus video lesson of Indefinite Integration will help you to gain more concept.

UCI Math 4: Math for Economists (Summer 2013)
Lec 01. Math for Economists
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Instructor: Jason Kronewetter, Ph.D.

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Description: UCI Math 4 covers the following topics: linear algebra and multivariable differential calculus suitable for economic applications.

Recorded on August 5, 2013

Required attribution: Kronewetter, Jason. Math for Economists 4 (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

Aakash iTutor: Class 9th Mathematics Video Lectures (Number Systems: Representation of rationals on number line) to study through online coaching tablet by Aakash Institute. Enquire for Full Video-Lectures @ ( and prepare for NTSE and Board Exams.

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 09. Single-Variable Calculus -- Mid-Term Review --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on October 16, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

UCI Math 2A: Single-Variable Calculus (Fall 2013)
Lec 05. Single-Variable Calculus -- Tangents, Slopes, and Limits --
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Instructor: German A. Enciso, Ph.D.

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Description: UCI Math 2A is the first quarter in Single-Variable Calculus and covers the following topics: Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.

Recorded on October 7, 2013

Required attribution: Enciso, German A. Math 2A (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

Class XI Physics. Class room lectures by Pradeep Kshetrapal. Chapter : Kinematics. Topic : Integral Calculus and its application. Language : Hindi and English mixed.

UCI Math 2B: Single-Variable Calculus (Fall 2013)
Lec 20. Single-Variable Calculus -- Series --
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Instructor: Natalia L. Komarova Ph.D.

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Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: 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.

Recorded on November 15, 2013

Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (

Calculus 2 Lecture 9.1: Convergence and Divergence of Sequences

Calculus 1 Lecture 1.4: Continuity of Functions