This 9-minute video lesson gives an antidrivative example: finding öÇ(2^ln x)/x dx. [Calculus playlist: Lesson 128 of 156]
This Internet resource provides introductory information, concept or skill development in Mathematics for grade 9, 10, 11, and 12 students who are at grade level in a single student situation. This text was initially written by David Guichard. The single variable material (not including infinite series) was originally a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original.
This digital textbook was reviewed for its alignment with California content standards.
The textbook "Calculus" by Gilbert Strang, is a modern calculus text written in a human-friendly style. Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.
This digital textbook was reviewed for its alignment with California content standards.
This 10-minute video lesson provides more on why the antiderivative and the area under a curve are essentially the same thing. [Calculus playlist: Lesson 66 of 156]
This 10-minute video lesson provides examples of using definite integrals to find the area under a curve. [Calculus playlist: Lesson 67 of 156]
This 10-minute video lesson provides more examples of using definite integrals to calculate the area between curves. [Calculus playlist: Lesson 68 of 156]
This 10-minute video lecture provides more on why the antiderivative and the area under a curve are essentially the same thing. [Calculus playlist: Lesson 65 of 156]
This 9-minute video lesson looks at how to solve a definite integral with substitution (or the reverse chain rule). [Calculus playlist: Lesson 69 of 156]
This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and L’hopital’s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using Newton’s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)
This contemporary calculus course is the second in a three-part sequence. In this course students continue to explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.
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Topics in this course include transcendental functions, techniques of integration, applications of the integral, improper integrals, l'Hospital's rule, sequences, and series.
This 9-minute video lesson provides examples of taking the indefinite integral (or anti-derivative) of polynomials. [Calculus playlist: Lesson 57 of 156]
This 10-minute video lesson examines integration by doing the chain rule in reverse. [Calculus playlist: Lesson 58 of 156]
This 10-minute video lecture examinesiIntegration by substitution (or the reverse-chain-rule). [Calculus playlist: Lesson 59 of 156]
This 9-minute video lesson demonstrates how to use the definite integral to solve for the area under a curve. It also provides intuition on why the antiderivative is the same thing as the area under a curve. [Calculus playlist: Lesson 64 of 156]
This 17-minute video lesson shows that if a vector field is the gradient of a scalar field, then its line integral is path independent. [Calculus playlist: Lesson 142 of 156]
This 16-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 52: Periodic Definite Integral. The second term at about minute 14 should have a positive sign. Luckily, it doesn't effect the final answer! [Calculus playlist: Lesson 73 of 156]
This 8-minute video lecture demonstrates how to use a position vector valued function to describe a curve or path. [Calculus playlist: Lesson 133 of 156]
This 9-minute video lesson provides an introduction to the indefinite integration of polynomials. [Calculus playlist: Lesson 56 of 156]
This 11-minute video lesson provides an introduction to the triple integral. [Calculus playlist: Lesson 125 of 156]
