Calculus is the heart of mathematics including derivatives, functions, infinite series, integrals, and limits. Though most of us know that calculus was invented in 17th century by Isaac Newton and Leibniz, the idea of calculus has a very long history from the distant past. Ancient mathematicians like Archimedes already used infinitesimals to calculate the volume of a sphere - in a way that is similar to modern integral calculus. Here are some great calculus lectures available online for free.
1) Highlights of Calculus
This introduces the basics of calculus - how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.
This consists of 39 video lectures taught by Professor Herbert Gross, giving an overview of the topics: sets, functions, differential calculus, integral calculus, trigonometric functions, logarithms, and infinite series.
This consists of 26 video lectures taught by Professor Herbert Gross, on a study of the calculus of functions of several variables (vector arithmetic and vector calculus).
This consists of 20 video lectures given by Professor Herbert Gross, providing an introduction to Complex Variables, Ordinary Differential Equations and Linear Algebra.
Taught by Professor German A. Enciso. This course offers an introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization.
Taught by Professor Natalia L. Komarova. This course focuses on integral calculus and its applications, and infinite sequences and series.
This consists of 31 video lectures by Professor Richard Delaware of the University of Missouri-Kansas city. This course introduces the concepts and techniques of differential calculus and integral calculus.
This consists of 26 video lectures given by Professor Matthew Leingang. This course discusses the foundations of calculus, the study of functions and their rates of change.
9) Vector Calculus
This consists of 15 video lectures given by Professor Chris Tisdell, presenting vector calculus in an applied and engineering context. The lectures may be useful to students of mathematics, but also to those of engineering, physics and the applied sciences.
Taught by UCLA's Professor Steve Butler. This course covers the differential calculus and integration through the fundamental theorem of calculus, and provides insight into differential calculus and applications as well as an introduction to integration.
This consists of 39 video lectures given by Professor David Jerison, on single variable calculus. This is an introductory calculus course covering differentiation and integration of functions of one variable, with applications.
This consists of 35 video lectures given by Professor Denis Auroux, covering vector and multi-variable calculus. Topics covered in this course include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
Given by Professor Edward Frenkel. This course covers essential topics in multivariable calculus, including partial derivatives, multiple integrals, vector calculus, Green's theorem, divergence theorem, and Stokes's theorem.
This consists of 33 video lectures given by Professor Arthur Mattuck, studying Ordinary Differential Equations (ODEs), including modeling physical systems. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time.
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