College Algebra Textbook with chapters about Linears, Systems, Quadratics, and FunctionsCC x BY Ben Atchison

This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.

This book was designed as an introductory trigonometry textbook for college students with the explicit goal of reducing textbook costs.

The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.

Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It revolves around complex analytic functions—functions that have a complex derivative. Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Applications reviewed in this class include harmonic functions, two dimensional fluid flow, easy methods for computing (seemingly) hard integrals, Laplace transforms, and Fourier transforms with applications to engineering and physics.

This course provides the fundamental computational toolbox for solving science and engineering problems. Topics include review of linear algebra, applications to networks, structures, estimation, finite difference and finite element solutions of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, the discrete Fourier transform, and convolution. We will also explore many topics in AI and machine learning throughout the course.

This 6-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.

This 11-minute video lesson continues to look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.

This 9-minute video lesson continues to look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.

This 11-minute video lesson continues to look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.

This 12-minute video lesson concludes the look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.

This 13-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 46 Circle Hyperbola Intersection.