Calculus 2, part 1 of 2: Integrals with applications

Calculus 2, part 1 of 2: Integrals with applicationsSingle variable calculusS1. Introduction to the courseYou will learn: about the content of this course and about importance of Integral Calculus. The purpose of this section is not to teach you all the details (this comes later in the course) but to show you the big picture.

S2. Basic formulas for differentiation in reverseYou will learn: the concept of antiderivative (primitive function, indefinite integral); formulas for the derivatives of basic elementary functions in reverse. S3.

Integration by parts: Product Rule in reverseYou will learn: understand and apply the technique of integration called "integration by parts"; some very typical and intuitively clear examples (sine or cosine times a polynomial, the exponential function times a polynomial), less obvious examples (sine or cosine times the exponential function), mind-blowing examples (arctangent and logarithm), and other examples. S4. Change of variables: Chain Rule in reverseYou will learn: how to perform variable substitution in integrals and how to recognise that one should do just this.

S5. Integrating rational functions: partial fraction decompositionYou will learn: how to integrate rational functions using partial fraction decomposition. S6.