Mathematics 2B

I will explain what the subject and what are the important questions and how to understand the problems and how to remember differential and integration formulas 

Mathematics 2B, typically a continuation of a calculus sequence at the university level, often covers the following topics:

Integration Techniques:

Integration by parts

Trigonometric integrals

Trigonometric substitution

Partial fraction decomposition

Improper integrals

Applications of Integration:

Area between curves

Volumes of solids of revolution (disk/washer method and shell method)

Arc length

Surface area of solids of revolution

Work and fluid forces

Sequences and Series:

Definitions and properties of sequences

Convergence and divergence of sequences

Infinite series and convergence tests (e.g., integral test, comparison tests, alternating series test, ratio test, root test)

Power series

Taylor and Maclaurin series

Applications of Taylor series

Parametric Equations and Polar Coordinates:

Parametric equations and their graphs

Calculus with parametric equations (derivatives and integrals)

Polar coordinates and graphs

Calculus in polar coordinates (area and arc length)

Vectors and Geometry of Space (sometimes included in 2B or deferred to 2C):

Vectors in two and three dimensions

Dot product and cross product

Lines and planes in space

Vector functions and their derivatives

These topics build upon the foundational concepts learned in earlier calculus courses, such as differentiation and basic integration, providing students with a deeper understanding and more advanced tools for mathematical analysis.