This course is the second installment of Single-Variable Calculus. In Part I(MA101), we studied limits, derivatives, and basic integrals as a means to understand the behavior of functions. In this course (Part II), we will extend our differentiation and integration abilities and apply the techniques we have learned.Additional integration techniques, in particular, are a major part of the course. In Part I, we learned how to integrate by various formulas and by reversing the chain rule through the technique of substitution. In Part II, we will learn some clever uses of substitution, how to reverse the product rule for differentiation through a technique called integration by parts, and how to rewrite trigonometric and rational integrands that look impossible into simpler forms. Series, while a major topic in their own right, also serve to extend our integration reach: they culminate in an application that lets you integrate almost any function you’d like.Integration allows us to calculate physical quantities for complicated objects: the length of a squiggly line, the volume of clay used to make a decorative vase, or the center of mass of a tray with variable thickness. The techniques and applications in this course also set the stage for more complicated physics concepts related to flow, whether of liquid or energy, addressed in Multivariable Calculus(MA103).Part I covered several applications of differentiation, including related rates. In Part II, we introduce differential equations, wherein various rates of change have a relationship to each other given by an equation. Unlike with related rates, the rates of change in a differential equation are various-degree derivatives of a function, including the function itself. For example, acceleration is the derivative of velocity, but the effect of air resistance on acceleration is a function of velocity: the faster you move, the more the air pushes back to slow you down. That relationship is a differential equation.
Days of the Week:
Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
- Level of Difficulty: Intermediate
- Size: One-on-One
- Cost: Free
- Institution: Saylor
- Topics: Calculus, Differential Equations, Physics