- Tuesday 4/30/13: Making website.
This course is entitled "Integration, Differential Equations, and Approximation." At other schools it is generally called ``Calculus II.'' Going into the course, the assumption is that you have an advanced grasp of:
- Real valued functions, their graphs, and examples of standard functions (polynomials, rational, root, trigonometric, arctrigonometric, exponential, and logarithmic).
- Algebraic manipulation of real valued variables
- The derivative, the geometric interpretation of the derivative, and applications of the derivative in optimization, related rates, and curve sketching
- The intergral, the geometric interpretation of the integral, its relation to the derivative via the fundamental theorem of calculus, and applications of the integral in finding the area between two curves, or the volume of an three dimensional object which has uniform cross sections or is constructed from revolving a curve around a line.
- What a limit of a function is, how the derivaive is defined as the limit of average rate of change around the point, how the integral is defined as the limit of the area by rectangles.
This course will be divided into several parts.
- Advanced Intergration Techniques: We learn how to integrate a broader set of functions using the integration by parts, trigonometric substituion, partial fractions.
- Approimating Integrals: We learn a few techniques for approximating the value of an integral, such as partial Riemann sums, the midpoint rule, the trapizodial rule, and Simpson's rule
- Differential Equations: We learn how to solve a set of differential equations, called seperable differential equations.
- Sequences and Series: We look at sequences of real numbers, define the notion of convergence. Then we look at sequences of sums of real numbers (series), and look at when those converge.
- Parametization, Polar Coodinates, and Vectors
- We look at some other ways to represent functions and numbers, and then go from 2 dimensions to three dimensions.