Intro To Calculus 2

In this video, I will introduce the Riemann Sum which is basically estimating the area under a curve by making small rectangles finding the area of each rectangles and then adding them up. I'll go over the different techniques of estimating area under the curve such as: right, left, midpoint, and trapezoidal method of riemann sum.

This is part 2 of riemann sum.

This is part 3 of riemann sum.

In this video, I will introduce sigma notation and limits of finite sums which is basically the formal definition of a Riemann Sum and definite integral. In this video, you will solve limit problems by taking a function and express it as the limit of a sequence of Riemann Sums over an interval.

In this video, I will go over some common integration rules, and go over the difference between definite and indefinite integral.

In this video, I will integrate integral using the u-substitution method. I will use bounded and unbounded integrals.

In this video, I will integrate using u substitution using medium-hard examples.

In this video, I will do example 1 of a harder example of u-substitution.

This is example 2 of a harder example of u-substitution that requires back substitution.

In this video, I will do example 3 of a harder u-substitution that requires double substitution.

In this video, I will go over the common derivative rules of an exponential function. I will do examples both bounded and unbounded integral.

In this video, I will go over some common basic integration rules both indefinite and definite integrals. We will review trigonometric identities such as pythagorean identities to simplify integrals.

In this video, I will go over integrating powers of sines and cosines. This is not integrating with trig substitution.

In this video, I will go over the quiz on integrating powers of sines and cosines when both power are odd.

In this video, I will go over how to integrate powers of tangents and secants.

In this video, I will go over all the steps for integration by substitution.

In this video, I will do example 2 of integration by trigonometric substitution.

In this video, I will do example 4 of trigonometric substitution.

This is example 5 of integration by trigonometric substitution with completing the square.

This is example six of trigonometric substitution integration with completing the square.

In this video I will go over a quiz on integration with trigonometric substitution.

In this video, I will go over integration by parts.

In this video, I will do example two of integration by parts involving ln(x).

This is example 3 of integration by parts more than once.

In this video, I will introduce the tabular method for integration by parts.

In this video, I will do integration by parts with definite integral.

In this video, I will integrate by parts with the help of LIATE.

In this video, I will integrate with partial fraction using two examples with non repeating linear factor, and repeated linear factor.

In this video, I will integrate a partial fraction with a distinct quadratic or higher degree factor.

In this video, I will integrate partial fraction with linear and repeating quadratic.

In this video, I will integrate partial fraction with improper rational function with synthetic division.

In this video, I will do a quiz on partial fraction integration.

In this video, I will go over fundamental theorem of calculus part 1 and part 2. I will also review integration rules and properties.

In this video, I will explain how to find the area under two curves in both terms of x(vertical) and terms of y (horizontal).

In this video, I will do a quiz on the area between curves.

In this video, we will go over all the steps of finding the volume using known cross sections. We will slice the region perpendicular to either the x-axis or y-axis to create a certain shape such as: square, equilateral triangle, isosceles triangle, right triangle, semicircles, rectangle. Each shape will have different formulas.

In this video, I will go over how to solve first- order differential equations when given initial value. I will go over the steps for solving a separable equation, and solve for the general solution when given an initial constraint.

In this video, I will do three examples of more difficult separable differential equations.

In this video, I will solve a separable differential equation involving application in geometry.

In this video, I will do a quiz on separable differential equation.

In this video, I will introduce the first order linear differential equation, and how to solve this specific differential equation. I will also do initial-value problem.

In this video, I will do a mixing word problem involving a linear differential equation.

In this video, I will do a quiz on first order linear differential equation with given initial value.

In this video, I will go over exponential growth and decay, and how to find an equation of an exponential function when given pieces of information. After finding the equation of an exponential function, you can find the unknown.

In this video, I will introduce Euler's method which is basically a numerical method that uses the idea of tangent lines for a short distance to approximate the solution to an initial-value problem.

In this video, I will introduce the logistic differential equation also referred to as the verhulst model or logistic growth curve, then I will find the limiting capacity and maximum growth rate for logistic functions.

In this video, we will go over polar coordinates, which is a coordinate system represents a point in the plane by an ordered pair of numbers called coordinates. In this video, we will learn to convert to polar to rectangular coordinates, and convert rectangular to polar coordinates. We will learn how to graph polar coordinates, and how to find co terminal coordinate pairs. finally, convert polar equation to rectangular form, and convert rectangular equations to polar curves.

In this video, we will learn how to graph the five basic polar graphs such as: limacons, rose curves, circles, lemniscates, and spirals. Also we will learn two different methods for graphing each polar equation such as: transformations and table of values.

In this video, we will go over the difference between finding the derivative of a polar function and finding the slope of the tangent line. Then, we will learn how to find horizontal and vertical tangents with respect to polar curves.

In this video, we will go over how to find area of a polar curve, and how to find area enclosed by two polar curves, Finally, we will go over how to find the length or the total distance of a polar curve.

In this video, we will continue with nine infinite series test for determine convergence/ divergence for any infinite series. In this video, we will focus on the nth term test which also called the divergence test.

In this video, we will go over the p-series test.

In this video, we will go over/review sequences, series, and go over the term convergence, divergence, factorial, monotonic, bounded, infinite. We will go over the difference between a sequence and series. Finally, we will learn how to generate general terms and simplify factorials for both finite and infinite sequence and series, then we will determine whether or not a sequence converges or diverges using nth term test for sequences. We will go over the acronym riddle for memorizing the series test.

In this video, we will go the geometric series test.

In this video, we will go the limit comparison test.

In this video, we will go over the integral test to determine if a series converges or diverges