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Math 114: Calculus II – Homework

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Your lesson was successfully proposed. Until we receive confirmation, this lesson will not be added to your list of upcoming lessons. Lesson Reschedule Proposal Submitted. Series — The Basics — In this section we will formally define an infinite series. We will also give many of the basic facts, properties and ways we can use to manipulate a series. We will also briefly discuss how to determine if an infinite series will converge or diverge a more in depth discussion of this topic will occur in the next section.

We will illustrate how partial sums are used to determine if an infinite series converges or diverges. We will also give the Divergence Test for series in this section. Special Series — In this section we will look at three series that either show up regularly or have some nice properties that we wish to discuss. Integral Test — In this section we will discuss using the Integral Test to determine if an infinite series converges or diverges.

The Integral Test can be used on a infinite series provided the terms of the series are positive and decreasing. A proof of the Integral Test is also given. In order to use either test the terms of the infinite series must be positive.

Proofs for both tests are also given. Alternating Series Test — In this section we will discuss using the Alternating Series Test to determine if an infinite series converges or diverges. The Alternating Series Test can be used only if the terms of the series alternate in sign. A proof of the Alternating Series Test is also given.

Absolute Convergence — In this section we will have a brief discussion on absolute convergence and conditionally convergent and how they relate to convergence of infinite series. Ratio Test — In this section we will discuss using the Ratio Test to determine if an infinite series converges absolutely or diverges. The Ratio Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge.

A proof of the Ratio Test is also given. Root Test — In this section we will discuss using the Root Test to determine if an infinite series converges absolutely or diverges. The Root Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge.

A proof of the Root Test is also given. Strategy for Series — In this section we give a general set of guidelines for determining which test to use in determining if an infinite series will converge or diverge.

A summary of all the various tests, as well as conditions that must be met to use them, we discussed in this chapter are also given in this section. Estimating the Value of a Series — In this section we will discuss how the Integral Test, Comparison Test, Alternating Series Test and the Ratio Test can, on occasion, be used to estimating the value of an infinite series.

Power Series — In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series. We will also illustrate how the Ratio Test and Root Test can be used to determine the radius and interval of convergence for a power series.

Power Series and Functions — In this section we discuss how the formula for a convergent Geometric Series can be used to represent some functions as power series. To use the Geometric Series formula, the function must be able to be put into a specific form, which is often impossible. However, use of this formula does quickly illustrate how functions can be represented as a power series. We also discuss differentiation and integration of power series.

This will work for a much wider variety of function than the method discussed in the previous section at the expense of some often unpleasant work. Applications of Series — In this section we will take a quick look at a couple of applications of series.

We will illustrate how we can find a series representation for indefinite integrals that cannot be evaluated by any other method. We will also see how we can use the first few terms of a power series to approximate a function. Basic Concepts — In this section we will introduce some common notation for vectors as well as some of the basic concepts about vectors such as the magnitude of a vector and unit vectors. We also illustrate how to find a vector from its staring and end points.

Vector Arithmetic — In this section we will discuss the mathematical and geometric interpretation of the sum and difference of two vectors. We also define and give a geometric interpretation for scalar multiplication. Dot Product — In this section we will define the dot product of two vectors. We give some of the basic properties of dot products and define orthogonal vectors and show how to use the dot product to determine if two vectors are orthogonal.

We also discuss finding vector projections and direction cosines in this section. Cross Product — In this section we define the cross product of two vectors and give some of the basic facts and properties of cross products. The 3-D Coordinate System — In this section we will introduce the standard three dimensional coordinate system as well as some common notation and concepts needed to work in three dimensions. Equations of Lines — In this section we will derive the vector form and parametric form for the equation of lines in three dimensional space.

We will also give the symmetric equations of lines in three dimensional space. Note as well that while these forms can also be useful for lines in two dimensional space. Equations of Planes — In this section we will derive the vector and scalar equation of a plane. We also show how to write the equation of a plane from three points that lie in the plane.

Quadric Surfaces — In this section we will be looking at some examples of quadric surfaces. Some examples of quadric surfaces are cones, cylinders, ellipsoids, and elliptic paraboloids. Functions of Several Variables — In this section we will give a quick review of some important topics about functions of several variables. In particular we will discuss finding the domain of a function of several variables as well as level curves, level surfaces and traces.

Vector Functions — In this section we introduce the concept of vector functions concentrating primarily on curves in three dimensional space. We will however, touch briefly on surfaces as well. We will illustrate how to find the domain of a vector function and how to graph a vector function. We will also show a simple relationship between vector functions and parametric equations that will be very useful at times.

Calculus with Vector Functions — In this section here we discuss how to do basic calculus, i. Tangent, Normal and Binormal Vectors — In this section we will define the tangent, normal and binormal vectors. Arc Length with Vector Functions — In this section we will extend the arc length formula we used early in the material to include finding the arc length of a vector function. Curvature — In this section we give two formulas for computing the curvature i.


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Get online tutoring and college homework help for Calculus. We have a full team of professional Calculus tutors ready to help you today! Calculus II. Here are my online notes for my Calculus II course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus II or needing a refresher in some of the topics from the class.

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Online Homework My Math Lab Login. Course ID: rimmer For instructions on how to create a login, follow the directions here. All homework will be due at midnight on the day listed. Online Hw # 1 - Due Sunday 1/ and 3D Coordinates and Introduction to Vectors Note this is actually broken into 2 links in My Math Lab. I need help with Calculus II, webAssign homework. The questions is basic and about anti-direvitives. Please contact me for more information.