Analytic Geometry and Calculus II

Math. 114, Sec. 003, Spring 2018

Homework and Announcements


Important Stuff

Note! Here I will post important announcements to the class.


General Info

For general information regarding this course, please read the Syllabus here below. It should answer all practical questions, like when tests are, what the grading policies are etc.

NB! All handouts for this class, listed below, will be labeled with an itemized icon.

Your teaching assistant (TA) is Long Nguyen. He will see you during the recitation sessions (RCT) on Mondays and discuss homework (HW) exercises and give you quizzes. His email is: "lnguye33 the-at-sign masonlive dot gmu dot edu".


Homework Info

Below are the homework assignments (HW) so far in the course. All HW is from the text book of this course. They includes exercises to be discussed in your recitation sessions by your TA. Be sure to attempt them before going to the sessions.

  1. Lectures and Homework (HW) from Week 1. HW for RCT January 29. : Be sure that you know how to differentiate any function, be it a product, quotient or composite of functions. In theory, you should be able to find the derivative of any function that is handed to you! This is the reason why differentiation is easier that integration, since it is not always possible to find a closed form of an indefinite integral. Review how to integrate the basic functions, like polynomials, exponential functions, logarithmic functions and the trig functions. -- The main thing about slicing method is that the total volume is always the integral of the area A(x) of the slice, where x goes from one bounding value to the other.
  2. Lectures and Homework (HW) from Week 2. HW for RCT February 5. : The main thing to remember is that the total volume V is always the integral of dV, whether dV is (1) a small circular disc with thickness dx (or dy), or (2) a cylindrical shell of height f(x), thickness dx and circumference 2 times pi times the radius of the cylinder. Similarly, the total arc length is always the integral of ds, whether we view it in terms of x and dx, or in terms of y and dy. Using some general principles of centers of mass, we can compute the CM of various regions and curves. We derived some of such formulas in class that can be applied to a variety of examples.
  3. Lectures and Homework (HW) from Week 3. HW for RCT February 12. : As we have now seen, we can use integration to compute volumes, arc lengths, center of masses (CM) and surface areas of regions obtained when rotating curves around either x-axis or y axis. The method is pretty much the same, that we integrate some designated "small piece", that is dM, xdM or ydM. Hence, we always use the same principle, as the various formulas for uniform regions or uniform strings indicate. Note! If the plates or strings are not uniform, then we cannot cancel out the density delta in the formulas. Also, keep an eye open for various geometrical symmetries when computing CM, since that can simplify many of your calculations. -- When computing CM for uniform plates or strings, you can cancel out the density and use the nice formulas that I presented in class. Never forget to keep an eye open for various symmetries of the geometrical figures! -- The precise definition of the natural logarithm is given by an integral. From this definition alone we are able to derive all the properties of the logarithm and also the exponential funtion as well. Note that this gives us a way to define the number e as the inverse of the natural logarithm at 1 (that is, the exponential function at 1). Also we have that the limit of (1+x) to the power of 1/x goes to e when x goes to zero. This is an important limit!
  4. Lectures and Homework (HW) from Week 4. HW for RCT February 19. : A consequence of the limit of (1+x) to the power of 1/x when x goes to zero, is that continuously compounded interest is always more profitable than any discrete one, no matter how often per yeat the discrete one is performed. -- Hyperbolic functions are defined in terms of the exponential function. They have properties that very closely resemble those of the trig functions. Many identities are almost the same as for trig functions (usually only differ in sign somewhere...) This can be very useful when integrating. The hyperbolic functions are yet another group of new functions that can be helpful for integration. The main hyperbolic functions are the hyperbolic cosine, the hyperbolic sine and the hyperbolic tangent. Hence, we have added some new functions to our tool bag of functions, the hyperbolic functions, that can be helpful for certain substitutions as we discussed in class. -- When we face an integral involving a square root of a second degree polynomial it is always a good rule of thumb to complete the square and then use the corresponding substitution.
  5. Lectures and Homework (HW) from Week 5.


Exam Info (Quizzes, Midterm and Final)

QUIZZES:

Here below are the handwritten solutions to the quizzes so far.


MATHEMATICA Info


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