This is Razvan Gelca's webpage dedicated to teaching Calculus III during the Coronavirus pandemic.

I am Razvan Gelca, I am a Full Professor of Mathematics at Texas Tech University. I was born in Romania and I have moved to Texas right when the third millenium started. I love teaching differential and integral calculus, within my best-seller problem book Putnam and Beyond more than 100 pages are devoted to calculus problems. For a very long time I have been one of the coaches of the US International Mathematical Olympiad Team, which is currently the best IMO team in the world. I have worked with students between sixth grade and doctoral level, I have thirty years of teaching experience, and I will do my best to guide your learning of calculus in these times of crisis. I really miss being in the classroom, and I will use this web page to communicate with you.

Before you proceed, please read the syllabus, which can be found here.

I have written detailed instructions about how to study, do the homework, and take quizzes, and exams. These instructions can be read here.


As the class progresses, I will give you a week-by-week outline, with details of what to study. Each week is indexed by its dates. Please make sure you follow the weekly schedule as described.


Click here to start doing homework.

You can find information about WebWork here and about how to enter homework here.

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Quiz 1 (due Friday, 09.04.2020 at noon): Find the unit tangent vector \({\bf T}(t)\) and the principal unit normal vector \({\bf N}(t)\) for the curve given by \begin{eqnarray*} {\bf R}(t)=3t^2{\bf i}+2t^3{\bf j},\quad t\neq 0. \end{eqnarray*} Click here for the answer.

Quiz 2 (due Friday, 09.11.2020 at noon): For the curve given by \begin{eqnarray*} {\bf R}(t)=(\sin t){\bf i}+(\cos t){\bf j}+t{\bf k} \end{eqnarray*} find the curvature when \(t=\pi\) and the length of the curve from \(t=0\) to \(t=2\pi\).
Click here for the answer.
Quiz 3 (due Friday, 9.18.2020 at noon): Using implicit differentiation, find \(dy/dx\) for the function \(y\) defined implicitly by the equation \begin{eqnarray*} e^{xy}+x\sin y=3. \end{eqnarray*}
Quiz 4 (due Friday 9.25.2020 at noon): Find the absolute extrema of the function \(f(x,y)=3x^2+2y^2\) in the region \(x^2+y^2\leq 4\).
Click here for the answer.
Exam 1 has been posted here. The solutions are now posted here.
Quiz 5 (due Sunday 10.11.2020 at 3pm) Find the area of the portion of the paraboloid \(z=x^2+y^2\) that lies inside the cylinder \(x^2+y^2=4\).
Quiz 6 (due Friday 10.16.2020 at 3pm) Evaluate the integral \begin{eqnarray*} \iiint_D (x^2+y^2+z^2)dxdydz, \end{eqnarray*} where \(D\) is defined by \(x^2+y^2+z^2\leq 2\).
The solution is here.
Quiz 7 (due Friday 10.23.2020 at 3pm) Find the work done by the force field \({\bf F}=(2x^2+2y^2){\bf i}+(3x+3y){\bf j} \) as an object moves counterclockwise along the circle \(x^2+y^2=4\) from \((2,0)\) to \((-2,0)\) and then back to \((2,0)\) along the \(x\)-axis.
The solution is here.
Quiz 8 (due Friday 10.30.2020 at 3pm) Show that the vector field \({\bf F}(x,y,z)=yz^2{\bf i}+xz^2{\bf j}+2xyz{\bf k}\) is conservative, find a potential function \(f\) and evaluate \(\int_C{\bf F}\cdot d{\bf R}\) where \(C\) is a smooth path from \((1,0,1)\) to \((2,2,3)\).
The asnwer is here.
Quiz 9 (due Friday 11.06.2020 at 3pm) Compute \begin{eqnarray*} \oint_C (ydx +zdy+xdz) \end{eqnarray*} where \(C\) is the triangle with vertices \((3,0,0)\), \((0,0,2)\), and \((0,6,0)\) traversed in this order. The solution is here.
Quiz 10 (due Saturday 11.14.2020 at 12.01pm, so that we avoid the Friday 13 due date) Use the divergence theorem to evaluate \(\iint_S {\bf F}\cdot {\bf N}dS\) for \({\bf F}=xyz{\bf j}\), where \(S\) is the cylinder \(x^2+y^2=9\), \(0\leq z\leq 5\) with the two disk ends included. The solution is here.
Exam 2 has been posted here. The solutions are now posted here.

The Final Exam has been posted here. You have until next Tuesday at 1 pm to solve it. Exactly 7 days!
End of page.