## Words From Hong-Jian:

This is the area where you may find something arisen from working on the problems in Calculus. Now it is in the beginning stage. I hope this will grow and will offer Calculus learning students certain help outside the classroom. Students are the most important for making this place to grow and to become a spot where the Calculus learning students would find helpful. Please send your feedback and suggestions to me at hjlai@math.wvu.edu and I will appreciate your comments very much.

 Click the Tip to see if that will be helpful for you. All these reviews are in PDF format, which may require an Acrobat Reader to view them. If you do not have an Acrobat Reader, you can download one free by clicking Acrobat Reader.

 Tip ·        Operations involving 3D vectors ·        Compute the angle between two vectors ·        Compute component of a vector a along a vector b Tip ·        Write the equation of a sphere ·        Compute the center and the radius of a sphere ·        Determine if two vectors are parallel or perpendicular Tip ·        Determine if three points are coline ·        Compute the direction cosines of a vector ·        Verify the triangle inequality ·        Compute the  cross (vector) product of two vectors ·        Find unit vectors perpendicular to two given vectors ·        Compute areas ·        Compute volumes ·        Compute the equations of a line in space ·        Determine the relationship of two lines ·        Write the equation of a plane ·        Determine the relationship of a line and a plane ·        Find the angle between two planes ·        Write equations of a line as intersections of two planes ·        Determine the relationship of a line and a plane (in parametric equations) ·        Determine the relationship of two planes (in parametric equations) ·        Show a parametric curve is lying on a surface ·        Evaluate vector functions ·        Find velocity and acceleration vectors ·        Compute the integrals of vector functions ·        Compute the derivative of vector functions ·        Find position vectors ·        Show facts on vectors ·        Compute the arc length of curves ·        Compute the curvature of a curve ·        Search the place with maximum curvature Tip ·        Compute unit tangent and unit normalvectors, tangential and normal components ·        Write an equation for the surface generated by revolving a plane curve around an axis ·        Determine the projection of the intersection curve of two surfaces ·        Convert from one coordinate system to another Tip ·        Convert equations from one coordinate system to another, I ·        Convert equations from one coordinate system to another, II ·        Determine the largest possible domain of a function ·        Use limit laws to evaluate limits ·        Determine if the limit does not exist ·        Compute partial derivatives ·        Find an equation of the tangent plane Tip ·        Find the points with horizontal tangent planes ·        Find the lowest or highest point of surfaces ·        Find the maximum and minimum values of f(x,y) over a region R Tip ·        Compute partial derivatives with Chain Rule ·        Compute the Gradient Vector ·        Compute the directional derivative of a function ·        Find the maximum directional derivatives of a function at a given point ·        Find tangent planes with normal gradient vector ·        Find and classify critical points ·        Compute the (double integral) Riemann sum ·        Evaluate double integrals over rectangular regions ·        Evaluate double integrals over general regions (and change order of integration) ·        Compute area and volume by evaluating double integrals ·        Compute double integrals in polar coordinates ·        Compute iterated triple integrals Tip ·        Compute integrals in cylindrical coordinates ·        Compute integrals in spherical coordinates ·        Compute the mass and the centroid and the moments of a solid ·        Compute the line integrals ·        Compute the line integrals in conservative fields and search for potential functions ·        Compute integrals using Green's Theorem If you think that this webpage has been useful in helping your study, please send a message to hjlai@math.wvu.edu to acknowledge it. Your email will support the further development of this and other similar assistance for Calculus studying students.

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