How to learn Multivariable Calculus for AP Calculus

Also learn Visualizing Vectors: Polar coordinates and Line Integrals

Hi, I am Suman Mathews, math educator. I can help you learn how to integrate over a region by simple curve sketching, how to change the order of integration and more in this course. I can help you overcome your doubts over this topic.

If you want to learn more about integration in Multivariable Calculus, then join this course. If not, then you can benefit from the preview. My students have always found my teaching interesting.

Here, you will learn how to integrate double and triple integrals, Basic techniques of evaluating definite double and triple integrals are taught. You need to remember basic curves such as circle, parabola, ellipse, straight lines.

You will then proceed to evaluating double integrals over a specified region. Some of the regions explained include the first quadrant of an ellipse, a triangle bounded by the lines y = 0, y = x, y+x=2 . Given two curves, you need to note that is important to first find the point of intersection of the two curves.

Next , you will learn how to change the order of integration. How to change the limits when dx dy changes to dy dx and vice versa. How to change the limits for unbounded regions is also shown. One of the examples include changing the order of integration when the region is enclosed between a parabola and a straight line. Another example is changing the order of integration of a semicircle.

The session concludes with an assignment. You will learn how to evaluate the integral of an odd function within the limits -a to a. Integrating over a region bounded by the x axis, the ordinate x = 2a and the parabola x^2=4ay is also shown.

Bonus:You are introduced to polar coordinates and how to integrate using these. It is exciting to note how the limits change and how to calculate them. Note that polar coordinates are extremely important in Mathematics.

Learn about Vector fields and Line Integrals and how to evaluate line integrals over a curve. Also learn how to evaluate line integrals of parametric functions.

Tackle Green's Theorem-Problems and Solutions. Learn Fundamentals of Gauss Divergence Theorem in Problem Solving.

You'll learn about arc length, differential displacement and conservative fields.

AP Calculus

Learn how to find the volume of a solid bounded by curves where cross sections perpendicular to the x axis are squares or semicircles with distances spanning the vertical distances between the curves. Also learn how to find the volume of the solid bounded by curves whose cross sections perpendicular to the x axis are equilateral triangles. You'll learn how to find the volume of a solid bounded by curves and cross sections perpendicular to the y axis are isosceles right triangles.

Find the volume of a solid obtained by revolving a region about the x axis, the y axis and a line y = c.

Don't be afraid to take the first step to start learning!