Interactives for M1920

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Lecture 1: Vectors in the Plane and the Space

• Vectors in the plane

• The 3d Space

• A point in the space

• A vector in the space

• Length of a vector in the space

• The coordinate planes

• The equation of a line in the space

• Summary of two lines in the space

Lecture 2: Dot Product

• The dot product between vectors in the plane

• The dot product between two vectors in the space

Lecture 3: The Cross Product

• The cross product and area of a parallelogram

• Parallelepiped formed by three vectors in the space

• Volume of a parallelepiped using cross products

Lecture 4: Planes in the Space

• A line and a plane in the space

• Intersection of two planes

• Traces of a plane

Lecture 5: Quadric Surfaces

• Summary of Quadric Surfaces

• Quadric surface grapher using plane (xy)-sections

Lecture 6: Cylindrical and Spherical coordinates

• Cylindrical coordinates

• Spherical coordinates

Lecture 7: Vector Valued Functions

• Planar curves grapher

• Space curves grapher

Lecture 8: Derivatives of Vector Valued Functions

• Derivatives of vector valued curves

Lecture 9: Arc Length

• Arc length of vector and space curves

Lecture 10: Multivariable Functions

• Contour map and Level Curves

Lecture 11: Limits and Continuity

• Some curious surfaces

Lecture 12: Partial Derivatives

• Partial derivatives for two variable functions visualizer

Lecture 14: Tangent Plane and Differentiability

• Tangent plane visualizer

Lecture 15: Gradient and Directional Derivatives

• Directional Derivatives for two variable functions visualizer

Lecture 18: Introduction to Double Integrals

• Double integrals over rectangles

Lecture 19: Double integrals over simple domains

• Double integrals over simple domains

Lecture 20: Triple Integrals

• Simple solids in Cartesian Coordinates

Lecture 21: Triple Integrals in Cylindrical and Spherical Coordinates

• Simple solids in Cylindrical Coordinates

• Simple solids in Spherical Coordinates

Lecture 23: General Change of coordinates

• Some videos showcasing change of coordinates

• Tool to visualize transformation of quadrilaterals and triangles

Lecture 28: Orientable Surfaces

• An orientable surface: Cylinder

• A non-orientable surface: Mobius strip