Department of Mathematics
University of California, Santa Barbara
Math 6A
Vector Calculus I
| Text | Introduction to dot product |
| Video - 7:26 | Video on dot product |
| Text | Introduction to cross product |
| Video - 8:05 | Video on cross product |
| Text | Introduction to writing lines in parametric form |
| Text | Finding equations for planes using its normal vector |
| Text | Introduction to the 3D coordinate system |
| Text | Introduction level curves and traces |
| Text | Examples of graphing functions written in vector form |
| Java | Graphs of surfaces, curves, slope fields |
| Java | Graphs some preset surfaces |
| Video - 8:45 | Graphing parametric curves |
| Video - 8:17 | Finding arc length of a parametric curve |
| Video - 5:50 | Finding derivatives of parametric functions |
| Video - 6:57 | Graphing a curve in polar coordinates |
| Video - 6:21 | Finding the domain of a multivariable function |
| Video - 8:39 | Showing the limit of a multivariable function does not exist |
| Video - 9:40 | Chain rule for a multivariable function |
| Text | Introduction to cylindrical coordinates |
| Text | Introduction to spherical coordinates |
| Text | Examples of finding limits of functions of several variables |
| Text | Introduction to partial derivatives |
| Text | Introduction to partial derivatives of higher order |
| Text | Explanation of chain rule for functions of several variables |
| Video - 11:11 | First of 2 videos on partial derivatives |
| Video - 7:12 | Introduction to partial derivatives |
| Text | Notes on directional derivatives and gradient |
| Video - 9:45 | First of 2 videos on gradients |
| Video - 2:13 | Introduction to the gradient |
| Video - 6:42 | Examples to the directional derivative |
| Text | Notes on tangent planes and linear approximation |
| Text | Notes on obtaining tangent planes via the gradient |
| Video - 7:40 | Finding a plane that contains three given points |
| Video - 5:38 | Finding the intersection between a line and plane |
| Video - 12:15 | Finding tangent planes to a surface and using it to approximate points on the surface |
| Text | Notes on relative min's and max's |
| Text | Notes on finding extreme min's and max's |
| Text | Notes on Lagrange multipliers |
| Java | Applet for visualizing the Lagrange multiplier |
| Video - 9:57 | Introduction to Lagrange multipliers |
| Video - 7:45 | Video on parametrizing paths |
| Java | Plot curves from a list of parametrizations |
| Video - 7:41 | Writing a line in vector form |
| Video - 14:45 | Video on the derivative of a parametrized path |
| Video - 18:48 | Video on line integrals |
| Text | Examples of path parametrization and line integrals | Continues to a second page |
| Video - 7:29 | Evaluating a line integral along a straight line |
| Text | Introduction to vector fields and the gradient vector field |
| Video - 8:10 | Sketching vector fields |
| Video - 9:32 | First of 3 videos on curl |
| Video - 10:20 | First of 3 videos on divergence |
| Text | Notes on divergence and curl |
| Video - 6:10 | Example of showing a vector field is conservative |
| Video - 16:46 | Video on line integrals |
| Text | Notes on line integrals of vector fields |
| Video - 11:32 | Calculating work over a line |
| Text | Notes on path independence |
| Video - 17:14 | Video on path independence |
| Text | Notes on conservative vector fields | Uses notion of path independence |
| Video - 8:25 | Video on integrals of conservative vector fields | Uses notion of path independence |
| Video - 4:15 | Video on path independence |
| Video - 10:29 | First of 6 videos on double integrals |
| Text | Introduction to double integrals |
| Text | Examples evaluating double integrals |
| Text | Double integrals over non-rectangular regions |
| Text | Using polar coordinates with double integrals |
| Text | Change of variables formula (double and triple integral examples) |
| Text | Notes on surface area |
| Video - 8:45 | Introduction to double integrals |
| Video - 10:20 | Double integrals over non-rectangular regions |
| Video - 5:15 | First of 3 videos on double integrals using polar coordinates |
| Video - 4:20 | Changing order of integration |
| Video - 10:38 | First of 3 videos on triple integrals |
| Text | Examples of evaluating triple integrals |
| Text | Using cylindrical coordinates with triple integrals |
| Text | Using spherical coordinates with triple integrals |
| Video - 5:59 | Examples of triple integrals |
| Video - 6:03 | Example of a triple integral using spherical coordinates |
| Text | Parametrizing surfaces |
| Video - 22:14 | Video on surface integrals |
| Text | Notes on surface integrals |
| Text | Notes on surface integrals over vector fields |
| Video - 7:08 | Surface integral example |
| Video - 8:23 | Video on flux |
| Java | Visualize the flux across a circle |
| Java | Visualize the flux across a surface |
| Video - 14:26 | First of 4 videos on Green's Theorem |
| Text | Notes on Green's Theorem |
| Video - 6:42 | Video on Green's Theorem |
| Video List | List of Khan Academy videos on Divergence Theorem |
| Text | Notes on Divergence Theorem |
| Text | Notes on Stoke's Theorem |
| Video - 12:12 | First of 11 videos on Stoke's Theorem |
