Vector calculus - Study guides, Study notes & Summaries

Detailed and understandable summary of the derivatives and integrals of vector functions. Packed with exam problems and colourful hints. Contains: - Background on derivatives of vector functions - Basic derivatives of vector functions - Point of tangency and tangent vector examples - Unit tangent vectors - Tangent line examples - Integrals of vector functions - Initial Value problems and examples

Detailed and understandable summary of the derivatives and integrals of vector functions. Packed with exam problems and colourful hints. Contains: - Background on arc length and how the formula are derived - Detailed method sheets for calculating both arc length and how to reparametrise - 3 Examples of finding exact arc length and arc length function - 2 examples of arc length reparametrisation

For every natural number n we define n-dimensional space as the set Rn of all ordered n-tuples x1 x2  xn where xi  R for i  1 2  n. One-dimensional space R1 corresponds with the set of real numbers R. For n  2 we usually denote the ordered n-tuple x1 x2     xn by x, the ordered n-tuple a1 a2     an by a, and so on. If x  x1 x2  xn, we say that xi is the i’th coor...

Detailed and understandable summary of the derivatives and integrals of vector functions. Packed with exam problems and colourful hints. Contains: - Basic introduction into TNB Frames - Explanation of what each unit vector means geometrically - Formula to calculate each unit vector - Proof of why the unit tangent, normal and binormal are mutually orthogonal