MAM2000W

Detailed and understandable summary of the Introduction to Matrices. Packed with exam problems and colourful hints. Contains: - Background to systems of linear equations - Matrix notation - Types of matrices and examples - Multiplication of matrices by inner products and linear combinations (detailed explanation and examples) - Transposes of matrices - Properties of matrix transposes and multiplication

Detailed and understandable summary of the Derivatives of Multivariable Functions . Packed with exam problems and colourful hints. Contains: - Background on to derive multivariable (MV) functions - Different notations explained - 7 Examples on finding MV derivatives - 2 Examples finding implicit derivatives of MV functions - 3 Examples of higher order MV derivatives - 1 Examples using a word problem

Detailed and understandable summary of curvature, torsion and equation of planes for vector functions. Packed with exam problems and colourful hints. Contains: - Background on how curvature and torsion equations are derived - All relevant formula's for unit vectors, curvature and torsion and when to apply each - Theory of oscillating circle - 2 Examples testing all unit vectors (T,NB), curvature and normal plane - 2 Examples of finding curvature

Detailed and understandable summary of the Intro to Multivariable Functions. Packed with exam problems and colourful hints. Contains: - Background on multivariable functions - Detailed methods on how to graph domain and functions - 1 Example to find points using a curve - 3 Examples on how to find the domain of a MV function - 4 Examples of graphing the domain of MV function - 3 Examples of graphing a MV function - 5 Examples on finding level curves and contour plots

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

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

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 introduction to vector functions. Packed with examples and colourful hints. Contains: - Background on parametric curves - Conceptual understanding of vector functions - Domain of vector functions - Sketching vector functions (+ 6 examples) - Limits of vector functions (+ 2 examples) - Continuity of vector functions (+ 2 examples)