TheActSciGuy

Detailed and understandable summary on the Economics of the Environment. Covers the entire chapter and makes it easily understandable. Packed with graphs and colourful hints.

Detailed and understandable summary on the Economics of the Environment. Covers the entire chapter and makes it easily understandable. Packed with graphs and colourful hints.

Detailed and understandable summary notes of the entire MAM2000W Linear Algebra course. Packed with exam problems and colourful hints. *Contains no proofs*. Work through all note packs, in order, and you'll be ready to ace the test/exam. Notation has been simplified so it's easy to understand. Lots of detailed method sheets for questions.

Detailed and understandable summary of Vector Spaces and Subspaces Packed with exam problems and colourful hints. Contains: - Detailed definition of a vector space - Closure of vector spaces - 10 Axioms - 7 Examples of proving sets of elements are vector spaces - Explanation of The Span to prove Subset Theorem - 4 Examples of prior theorem - Detailed explanation of the null space, column space with 2 examples each - Differences between null space and column space

Detailed and understandable summary of the Basis of a Vector Space/Subspace. Packed with exam problems and colourful hints. Contains: - Basic explanation of a Basis and Dimension of a Basis - Detailed method for basis of the column space, a span of vectors, null space, general subspace, and row space - 1 Example to find basis of span - 1 Examples to find basis of general subspace - Definition of Row space - Explanation of dimensions of vector spaces - Standard basis of vector spaces and polynom...

Detailed and understandable summary of Markov Chains and Steady State Vectors. Packed with examples and colourful hints. Contains: Detailed explanation Markov Chains - Transition diagrams - 1 Detailed Example - Initial and Future state vectors - Transition Matrices - Steady state vectors explained and formula - 1 Example of finding the steady state vector

Detailed and understandable summary of The Rank-Nulity Theorem. Packed with examples and colourful hints. Contains: Detailed explanation of the Rank-Nulity Theorem - How the results of the Rank-Nulity Theorem are added to the Invertible Matric Theorem - 9 Easy to Complex examples of applying the Rank-Nulity theorem.

Detailed and understandable summary of Invertible Matrices and The Invertible Matrix Theorem. Packed with examples and colourful hints. Contains: Notation - 2x2 Inverse - 2 Examples of 2x2 inverse - 3x3 Inverse by row equivalence and expansion formula - 4 Examples of 3x3 case for both methods - Properties of inverse matrices - The invertible matrix theorem detailed breakdown - 4 Application questions on the invertible matric theorem.

Detailed and understandable summary of Eigenvalues, Eigenvectors and Diagonalization. Packed with examples and colourful hints. Contains: Important notation -Detailed method to find eigenvalues and eigenvectors - Eigenspaces - 2 detailed and annotated examples - All possible question types for eigenvalues and eigenvectors explained - Clear explanation of diagonalization - Detailed method of Diagonalization - 1 Example of Diagonalization

Detailed and understandable summary of Determinants and Cramer's Rule. Packed with examples and colourful hints. Contains: Explanation and notation of determinants - 2x2 determinant case - 3x3 determinant case by cofactor expansion via column or row - 2 Examples of cofactor expansion - Determinants of triangular matrices - Effects of row operation on determinants - Cramer's Rule explanation - 3 Examples of Cramer's Rule - Cramer's Rule for inverse matrices, with examples.

Detailed and understandable summary of Coordinates with respect to a basis. Packed with examples and colourful hints. Contains: Important notation - An explanation of the coordinate system - The Standard basis - Basis of polynomials - 3 Examples of all possible variations (find coordinate vector, basis or vector) - Change of coordinates between two different basis.

Detailed and understandable summary of how to Solve Matrices. Packed with exam problems and colourful hints. Contains: - Types of row operations - Row echelon form and Reduced Row echelon form - Row echelon terminology - Types of solutions - Parametric form for solution (detailed) - Elementary matrices - Inverse elementary matrices - Row equivalence

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 on Theory of the Firm. Covers costs, production and perfect competition. Packed with graphs and colourful hints. Contains: - Production in the long and short run - Average, marginal and total product - Types of production functions - Costs in the long and short run - Average, marginal and total cost curves - Theory on perfect competition in the long and short run - Industry and firm supply curves - Consumer and producer surplus.

Detailed and understandable summaries of the MAM2000W advanced calculus test 1 content. Packed with exam problems and colourful hints. Contains all notes for vector functions and partial notes for multivariable functions.

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