Summary Notes for Entire Course

Description

These notes thoroughly cover all lecture content for the entire course - for the final exam. Notes include but not limited to the following topics: Tuesday, 2 March 2021 7:32 pm MATHS Matrices Rules of addition Multiplication of Matrices 'Strange' Properties of Matrix Multiplication Identity matrix - matrix equivalent of the number 1 The Inverse of a Matrix Transpose matrix Summary: rules of matrix algebra Linear Equations Linear Equations Solving Linear Systems Row Reduction and Echelon Form Finding the Inverse of a 3x3 Matrix An Application In Electrical Engineering Determinants PROPERTIES Invertible Matrix Theorem Eigenvalues and Eigenvectors Linear Transformations Reflections Matrices in R2 Definition of Functions of Several Variables Graph of Functions Limit for a One-Variable Function Limits in Two Dimensions Continuity in Two Dimensions Partial Derivatives High order partial derivatives Clairaut's Theorem Laplace's Equation Wave Equation Tangent Lines and Planes Linear Approximation Differentials Chain Rule with One Independent Variable Changing Coordinates Implicit Differentiation STATISTICS Types of Data CATEGORICAL NUMERICAL Major Branches of Statistics INFERENTIAL STATISTICS Numerical Descriptions of Data Measures of Central Tendency MEAN MEDIAN MODE Symmetry Measures of Variability RANGE VARIANCES STANDARD DEVIATION QUARTILES INTERQUARTILE RANGE Displaying Categorical Data Measures of Relative Standing Z SCORES Random Variables Discrete Random Variables Expectation and Variance Binomial Distribution Poisson Distribution Continuous Random Variables Probability Density Functions Cumulative Distribution Function Calculating Probabilities Mean and Variance of a Distribution (continuous random variable) Exponential Distribution Poisson and Exponential Distributions Lack of Memory (concept) - exponential distribution Normal Distribution Special Case: Standard Normal Distribution Using the Normal Tables Finding Normal Probabilities Statistical Independence Components in Series Components in Parallel Linear Combinations of Random Variables Central Limit Theorem Estimation Determining Sample Size