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ModuleInformation

ELE1012

Mathematics 1

Course Contents

  1. Fundamentals Survey
    •Measurement Error, Dimensionality, Trigonometry, Polynomials, Logarithms

  2. Complex Mathematics
    •Fundamentals; Cartesian, Polar and Exponential Representations; DeMoivre’s Theorem

  3. Vector Mathematics
    •Fundamentals; Lines and Planes; Dot and Cross Products

  4. Matrix Mathematics
    •Fundamentals; Matrix Manipulation; Matrix Triangularisation

  5. Linear Equations
    •Fundamentals;  Matrix Inverse Solution; Cramer’s Rule; Gaussian Elimination

  6. Differentiation
    •Fundamentals; Curve Sketching; Product and Chain Rules; Parametric Differentiation; Logarithmic Differentiation; Parital Differentiation

  7. Differential Equations
    •Fundamentals; 1st Order Methods; 2nd Order Methods

  8. Integration
    •Fundamentals; Integrating functions of functions; Integration functions of linear functions; Integration by parts; Integration by substitution; Integration by Reduction Formula; Applications

  9. Sequences and Series
    •Fundamentals; Convergence and Limits; Tests of Convergence; Power Series Properties; Limits for Indeterminate Solutions; L’Hopitals’s Rule;

  10. Function Approximation
    •Fundamentals; Limiting Indeterminate Analytical Functions; Taylor’s and Maclaurin’s Series; Compositie Series Approximations; Accuracy Limitations

Supplementary Notes

None

Learning Outcomes

On completing this module, a student will:

  1. Have a strong grasp on the fundamental mathematical concepts pertaining to Electrical and Electronic Engineering

  2. Understand the fundamental concepts associated with, and solve problems on:
    1. Complex and vector mathematics,
    2. Triangularisation and inversion of matrices of any size
    3. Solution of linear equations of n variables;
    4. Differentiation of simple, parameteric and logarithmic functions
    5. 1st and 2nd order differential equations
    6. Integration of functions of functions, functions of linear functions, by parts, substitution or reduction;
    7. Sequences and series
    8. Functional approximation

Skills

See Learning Outcomes.