Engineering Mathematics
Overview of Course¶
This course contains the below content, however the delivery of this course is such that the student can choose the topics they wish to delve into.
Foundational Topics¶
- Arithmetic
- Introduction to Algebra
- Expressions and Equations
- Graphs
- Linear Equations
- Polynomial Equations
- Binomials
- Partial Fractions
- Trigonometry
- Functions
- Trigonometric and Exponential Functions
- Differentiation
- Integration
Engineering Mathematics¶
- Complex Numbers
- Hyperbolic Functions
- Determinants
- Matrices
- Vectors
- Differentiation
- Differentiation Applications
- Tangents, Normals and Curvature
- Sequences
- Series
- Curves and Curve Fitting
- Partial Differentiation
- Integration
- Reduction Formulas
- Integration Applications
- Approximate Integration
- Polar Coordinate Systems
- Multiple Integrals
- First-Order Differential Equations
- Second-Order Differential Equations
- Introduction to Laplace Transforms
- Statistics
- Probability
Further Engineering Mathematics¶
- First-Order ODEs
- Second-Order Linear ODEs
- Higher Order Linear ODEs
- Systems of ODEs, Phase Plane, Qualitative Methods
- Series Solutions of ODEs, Special Functions
- Laplace Transforms
- Linear Algebra: Matrices, Vectors, Determinants, Linear Systems
- Linear Algebra: Matrix Eigenvalue Problems
- Vector Differential Calculus, Grad, Div, Curl
- Vector Integral Calculus, Integral Theorems
- Fourier Analysis
- Partial Differential Equations (PDEs)
- Complex Numbers and Functions, Complex Differentiation
- Complex Integration
- Power Series, Taylor Series
- Laurent Series, Residue Integration
- Conformal Mapping
- Complex Analysis and Potential Theory
- Numerics in General
- Numeric Linear Algebra
- Numerics for ODEs and PDEs
- Unconstrained Optimization, Linear Programming
- Graphs, Combinatorial Optimization
- Data Analysis, Probability Theory
- Mathematical Statistics
Delivery of Content¶
Concepts will be explained using key examples and with as much engagement as possible, and throughout the course tutorial questions will be used as well as for homework to enable constant practice.
The primary reference works for this course are a handful of respected selected textbooks.