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Introduction to Complex Numbers
The ChemEng Student > Lessons > Introduction to Complex Numbers

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Course Content
Module 1: Engineering Mathematics
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Introduction to Vectors
Basic Applications of Vectors
Scalar & Corss Product
Equations of Lines with Vectors
Equations of Vector Planes
Intersection of Vector Planes
Intersection of Planes & Lines
Determining the Angles
Additional Learning Material
Introduction to Matrices
Matrix Multiplication
Transpose of a Matrix
Identity Matrix
Determinant & Inverse Matrices
Linear Equations with Matrices
Additional Learning Material
Introduction to Differential Equations
First Order Equations
The Integrating Factor
Second Order Homogeneous Equations
Second Order Non-Homogeneous Equations
Additional Learning Material
Introduction to Complex Numbers
Polynomials with Complex Numbers
The Argand Diagram
Polar Form
De Moiver’s Theorem
Additional Learning Material
Trigonometric Functions
Welcome to The course
Recap of Indices
Sine & Cosine Rules
Sketching Quadratics
Introduction to Functions
Applications of Functions
Logarithmic Functions
Additional Learning Material
Introduction to Partial Fractions
The Repeated Factor Problem
Introduction to Factorials
The Binomial Coefficients
The Binomial Expansion Theorem
Additional Learning Material
Introduction to Differentiation
General Applications
The Chain Rule
The Product Rule
The Quotient Rule
Inverse Trig Differentiation
Displacement & Velocity Applications
Optimisation Differentiation
Implicit Differentiation
Parametric Differentiation
Additional Learning Material
Introduction to Integration
General Applications
Definite Integrals
Area Between Two Curves
Integration by Parts
Integration by Substitution
Additional Learning Material
Module 2: Mass & Energy Balances
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Introduction to Mass Balances
Types of Mass Balances
Exercise 1: Mass Balance Distillation Column
Reacting Systems: Stoichiometry
Reacting Systems: Excess & Limiting Reactants
Reacting Systems: Fractional Conversion
Reacting Systems: Chemical Equilibrium
Reacting Systems: Selectivity & Yield
Exercise 2: Reacting Systems
Introduction to Energy Balances
Different Forms of Energy
What is Enthalpy
What is Specific Heat Capacity
Defining Latent Heat
What is Heat of a Reaction
How to use Steam Tables
How to Read Enthalpy Charts
Additional Learning Material
Steps to Modelling Systems
Exercise 3: Mass Balances
Why use a Recycle
Why use a Purge
Exercise 4: Recyle Integration
Energy Balance for Reacting Systems
What is Extent of Reaction
Exercise 5: Extent of Reaction
Additional Learning Material
Single-Stage Equilibrium Gas-Liquid Systems
Exercise 6: Single-Stage Gas-Liquid Systems
Counter-Current Multi-Stage Systems
Exercise 7: Counter-Current Multi-Stage Systems
Dilute Systems
Exercise 8: Analytical Solution for Dilute Systems
Design of Plate Absorption Tower
Exercise 9: Designing Plate Absorption Towers
Module 3: Reactor Design
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Introduction to Rate of Reaction
Exercise 1: Reaction Rate
Arrhenius Equation
Exercise 2: Arrhenius Equation
Introduction to Batch Reactors
Exercise 3: Batch Reactor Modelling
Introduction to CSTR’s
Exercise 4: CSTR Modelling
Introduction to Plug Flow Reactors
What are Stoichiometric Tables
Exercise 5: Stoichiometric Tables
Additional Learning Material
Introduction to Non-isothermal Reactors
Non-Isothermal Batch Reactors
Adiabatic Batch Time
Non-Adiabatic Batch Time
Non-Isothermal CSTR’s
CSTR Design Algorithms
Rate Data Analysis: Differential
Rate Data Analysis: Integral
Rate Data Analysis: Half-Life
Additional Learning Material
Fixed Bed Catalytic Reactors Preliminary Deigns
Modelling of FBCR
Pseudo-Homogeneous Mass Balance
Pseudo-Homogeneous Energy Balance
Heat Transfer in a FBCR
What is the Friction Factor
Mass Transfer Only
Instantaneous Reactions
Stirred Tank Incomplete Mixing
Laminar Flow in Tubular Reactors
Characteristics of Non-Ideal Behavior
Ideal Tracer Response
Residence Time Distribution
Non-Ideal Tracer Response
What is The Pulse Input
What is The Step Input
Additional Learning Material
Module 4: Dimensional Analysis
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Introduction to Dimensional Analysis
Defining Variables
What are Dimensionless Numbers
Introduction to the Buckingham Pi Method
Exercise 1: Buckingham Pi Method
Additional Learning Material
Fundamental Bundle
About Lesson

What you will learn

In this lesson, we will take a look at an introduction to complex numbers. This topic focuses on the solving of equations that would otherwise be unsolvable, using only real numbers. Here we introduce the concept of imaginary numbers, and how the formation of a complex number can help us solve problems that cannot be processed by a calculator. This branch of mathematics can be difficult if you don’t follow a systematic approach.

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