Differentiation
- Introduction to Differentiation
- General Differentiation Applications
- Product Rule
- Quotent Rule
- Displacement & Velocity Applications
- Optimisation Differentiation
- Parametric Differentiation
Mathematics · Year 1
Engineering Mathematics for chemical engineers
A comprehensive engineering mathematics course spanning algebra, functions, calculus, vectors, matrices, differential equations and complex numbers for STEM applications.
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- 52
- 179
- 8
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The subject
What Engineering Mathematics covers
This course covers a comprehensive range of topics found across STEM and engineering degrees, building in-depth mathematical skills essential to engineering applications. It develops a deep understanding of the fundamentals of algebra and functions that underpin the advanced calculus topics of differentiation and integration. Differentiation is explored through general applications, the chain, product and quotient rules, trigonometric differentiation, optimisation, and implicit and parametric techniques. Integration covers definite and indefinite forms, integration by parts and by substitution, and the area between curves. A thorough exploration of vectors and matrices equips learners with the tools required for AI, machine learning, automation and process modelling in industry, and the course completes with complex numbers, the Argand diagram, polar form and De Moivre's theorem. Further calculus extends to differential equations for homogeneous and heterogeneous systems and higher order equations.
What you’ll be able to do
- Explain the role of differentiation within calculus mathematics
- Define integration as the inverse of differentiation
- Define a complex number as a real and imaginary combination
- Define a matrix as a representation of a series of numbers
- Apply basic vector operations to typical problems
- Explain why a differential equation involves integration
The lessons
Every lesson, theme by theme
52 lessons in 8 themes, pitched at Year 1. Your year decides what comes first, never what you can open.
Integration
- Introduction to Integration
- Definite Integrals
- Integration by Parts
- Integration By Subsitution
- The Integrating Factor
Complex Numbers
- Introduction to Complex Numbers
- Polynomial Equations with Complex Numbers
- The Argand Diagram
- Polar Form
- De Moivre's Theorm
Matrices
- Introduction to Matrices
- Transpose of a Matrix
- Identity Matrix
- Linear Equations with Matricies
Vectors & Planes
- Basic Applications of Vectors
- Scalar & Cross Product
- Equations of Planes
- Intersection of Vector Planes
- Determining The Angle Between A Line & Plane
Differential Equations
- Introduction to Differetial Equations
- Second Order Homogenous Equations
Algebra & Series
- Reacp on Indicies
- Sketching Quadratics
- Introduction to Fucntions
- Logarithmic Function
- Trignometric Graphs
- The Repeated Factor Problem
- Introduction to Factorials
- The Binomial Expansion Theorem
More in Engineering Mathematics
- Sine & Cosine Rules
- Applications of Functions
- Introduction to Partial Fractions
- The Bionmial Coefficients
- Chain Rule
- Inverse Trigonometric Functions
- Implicit Differentiation
- General Integration Applications
- Area Between Two Curves
- Introduction to Vectors
- Eqaution of a Line with Vectors
- Intersection of Vector Planes & Lines
- Matrix Multiplication
- Determanints & Inverse Matrices
- First Order Differential Equations
- Second Order Non-homogenous Equations
Before you start
What it builds on
How you’ll learn it
Engineering Mathematics, at your pace
Video lessons
52 lessons and 52 videos, each with what you’ll be able to do by the end.
Practice, marked as you go
179 practice questions, marked the moment you answer, with hints when you’re stuck. Step-by-step worked solutions come with Core.
CERA, when it doesn’t click
Ask CERA to explain any idea in Engineering Mathematics another way, or to test you on it. Every day, on every plan.
Keep exploring
See every subjectDimensional Analysis
An introduction to dimensional analysis, covering fundamental dimensions, dimensionless groups and the Buckingham Pi method.
Mass & Energy Balances
A course on mass and energy balances, covering reacting systems, enthalpy, process modelling, recycle and purge, and multi-stage systems.
Thermodynamics
A comprehensive grounding in thermodynamic principles and cycles, covering energy, efficiency, the ideal gas law and the OTTO, Diesel, Brayton, Carnot and Rankine cycles.
Fluid Dynamics
A study of the properties and behaviour of fluids, covering fluid statics and dynamics, laminar and turbulent flow regimes, and Newtonian and non-Newtonian fluid modelling.
Ready when you are
Build a plan around exactly where you’re stuck
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