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Engineering Mathematics

Chemical Engineering · Level 6  ·  16 Chapters

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What Engineering Mathematics covers

In this unit, you will be able to confidently apply a wide range of mathematical concepts and techniques essential for engineering, from solving complex equations and working with sequences to interpreting data and graphs accurately. You’ll master the use of matrices, vectors, and trigonometry to analyze real-world problems, while also developing skills in differentiation and logarithmic functions to understand rates of change and system behaviors. By the end, you’ll be equipped to tackle practical engineering challenges with precision and insight, turning mathematical theory into powerful tools for your trade.

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Careers after Engineering Mathematics

Engineering Mathematics is not just about numbers and formulas—it's the foundation that supports nearly every technical profession in Kenya. Whether you dream of working in a busy construction site, running your own jua kali workshop, or contributing to the growth of our energy sector, the skills you gain in this unit are used every single day by successful professionals. Here’s how mastering Engineering Mathematics opens real doors:

  • Construction sites: Civil engineers, site supervisors, and quantity surveyors use arithmetic, ratios, and geometry to estimate materials, costs, and measurements for roads, bridges, and buildings—think of projects by companies like China Wu Yi, or county government construction works.
  • Jua kali sector: Metal fabricators, welders, and mechanics rely on algebra, sequences, and accurate measurements to design parts, price jobs, and optimize production—mathematics is the backbone of innovation and efficiency here.
  • KenGen and Kenya Power: Technicians and engineers use graphs, equations, and data analysis for power generation, grid management, and troubleshooting technical faults in power plants across the country.
  • Matatu industry: Owners and managers calculate profits, costs, routes, and maintenance schedules using percentages, ratios, and arithmetic sequences to keep their businesses running smoothly and profitably.
  • Agribusiness and KTDA: Farm managers and agronomists use data collection, analysis, and mathematical modelling to track yields, plan harvests, and optimize resource use for maximum profit.
  • Hospitality and event management: Managers use statistics, ratios, and data presentation to track occupancy, forecast demand, and make decisions that improve service and profitability.

Whether you pursue employment with a leading company or start your own venture, these mathematical skills will help you solve real problems, make smart decisions, and stand out as a professional. Mastering Engineering Mathematics is your ticket to a future full of opportunities—your journey to success starts here!

Chapters

1
Apply Algebra
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2
Apply Trigonometry and hyperbolic functions
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3
Apply complex numbers
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4
Apply Coordinate Geometry
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5
Carry out Binomial Expansion
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6
Apply Calculus
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7
Solve Ordinary differential equations
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8
Carry out Mensuration
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9
Apply Power Series
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10
Apply probability and Statistics
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11
Apply vector theory
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12
Apply matrix methods
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13
Solve partial differential equations
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14
Apply Laplace transforms
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15
Apply Fourier series
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16
Apply Numerical methods
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What Engineering Mathematics covers: 15 main topics in 15 chapters

1. Apply Algebra

  1. 1.1 · Base and Index · Law of indices · Indicial equations · Laws of logarithm · Logarithmic equations · Conversion of bases · Use of Scientific calculator · Solutions of simultaneous linear equations in three unknowns · Solution of equations reduced to quadratic form · Solutions of problems involving AP and GP

2. Apply Trigonometry and hyperbolic functions

  1. 2.1 · Trigonometric functions · Trigonometric identities · Trigonometric equations · Half -angle formula · Factor formula · Compound angle formula · Double angle formula · Parametric equations · Definition of hyperbolic equations · Properties of hyperbolic functions · Evaluations of hyperbolic functions Hyperbolic identities · Osborne's Rule · One-to-one relationship in functions · Ashx+bshx=C equation · Inverse functions for one-to-one relationship · Inverse functions for trigonometric functions

3. Apply complex numbers

  1. 3.1 · Definition of complex numbers · Stating complex numbers in numbers in terms of conjugate argument and Modulus · Representation of complex numbers on the Argand diagram · Arithmetic operation of complex numbers . Application of De Moivre's theorem · Application of complex numbers to engineering

4. Apply Coordinate Geometry

  1. 4.1 · Polar equations · Cartesian equation · Graphs of polar equations · Normal and tangents · Definition of a point · Locus of a point in relation to a circle · Loci of points for given mechanism

5. Carry out Binomial Expansion

  1. 5.1 · Pascal's triangle · Binomial theorem · Roots of numbers using binomial theorem. · Estimation of errors of small changes using binomial theorem · Factorials and combinations using binomial theorem

6. Apply Calculus

  1. 6.1 · Definition of derivatives of a function · Differentiation from first principle · Tables of some common derivatives · Rules of differentiation · Rate of change and small change · Turning/Stationery points of functions of two variables · Definition of integration · Indefinite and definite integral · Methods of integration · Integrals of hyperbolic and inverse functions · Application of integration.

7. Solve Ordinary differential equations

  1. 7.1 · Types of first order differential equations · Formation of first order differential equation · Solution of first order differential equations using different methods · Application of first order differential equations · Formation of second order differential equations for various systems · Solution of second order differential equations using method of undetermined coefficients · Application of second order differential equations

8. Carry out Mensuration

  1. 8.1 · Units of measurements · Perimeter and areas of regular figures · Volume and Surface area of regular solids · Area of irregular figures · Areas and volumes using Pappus theorem

10. Apply probability and Statistics

  1. 10.1 · Classification of data · Grouped data :unselected: · Ungrouped data :unselected: · Data collection · Tabulation of data o Class intervals :unselected: · Class boundaries :unselected: o Frequency tables :unselected: · Diagrammatic and graphical presentation of data e.g. o Histograms :unselected: o Frequency polygons :unselected: o Bar charts :unselected: :unselected: o Pie charts :unselected: o Cumulative frequency curves · Measures of central tendency mean, mode and median · Measures of disper

11. Apply vector theory

  1. 11.1 . Vectors and scalar in two and three dimensions · Operations on vectors: Addition and Subtraction, multiplication · Position vectors · Dot and cross product · Resolution of vectors

12. Apply matrix methods

  1. 12.1 · Matrix operation · Determinant of 3x3 matrix · Inverse of 3x3 matrix · Solution of linear simultaneous equations in 3 unknowns · Calculation of Eigen values and Eigen vectors

13. Solve partial differential equations

  1. 13.1 · Definition of partial differential equations. · Formation of first order partial differential equations · Solution of first order partial differential equations using different partial differential methods o Characteristics and methods of characteristics. o The method of separation of :unselected: variables. :unselected: o Linear and quasi-linear first order PDEs. :unselected: · Solution of second order partial differential equations using established methods. o Fourier series :unselected: :un

14. Apply Laplace transforms

  1. 14.1 · Definition of the Laplace transform. · Properties of Laplace transforms (linearity, time shifting, etc.). . The concept of the region of convergence. · Solutions of Laplace transforms using initial and final value theorems · Calculation of inverse Laplace transforms using partial fractions · Solution of differential equations using Laplace transforms

15. Apply Fourier series

  1. 15.1 · Definition of Fourier Series · Introduction to periodic functions · Obtaining Fourier series coefficients (a0, an, bn) · Derive and analyze Fourier series for functions defined over periods from 2x to T · Definition of odd and even functions · Obtaining Fourier series for odd and even functions · Introduction to harmonic analysis and its applications · Numerical methods for approximating Fourier coefficients

16. Apply Numerical methods

  1. 16.1 · Simpson · Newton-Raphson · Runge-Kutta

Revise this unit

Exam-style questions 196 Written to CDACC standard, with answers Test yourself 340 Multiple-choice, one at a time Practise questions 220 Quick recall — check you know the facts
3 more for this unit
Oral exam preparation 86 What the assessor asks, and how to answer out loud Worked calculations 66 Step-by-step maths with the common mistakes Quick cards 1,734 Myth busters, skill tips and scenarios

Beyond the syllabus

Decision simulator 9 On site, what would you do? Workplace scenarios 140 Real site situations — what would you do? Turn this into income 97 Where this skill earns — what to charge, how to find clients

Other units in Module II