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Engineering Mathematics II

Electrical Engineering · Level 6  ·  5 Chapters

Compiled by: Paul Nganga

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What Engineering Mathematics II covers

In this unit, you will be able to confidently tackle a wide range of engineering mathematics problems, from solving complex equations to mastering trigonometric and hyperbolic functions. You will develop the skills to accurately calculate angles, sides, and areas, and apply coordinate geometry to real-world engineering challenges. By the end, you’ll be equipped to use these mathematical tools effectively, empowering you to solve practical problems with precision and confidence in your trade.

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Careers after Engineering Mathematics II

Mastering the mathematics in this unit equips you with the analytical muscle that Kenyan engineers rely on every day. Whether you join a large firm, start your own service, or support community projects, these skills turn abstract numbers into real-world solutions and open pathways to rewarding careers.

  • Electrical design offices in Nairobi’s industrial estates - you use simultaneous equations, quadratic formulas and trigonometric ratios to size transformers, design distribution layouts and calculate fault currents, earning a salary as a design or project engineer.
  • Renewable-energy installation firms in Kisumu and Eldoret - you apply trigonometric and hyperbolic calculations to set optimal tilt angles for solar panels and blade pitch for wind turbines, charging clients for consultancy, design, and commissioning fees.
  • Construction and civil-engineering companies in Kiambu and Nakuru - you determine forces, angles and areas of beams, columns and roof trusses with trigonometric rules and Hero’s formula, earning wages as a structural analyst, estimator or site supervisor.
  • Telecommunications network-planning teams in Mombasa’s port area - you solve systems of equations and use coordinate geometry to locate antenna towers, model signal coverage and optimise link budgets, receiving remuneration as a network planner or RF engineer.
  • Manufacturing workshops for motor rewinding and PCB assembly in Thika - you perform index calculations and evaluate hyperbolic functions for motor speed-control circuits and filter designs, getting paid per project or as a maintenance technician.
  • Surveying and mapping services for county councils - you determine normals and tangents to plot terrain contours, apply coordinate-geometry methods to produce accurate topographic maps, earning fees per survey contract.
  • Academic tutoring centres in Westlands and Karen - you teach these mathematical concepts to secondary-school and diploma students, earning income from tuition fees while reinforcing your own expertise.
  • Freelance engineering consultancy through online platforms - you solve client problems ranging from power-factor correction to HVAC load calculations using quadratic and trigonometric methods, billing per hour or per solution.
  • Research labs at universities in Eldoret and Machakos - you evaluate hyperbolic functions in signal-processing experiments and control-system simulations, receiving stipends or research grants while contributing to innovation.

Keep sharpening these mathematical tools - you’ll find them at the heart of every engineering challenge across Kenya, and they’ll help you build a career that’s both stable and inspiring.

Chapters

1
Apply Calculus
43 topics
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2
Apply Statistics and probability
13 topics
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3
Apply matrices
13 topics
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4
Apply Vector Theory
8 topics
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5
Apply Complex Numbers
3 topics
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What Engineering Mathematics II covers: 64 main topics in 5 chapters

1. Apply Calculus

  1. 1.1 Introduction to calculus
  2. 1.2 Functional notation
  3. 1.3 The gradient of a curve
  4. 1.4 Differentiation from first principles
  5. 1.5 Differentiation of y = axn by the general rule
  6. 1.6 Differentiation of sine and cosine functions
  7. 1.7 Differentiation of eax and ln ax
  8. 1.8 Methods of differentiation
  9. 1.9 Some applications of differentiation
  10. 1.10 Practical problems involving
  11. 1.11 Tangents and normal
  12. 1.12 Small changes
  13. 1.13 Logarithmic differentiation
  14. 1.14 Introduction to logarithmic differentiation
  15. 1.15 Integral Calculus
  16. 1.16 Standard integration
  17. 1.17 The process of integration
  18. 1.18 The general solution of integrals of the form axn
  19. 1.19 Definite integrals
  20. 1.20 Integration using algebraic substitutions
  21. 1.21 Algebraic substitutions algebraic substitutions
  22. 1.22 Further worked problems on integration using algebraic substitutions
  23. 1.23 Change of limits
  24. 1.24 Integration using trigonometric substitutions
  25. 1.25 Integration using partial fractions
  26. 1.26 The t = tan 0 substitution
  27. 1.27 Integration by parts
  28. 1.28 Numerical integration
  29. 1.29 The trapezoidal rule
  30. 1.30 The mid-ordinate rule
  31. 1.31 Simpson's rule

2. Apply Statistics and probability

  1. 2.1 Measures of central tendency mean, mode and median
  2. 2.2 Measures of dispersion
  3. 2.3 Variance and standard deviation
  4. 2.4 Definition of probability
  5. 2.5 Laws of probability
  6. 2.6 Expectation variance and SD
  7. 2.7 Calculations involving discrete and continuous random variables
  8. 2.8 Types of distributions
  9. 2.9 Mean, variance and SD of probability distributions
  10. 2.10 Application of probability distributions

3. Apply matrices

  1. 3.1 Matrix
  2. 3.2 Order of a matrix
  3. 3.3 Square matrix
  4. 3.4 Compatibility in addition and
  5. 3.5 Multiplication of matrices
  6. 3.6 Multiplication of a matrix by a scalar Matrix multiplication
  7. 3.7 Identity matrix
  8. 3.8 Determinant of a 2 x 2 matrix
  9. 3.9 Inverse of a 2 x 2 matrix and
  10. 3.10 Singular matrix
  11. 3.11 Solutions of simultaneous equations in two unknowns by
  12. 3.12 Matrix method
  13. 3.13 Crammer rule

4. Apply Vector Theory

  1. 4.1 Vectors and scalar in two and three dimensions
  2. 4.2 Position Vectors
  3. 4.3 Resolution of vectors
  4. 4.4 Scalar and vector product
  5. 4.5 Gradient,
  6. 4.6 Curl
  7. 4.7 Divergence

5. Apply Complex Numbers

  1. 5.1 Argand diagrams
  2. 5.2 Complex numbers operations
  3. 5.3 De Moivres Theorem

Revise this unit

Exam-style questions 70 Written to CDACC standard, with answers Test yourself 115 Multiple-choice, one at a time Practise questions 27 Quick recall — check you know the facts
3 more for this unit
Oral exam preparation 26 What the assessor asks, and how to answer out loud Worked calculations 21 Step-by-step maths with the common mistakes Quick cards 583 Myth busters, skill tips and scenarios

Beyond the syllabus

Decision simulator 3 On site, what would you do? Workplace scenarios 20 Real site situations — what would you do? Turn this into income 12 Where this skill earns — what to charge, how to find clients

Other units in Module V