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Engineering Mathematics II

Electrical Engineering · Level 5  ·  5 Chapters

Compiled by: Martin Gitau

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What Engineering Mathematics II covers

Differentiation, statistics, matrices, vectors and complex numbers are covered in Engineering Mathematics II at Electrical Engineering Level 5. Calculus covers the gradient of a curve, differentiation from first principles, sine, cosine, exponential and logarithmic functions, tangents and normals. Statistics and probability bring measures of central tendency and dispersion, variance, standard deviation, laws of probability and distributions. Matrices cover order, multiplication, determinants, inverses and solving simultaneous equations by the matrix method and Cramer's rule. Vector theory includes position vectors, scalar and vector products, gradient, curl and divergence, and complex numbers end the unit with Argand diagrams and De Moivre's theorem.

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Careers after Engineering Mathematics II

In the world of electrical engineering, the math you master in this unit becomes the backbone of everyday problem-solving on the job. Whether you’re wiring a new solar mini-grid in Kitui or checking the load calculations for a factory in Nakuru, these skills turn numbers into reliable, safe, and efficient power solutions.

  • Electrical design offices in Nairobi’s industrial estates - you use simultaneous equations and quadratic formulas to size transformers, conductors and protective devices, earning a design-engineer salary or freelance fees for each project you complete.
  • Field service teams for rural electrification projects in the Rift Valley - you apply trigonometric ratios and triangle calculations to determine pole heights and cable sag, getting paid per day of field work or per kilometer of line installed.
  • Solar PV installation companies in coastal towns such as Mombasa and Malindi - you perform index and power-law calculations to size inverter capacities and battery banks, receiving commissions or a fixed wage for each system you commission.
  • Telecommunications tower erection crews in Western Kenya - you calculate normals and tangents using coordinate geometry to set antenna angles precisely, earning overtime pay and bonuses for meeting tight alignment tolerances.
  • Manufacturing workshops for motor-control panels in Kiambu - you solve systems of linear equations to balance three-phase loads and design protective relays, receiving a steady monthly salary as an electrical technician.
  • Construction sites building high-rise apartments in Nairobi’s CBD - you use Hero’s formula and trigonometric functions to verify concrete formwork dimensions and steel reinforcement angles, paid per project or through a site-based wage structure.
  • Instrumentation and calibration labs in Eldoret - you evaluate hyperbolic and trigonometric functions to fine-tune oscilloscopes and signal generators, earning hourly rates for specialist testing services.
  • Entrepreneurial ventures offering private tutoring in mathematics for engineering students across Kenya - you translate your problem-solving expertise into lesson plans and charge fees per session or per term.
  • Small-scale electrical contracting firms in Kisumu’s lakeside market - you apply integer arithmetic and basic algebra to prepare accurate material take-offs and cost estimates, earning profit margins on each contract you win.

Your ability to move fluidly between numbers, equations and geometry will open doors across Kenya’s growing power and technology sectors - turning today’s calculations into tomorrow’s career success. Keep sharpening those skills; the next circuit you design could light up a whole community.

Chapters

1
Apply Calculus
43 topics
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2
Apply Statistics and probability
13 topics
Open chapter →
3
Apply matrices
13 topics
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4
Apply Vector Theory
8 topics
Open chapter →
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 117 Multiple-choice, one at a time Practise questions 55 Quick recall — check you know the facts
3 more for this unit
Oral exam preparation 28 What the assessor asks, and how to answer out loud Worked calculations 22 Step-by-step maths with the common mistakes Quick cards 590 Myth busters, skill tips and scenarios

Beyond the syllabus

Decision simulator 3 On site, what would you do? Workplace scenarios 40 Real site situations — what would you do? Turn this into income 24 Where this skill earns — what to charge, how to find clients

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