Engineering Mathematics I

Electronics Engineering · Level 6  ·  10 Chapters

Compiled by: Peter Kiprono

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What Engineering Mathematics I covers

In this unit, you will be able to confidently apply essential mathematical concepts to solve real-world electronics engineering problems, from performing precise calculations with numbers and complex operations to tackling simultaneous equations and trigonometric challenges. By mastering these skills, you’ll be equipped to analyze circuits, interpret signals, and design systems with accuracy and confidence, laying a strong foundation for your success in the electronics trade.

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Careers after Engineering Mathematics I

Electronics engineering relies heavily on the kind of mathematics you’re mastering in this unit. Whether you end up designing circuits for a solar-power installer in Kitale, troubleshooting signal-processing equipment for a broadcast studio in Nairobi, or running your own hobby-electronics workshop in Mombasa, these mathematical tools become the language you use to turn ideas into working hardware.

  • Telecommunications network planning firms in Nairobi and Kisumu - you apply complex numbers and phasor diagrams to model signal propagation, solve simultaneous equations for multi-path routing, and use trigonometric calculations to optimise antenna tilt and placement, earning a salary as a network design engineer or as a freelance consultant on contract projects.
  • Renewable-energy installation companies in Kitale, Eldoret and Turkana - you use quadratic and trigonometric equations to size solar-panel arrays, calculate tilt angles for maximum sun exposure, and convert polar to Cartesian coordinates for mounting-frame layouts, receiving payment through project-based engineering fees or by offering your own design-service business.
  • Power-distribution utilities and sub-station engineering teams in Nakuru and Thika - you solve simultaneous equations and power-series expansions to analyse load-flow, determine fault currents, and design protective relays, earning a regular wage as a power-systems analyst or as an independent contractor for short-term studies.
  • Electronic-equipment manufacturing workshops in Kiambu and Machakos - you employ indices calculations and binomial expansions to predict component tolerances, use Hero’s formula to layout printed-circuit-board (PCB) panels efficiently, and plot polar graphs for RF filter design, earning income as a production engineer or by running a small-scale PCB-fabrication service.
  • Medical-device maintenance firms serving county referral hospitals in Kisumu and Nakuru - you use complex-number arithmetic and Argand diagrams to troubleshoot AC-driven diagnostic machines, convert polar measurements from sensors to Cartesian data for software calibration, and calculate angles for precise probe positioning, earning a technician’s salary or charging per-service fees for private repairs.
  • Audio-visual integration companies working on hotels and resorts along the coast - you apply trigonometric ratios to calculate speaker-placement angles, use simultaneous equations to balance multi-zone amplification systems, and determine normals and tangents for acoustic panel design, earning project fees as a systems integrator or by offering freelance AV-design consultancy.
  • Agricultural-automation start-ups in Meru and Nyeri - you model irrigation-pump control loops with hyperbolic functions, convert sensor outputs from polar to Cartesian form for microcontroller programming, and use power-series approximations to optimise algorithm speed, earning a salary as a control-systems engineer or by selling your own automation kits to farms.
  • University research labs and technical colleges across Kenya - you assist in teaching labs that require precise plotting of polar equations, derivation of normals for mechanical-electronics hybrid projects, and evaluation of trigonometric identities, earning stipends as a teaching assistant or by providing private tutoring services.

Mastering these mathematical techniques opens doors to both stable employment in Kenya’s growing tech and infrastructure sectors and the freedom to launch your own engineering-service venture. Keep building that confidence - each equation you solve brings you one step closer to shaping the devices and systems that power our country.

Chapters

What Engineering Mathematics I covers: 98 main topics in 10 chapters

1. Apply number systems

  1. 1.1 Types of numbers
  2. 1.2 Percentages
  3. 1.3 Factors
  4. 1.4 Divisibility Test
  5. 1.5 LCM
  6. 1.6 Integers
  7. 1.7 Fractions
  8. 1.8 Decimals
  9. 1.9 Arithmetic operation
  10. 1.10 Squares and square roots

2. Apply algebra

  1. 2.1 Indices and logarithms
  2. 2.2 Algebra
  3. 2.3 Simultaneous Equation
  4. 2.4 Solve simultaneous equation by;
  5. 2.5 Quadratic expressions and equations

3. Apply Trigonometry and Hyperbolic functions

  1. 3.1 Importance of trigonometry in engineering
  2. 3.2 Trigonometric Ratios and Functions
  3. 3.3 Trigonometric Identities
  4. 3.4 Solving Trigonometric Equations
  5. 3.5 Trigonometry in Triangles
  6. 3.6 Introduction to Hyperbolic Functions
  7. 3.7 Hyperbolic Identities
  8. 3.8 Solving Hyperbolic Equations
  9. 3.9 Applications of Hyperbolic Functions in Engineering

4. Perform coordinates geometry

  1. 4.1 Polar equations
  2. 4.2 Cartesian equation
  3. 4.3 Graphs of polar equations
  4. 4.4 Normal and tangents
  5. 4.5 Loci

5. Carry out binomial expansions

  1. 5.1 Basic concepts of binomial theorem
  2. 5.2 Binomial Expansion
  3. 5.3 Applications of Binomial Expansion
  4. 5.4 Engineering Applications
  5. 5.5 Estimating values in engineering calculations

6. Apply Calculus

  1. 6.1 Introduction to calculus
  2. 6.2 Functional notation
  3. 6.3 The gradient of a curve
  4. 6.4 Differentiation from first principles
  5. 6.5 Differentiation of y = axn by the general rule
  6. 6.6 Differentiation of sine and cosine functions
  7. 6.7 Differentiation of eax and ln ax
  8. 6.8 Methods of differentiation
  9. 6.9 Some applications of differentiation
  10. 6.10 Practical problems involving
  11. 6.11 Tangents and normal
  12. 6.12 Small changes
  13. 6.13 Logarithmic differentiation
  14. 6.14 Introduction to logarithmic differentiation
  15. 6.15 Integral Calculus
  16. 6.16 Standard integration
  17. 6.17 The process of integration
  18. 6.18 The general solution of integrals of the form axn
  19. 6.19 Definite integrals
  20. 6.20 Integration using algebraic substitutions
  21. 6.21 Algebraic substitutions algebraic substitutions
  22. 6.22 Further worked problems on integration using algebraic substitutions
  23. 6.23 Change of limits
  24. 6.24 Integration using trigonometric substitutions
  25. 6.25 Integration using partial fractions
  26. 6.26 The t = tan 0 substitution
  27. 6.27 Integration by parts
  28. 6.28 Numerical integration
  29. 6.29 The trapezoidal rule
  30. 6.30 The mid-ordinate rule
  31. 6.31 Simpson's rule

7. Apply Statistics and probability

  1. 7.1 Measures of central tendency mean, mode and median
  2. 7.2 Measures of dispersion
  3. 7.3 Variance and standard deviation
  4. 7.4 Definition of probability
  5. 7.5 Laws of probability
  6. 7.6 Expectation variance and SD
  7. 7.7 Calculations involving discrete and continuous random variables
  8. 7.8 Types of distributions
  9. 7.9 Mean, variance and SD of probability distributions
  10. 7.10 Application of probability distributions

8. Apply matrices

  1. 8.1 Matrix
  2. 8.2 Order of a matrix
  3. 8.3 Square matrix
  4. 8.4 Compatibility in addition and
  5. 8.5 Multiplication of matrices
  6. 8.6 Multiplication of a matrix by a scalar Matrix multiplication
  7. 8.7 Identity matrix
  8. 8.8 Determinant of a 2 x 2 matrix
  9. 8.9 Inverse of a 2 x 2 matrix and
  10. 8.10 Singular matrix
  11. 8.11 Solutions of simultaneous equations in two unknowns by
  12. 8.12 Matrix method
  13. 8.13 Cramer's rule

9. Apply Vector Theory

  1. 9.1 Vectors and scalar in two and three dimensions
  2. 9.2 Position vectors
  3. 9.3 Resolution of vectors
  4. 9.4 Scalar and vector product
  5. 9.5 Gradient,
  6. 9.6 Curl
  7. 9.7 Divergence

10. Apply Complex Numbers

  1. 10.1 Argand diagrams
  2. 10.2 Complex numbers operations
  3. 10.3 De Moivres theorem

Revise this unit

3 more for this unit

Beyond the syllabus

Other units in Module III