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Engineering Mathematics I

Automotive Mechatronics Technology · Level 6  ·  8 Chapters

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What Engineering Mathematics I covers

In this unit, you will be able to confidently tackle a wide range of engineering mathematics problems, from solving complex equations and working with indices and logarithms to mastering trigonometric, hyperbolic, and complex number calculations. You will skillfully use scientific calculators and graphical methods to analyze and represent mathematical concepts clearly, preparing you to apply these essential skills effectively in real-world engineering tasks. By the end, you’ll have a strong mathematical foundation that empowers you to solve practical problems with accuracy and confidence.

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Careers after Engineering Mathematics I

Understanding Engineering Mathematics I opens many doors in Kenya’s vibrant and growing industries. The skills you gain here are the backbone of problem-solving and innovation in technical fields, making you a valuable asset in numerous workplaces and entrepreneurial ventures.

  • In the construction sector, including county government projects and private firms, you’ll use indices, logarithms, and trigonometry to design structures, calculate loads, and ensure safety standards.
  • The jua kali industry benefits from your ability to solve simultaneous and quadratic equations when fabricating metal parts or designing machinery, helping artisans improve product quality and efficiency.
  • At KenGen and other energy firms, complex number calculations and logarithms are essential when analyzing electrical circuits and power systems, contributing to Kenya’s sustainable energy goals.
  • The matatu industry relies on precise calculations for engine tuning and maintenance, where your math skills help improve vehicle performance and safety.
  • In agribusiness, such as KTDA and large-scale farms, you’ll apply these mathematical concepts to optimize irrigation systems, analyze crop yields, and manage resources efficiently.
  • Hospitality and manufacturing sectors use these skills for process optimization, quality control, and equipment maintenance, making you indispensable in diverse workplaces.
  • With these skills, you can also venture into self-employment by offering technical consultancy, tutoring, or starting a small engineering workshop in your community.

Mastering Engineering Mathematics I not only equips you with critical thinking and analytical abilities but also empowers you to contribute meaningfully to Kenya’s development while building a rewarding and sustainable career. Keep pushing forward—your expertise will shape the future!

Chapters

1
Apply algebra
10 topics
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2
Apply trigonometry and hyperbolic functions
16 topics
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3
Apply complex numbers
5 topics
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4
Perform coordinates geometry
7 topics
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5
Carry out binomial expansion
4 topics
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6
Apply calculus
21 topics
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7
Solve ordinary differential equations
10 topics
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8
Carry out mensuration
6 topics
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What Engineering Mathematics I covers: 66 main topics in 8 chapters

1. Apply algebra

  1. 1.1 Base and index
  2. 1.2 Laws of indices using one on one
  3. 1.3 Indicial equations interviews
  4. 1.4 Laws of logarithm
  5. 1.5 Logarithmic equations assessment using
  6. 1.6 Conversion of bases a check list
  7. 1.7 Use of calculator Learning Outcome
  8. 1.8 Reduction of equations
  9. 1.9 Solution of equations reduced to quadratic form assessments using multiple choice
  10. 1.10 Solutions of simultaneous linear equations in three unknowns questions

2. Apply trigonometry and hyperbolic functions

  1. 2.1 Half -angle formula
  2. 2.2 Factor formula
  3. 2.3 Trigonometric functions
  4. 2.4 Parametric equations
  5. 2.5 Relative and absolute measures assessments
  6. 2.6 Measures calculation
  7. 2.7 Definition of hyperbolic equations exercises
  8. 2.8 Properties of hyperbolic functions
  9. 2.9 Evaluations of hyperbolic functions Hyperbolic identities
  10. 2.10 Osborne's Rule
  11. 2.11 Ashx + Bshx = C equation
  12. 2.12 One-to-one relationship in functions
  13. 2.13 Inverse functions for one-to- one relationship
  14. 2.14 Inverse functions for trigonometric functions
  15. 2.15 Graph of inverse functions
  16. 2.16 Inverse hyperbolic functions

3. Apply complex numbers

  1. 3.1 Definition of complex numbers
  2. 3.2 Stating complex numbers in numbers in terms of conjugate argument and modulus exercises
  3. 3.3 Representation of complex numbers on the Argand diagram assessments
  4. 3.4 Arithmetic operation of complex numbers application of De Moivre's theorem
  5. 3.5 Application of complex numbers to engineering Learning Outcome

4. Perform coordinates geometry

  1. 4.1 Polar equations assessments
  2. 4.2 Cartesian equation
  3. 4.3 Graphs of polar equations
  4. 4.4 Normal and tangents
  5. 4.5 Definition of a point
  6. 4.6 Locus of a point in relation to a circle
  7. 4.7 Loci of points for given mechanism

5. Carry out binomial expansion

  1. 5.1 Binomial theorem
  2. 5.2 Power series using binomial theorem assessments
  3. 5.3 Roots of numbers using binomial theorem
  4. 5.4 Estimation of errors of small changes using binomial theorem

6. Apply calculus

  1. 6.1 Definition of derivatives of a function exercises
  2. 6.2 Differentiation from fist principle
  3. 6.3 Tables of some common derivatives
  4. 6.4 Rules of differentiation
  5. 6.5 Rate of change and small change
  6. 6.6 Stationery points of functions of two variables
  7. 6.7 Definition of integration
  8. 6.8 Indefinite and definite integral
  9. 6.9 Methods of integration application of integration
  10. 6.10 Integrals of hyperbolic and inverse functions
  11. 6.11 Application of integration

7. Solve ordinary differential equations

  1. 7.1 Types of first order differential equations
  2. 7.2 Formation of first order differential equation
  3. 7.3 Solution of first order differential equations assessments
  4. 7.4 Application of first order differential equations
  5. 7.5 Formation of second order differential equations for various systems
  6. 7.6 Solution of second order differential equations using undetermined coefficient method
  7. 7.7 Application of second order differential equations

8. Carry out mensuration

  1. 8.1 Units of measurements
  2. 8.2 Perimeter and areas of regular figures
  3. 8.3 Volume of regular solids
  4. 8.4 Surface area of regular solids
  5. 8.5 Area of irregular figures
  6. 8.6 Areas and volumes using Pappus theorem using assessments exercises

Revise this unit

Exam-style questions 112 Written to CDACC standard, with answers Test yourself 313 Multiple-choice, one at a time Practise questions 179 Quick recall — check you know the facts
3 more for this unit
Oral exam preparation 79 What the assessor asks, and how to answer out loud Worked calculations 51 Step-by-step maths with the common mistakes Quick cards 1,538 Myth busters, skill tips and scenarios

Beyond the syllabus

Decision simulator 8 On site, what would you do? Workplace scenarios 121 Real site situations — what would you do? Turn this into income 72 Where this skill earns — what to charge, how to find clients

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