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Engineering Mathematics II

Electronics Engineering · Level 6  ·  9 Chapters

Compiled by: Julius Mwangi

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What Engineering Mathematics II covers

In this unit, you will be able to confidently tackle a wide range of mathematical challenges essential for engineering, from solving complex equations and working with numbers to mastering trigonometric and hyperbolic functions. By the end, you’ll skillfully apply these concepts to real-world problems, visualize complex numbers, and perform precise calculations that form the backbone of engineering solutions. This strong mathematical foundation will empower you to approach technical tasks with clarity and confidence.

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Careers after Engineering Mathematics II

Understanding Engineering Mathematics II opens doors to numerous exciting career paths and practical applications across Kenya’s dynamic industries. Mastering these skills equips you to tackle real-world problems, innovate solutions, and advance in sectors crucial to Kenya’s economy and development.

  • In the construction industry, especially in major urban projects and county works, precise calculations of angles, measurements, and forces ensure safe and efficient building designs. Skilled engineers use trigonometry and simultaneous equations to draft blueprints and supervise site operations.
  • The Jua Kali sector benefits from artisans and fabricators who apply complex number operations and arithmetic to design and repair machinery, metalworks, and electrical components, enabling them to run profitable small-scale workshops.
  • At KenGen and other energy firms, engineers apply quadratic equations and indices to optimize power generation, manage electrical circuits, and maintain renewable energy systems, ensuring Kenya’s energy stability.
  • In the matatu industry, logistics and route optimization rely on mathematical modeling and problem-solving skills to maximize profits and safety while minimizing costs.
  • Agribusiness companies like KTDA use mathematical calculations to forecast yields, manage resources, and improve processing techniques, helping farmers increase productivity and income.
  • In hospitality and tourism, precise calculations help manage inventories, optimize resource use, and plan events, contributing to efficient operations and customer satisfaction.

Mastering Engineering Mathematics II not only boosts your confidence and problem-solving skills but also positions you as a valuable professional capable of contributing to Kenya’s growth. Your expertise can lead to rewarding employment or empower you to start your own engineering enterprise, shaping the future you envision. Keep pushing forward—your mathematical skills are the foundation of Kenya’s innovation and progress!

Chapters

1
Apply Power Series
4 topics
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2
Solve Partial Differential Equations
4 topics
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3
Ordinary Differential Equations
9 topics
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4
Apply Laplace Transforms
18 topics
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5
Apply Fourier Series
5 topics
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6
Apply Multiple Integrals
4 topics
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7
Apply Matrices II
5 topics
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8
Apply Complex Variables
4 topics
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9
Apply Numerical Methods
4 topics
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What Engineering Mathematics II covers: 36 main topics in 9 chapters

1. Apply Power Series

  1. 1.1 Meaning of the Term Power Series
  2. 1.2 Taylors Theorem
  3. 1.3 Deduction of Maclaurins Theorem to Obtain Power Series
  4. 1.4 Application of Taylors and Maclaurins Theorems in Numerical Work

2. Solve Partial Differential Equations

  1. 2.1 Definition of Partial Derivatives

3. Ordinary Differential Equations

  1. 3.1 Formation and Solution of 1st and 2nd Order Differential Equations
  2. 3.2 2nd Order by the Determination of Coefficients
  3. 3.3 D-Operator Method
  4. 3.4 Applications of Differential Equations

4. Apply Laplace Transforms

  1. 4.1 Definition of Laplace Transform of a Function
  2. 4.2 Properties of Laplace Transforms
  3. 4.3 Determination of the Inverse Laplace Transform of Simple Transforms
  4. 4.4 Determination of Inverse Laplace Transforms of Partial Fractions
  5. 4.5 Differential Equations and Simultaneous Equations
  6. 4.6 Application of Theorem for the Laplace Transforms
  7. 4.7 Evaluations of Laplace Transform Using a Small Stock of Transform Key Pair
  8. 4.8 Application of Laplace Transforms to Impulse Response Problems

5. Apply Fourier Series

  1. 5.1 Definition of Fourier Series for a Function
  2. 5.2 Determination of Fourier Series of Non-Periodic Functions
  3. 5.3 Determination of Fourier Series for Non-Periodic Functions Over a Given Range
  4. 5.4 Determination of Fourier Series for Odd and Even Functions and Half-Range Series

6. Apply Multiple Integrals

  1. 6.1 Definition of Double and Triple Integrals
  2. 6.2 Using Double Integrals to Find Areas and Volumes
  3. 6.3 Apply Double and Triple Integrals in Polar, Cylindrical and Spherical Coordinates
  4. 6.4 Use of Triple Integrals in Solving Problems

7. Apply Matrices II

  1. 7.1 Definition of Eigen Values and Eigen Vectors
  2. 7.2 Calculation of Eigen Values and Eigen Vectors
  3. 7.3 Explanation of Function of Matrices
  4. 7.4 Definition of Jordan Form of a Matrix
  5. 7.5 State Transition Matrix

8. Apply Complex Variables

  1. 8.1 Functions of Complex Variable
  2. 8.2 Define Analytic (Regular) Functions
  3. 8.3 Cauchy Riemann Equation

9. Apply Numerical Methods

  1. 9.1 Define Numerical Methods
  2. 9.2 Definition of Interpolation and Extrapolation
  3. 9.3 Application of Interpolation and Extrapolation

Revise this unit

Exam-style questions 126 Written to CDACC standard, with answers Test yourself 278 Multiple-choice, one at a time Practise questions 169 Quick recall — check you know the facts
3 more for this unit
Oral exam preparation 72 What the assessor asks, and how to answer out loud Worked calculations 58 Step-by-step maths with the common mistakes Quick cards 1,472 Myth busters, skill tips and scenarios

Beyond the syllabus

Decision simulator 8 On site, what would you do? Workplace scenarios 101 Real site situations — what would you do? Turn this into income 96 Where this skill earns — what to charge, how to find clients

Other units in Module V