Engineering Mathematics II

Automotive Mechatronics Technology · Level 6  ·  8 Chapters

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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 indices, logarithms, and trigonometric functions to mastering the use of scientific calculators. You’ll develop the skills to analyze and represent complex numbers, draw precise graphs, and apply advanced theorems like De Moivre’s and the binomial expansion with accuracy. By the end, you’ll be equipped to apply these powerful mathematical tools effectively in real-world engineering problems, boosting both your problem-solving abilities and your confidence.

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Careers after Engineering Mathematics II

Understanding Engineering Mathematics II opens doors to a wide range of practical and rewarding careers across Kenya’s vibrant industries. Mastery of these mathematical skills equips you to tackle real-world problems, innovate, and contribute meaningfully to Kenya’s development.

  • Construction and Civil Engineering: Use indices, logarithms, and trigonometry daily on construction sites in Nairobi, Mombasa, or Kisumu, helping to design structures, calculate loads, and ensure safety. Employers like county works departments and private construction firms highly value these skills.

  • Energy Sector: Companies like KenGen and rural electrification projects rely on engineers who can solve complex equations and apply logarithmic calculations to optimize power generation and distribution.

  • Agribusiness and KTDA: Mathematical modelling using simultaneous and quadratic equations helps improve crop yield predictions, irrigation planning, and resource management, directly impacting Kenya’s tea and coffee industries.

  • Jua Kali and Manufacturing: Skilled artisans use precise measurements and calculations to craft quality products, from metalworks to electronics, turning their expertise into thriving businesses or employment in industrial hubs like Athi River.

  • Matatu Industry and Transport: Scheduling, route optimization, and financial management in the matatu sector benefit from a solid grasp of these mathematical principles, enabling better decision-making and profitability.

  • Hospitality and Tourism: Complex number calculations and trigonometry assist in designing efficient layouts, managing resources, and even in technological applications like sound engineering and lighting.

Mastering Engineering Mathematics II not only sharpens your problem-solving abilities but also sets you apart as a professional ready to innovate and lead in Kenya’s dynamic economy. Your future is bright—equip yourself with these skills and watch doors open to endless possibilities!

Chapters

What Engineering Mathematics II covers: 37 main topics in 8 chapters

1. Perform power series

  1. 1.1 Definition of the term power series
  2. 1.2 Taylor's theorem
  3. 1.3 Deduction of Mc Laurin's theorem to obtain power series
  4. 1.4 Application of Taylor's theorem and McLaurin's theorems in numerical work

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. Perform numerical methods

  1. 3.1 Definition of interpolation and extrapolation
  2. 3.2 Application of interpolation
  3. 3.3 Application of iterative methods to solve equations

4. Apply vector theory

  1. 4.1 Vectors and scalar in two and three dimensions
  2. 4.2 Operations on vectors: Addition and subtraction
  3. 4.3 Position vectors
  4. 4.4 Resolution of vectors
  5. 4.5 Scalar and vector products

5. Apply matrix

  1. 5.1 Matrix operation
  2. 5.2 Determinant of 3x3 matrix by
  3. 5.3 Inverse of 3x3 matrix
  4. 5.4 Application of matrices in solving linear simultaneous equations in three unknowns by

6. Solve partial differential equations

  1. 6.1 First order partial differential equations
  2. 6.2 Second order partial differential equations
  3. 6.3 Applications in;

7. Apply Laplace transforms

  1. 7.1 Meaning of Laplace transforms deriving Laplace transforms from first principles
  2. 7.2 State properties of Laplace transform
  3. 7.3 Determination of inverse LT of simple transforms and partial fractions
  4. 7.4 Solution of differential equation by LT
  5. 7.5 Solution of simultaneous differential equation by given initial conditions

8. Apply Fourier series

  1. 8.1 Determination of the Fourier series as a periodic function of the period 2x and extend to I
  2. 8.2 Determination of Fourier series of non-periodic functions over a given range
  3. 8.3 Determination of Fourier series for even and odd functions and the half-range series for a given function

Revise this unit

3 more for this unit

Beyond the syllabus

Other units in Module VI