BENG405 

Module Name Engineering Mathematics 2 
 Module Code BENG405 
Level Four 
 Credits 15  

  

  

Module Description and General Aims 

This module is intended at expanding the scope of engineering mathematics learning further, by introducing the student to the principles and applications of differential and integral calculus including vector calculus and complex analysis. The derivative and integration rules and techniques are brought out clearly, so as to enable the student to solve simple as well as complex engineering problems, using calculus. Further, a detailed overview of the concepts related to analytical geometry, probability and statistics and sets, so that the student will be able to use these mathematical techniques to effectively deal with problems in engineering application areas. 

  

Learning Outcomes 

On successful completion of this Module, students are expected to be able to: 

  1. Apply the principles of calculus and make use of numerical methods.  
    Bloom’s Level 3 
  1. Evaluate the concepts of analytical geometry 
    Bloom’s Level 4 
  1. Acquire knowledge of vector spaces and perform vector calculus by applying various theorems.  
    Bloom’s Level 4  
  1. Evaluate complex integration 
    Bloom’s Level 3 
  1. Apply concepts related to statistics and probability 
    Bloom’s Level 3 

 Student Assessment 

Assessment Type When assessed Weighting (% of total module marks) Learning Outcomes Assessed 
Assessment 1 Type: Multi-choice test / Group work / Short answer questions Example Topic: Differentiation basics Students may complete a quiz with MCQ type answers and solve some simple equations to demonstrate a good understanding of the fundamental concepts Due after Topic 3 10% 1 
Assessment 2 – mid-semester test Type: Multi-choice test / Extended answer questions/ Short answer questions Example Topic: Topics 1 to 6 Students may be asked to provide solutions to simple problems on various topics. Due after Topic 6 20% 1, 2 
Assessment 3 Type: Multi-choice test / Group work / Short answer questions / Practical Example Topic: Analytical geometry Students may complete a quiz with MCQ type answers or solve some simple problems or use software to complete a practical. Due after Topic 9 20% 3 
Assessment 4 Type: Examination Example Topic: All topics An examination with a mix of detailed report type questions and/or simple numerical problems to be completed in 3 hours Final Week 40% 1 to 5 
Tutorial attendance + Weekly homework 5% for tutorial attendance and 5% for weekly homework submission. Weekly homework will be discussed and assigned during live tutorials. Continuous 10% 1 to 5 

  

Overall Requirements: Students must achieve a result of 40% or above in the exam itself to pass the exam and must pass the exam to be able to pass the module. An overall final module score of 50% or above must be achieved to pass the module once all assessment, including the exam, has been completed. 

Prescribed and Recommended readings 

Suggested Textbooks 

  • Bird, J. Higher Engineering Mathematics, 7th edn, John Wiley & Sons, ISBN-13: 978-0415662802. 
  • P. O’Neil, Advanced Engineering Mathematics, SI Edition, 8th Edition. Cengage, 2018. ISBN 9781337274524 

Reference Materials 

  • Bird, J. Engineering Mathematics, 5th edn, John Wiley & Sons, ISBN-978-0-75-068555-9 
  • Kreyszig, E 2011, Advanced Engineering Mathematics, 10th edn, John Wiley & Sons, ISBN-13: 978-0470458365. 
  • IDC Technologies publications 
  • Other material and online collections as advised during the lectures and in the Reading Guide 

  

Module Content 

   

Topic 1 

Differentiation  

  1. Rules of Differentiation/Derivatives Summary 
  1. Applications of Derivatives 
  1. Rates of Change 
  1. Minimum and maximum value problems 
  1. ODEs 
  1. Initial Value Problem 
  1. Application Examples 
  1. Second order differential equations 

  

Topic 2 

Integration 1 

1. Integration Rules and Techniques 
2. Integration with trigonometric substitutions 
3. Integration with partial fractions 
4. Integration by parts 
5. Double and Triple Integrals 

  

Topic 3 

Integration 2 

1. Applications of Integration 
2. Areas and Arc Length 
3. Volumes of Solids of Revolution 
4. Centroids 
5. Theorem of Pappus 
6. Second Moments of Area 
7. Parallel Axis Theorem 
8. Perpendicular Axis Theorem 
9. Additional Applications 

  

Topic 4  

Numerical Methods  

  1. The trapezoidal Rule, Mid-ordinate Rule, and Simpson’s Rule 
  1. Euler’s method, Euler-Cauchy method and the Runge-Kutta method 
  1.  Solution of equations by iteration 

  

Topic 5 

Analytical Geometry 1 

1. Angles and Lines 
2. Triangles 
3. Quadrilaterals 
4. Polygons 
5. Circle Properties 
6. Irregular Areas 
7. Solid Figures 
8. Straight Lines and Equations 
9. Circle Equations 
10. Parabolas, Ellipses and Hyperbolas 

  

Topic 6 

Analytical Geometry 2 

1. Planes and spaces 
2. Other coordinate systems 
3. Parametric equations 
4. Spheres 
5. Conic sections 
6. Transformations in space 
7. Geometric intersections 
8. Volumes by integration 

  

Topic 7 

Vector Spaces 

  1. Linear combination and spans 
  1. Linear dependence and independence 
  1. Subspaces 
  1. Vector dot and cross product 
  1. Null space and column space 
  1. Linear transformations 

  

Topic 8 

Vector Differential Calculus 

1. Vectors in 2−space and 3−space 
2. Velocity, acceleration and Curvature 
3. Curves, Arc length  
4. Streamlines 
5. Gradient of a scalar field and directional derivatives 
6. Divergence and curl of a vector field 

  

Topic 9 

Vector Integral Calculus 

 
1. Path independence of line integrals 
2. Green’s Theorem in the plane 
3. Independence of path 
4. Surface integrals 
5. Triple integrals, Divergence theorem of Gauss 
6. Stokes’ theorem 

 Topic 10 

Complex Integration  

 
1. Line integral in the complex plane 
2. Properties of complex integrals 
3. Cauchy’s integral theorem 
4. Consequences of Cauchy’s theorem 
5. Deformation theorem 
6. Cauchy’s integral formula 

  

Topic 11 

Statistics and Standard Deviation 

  1. Data and data averages 
  1. Mean 
  1. Variance 
  1. Elementary probability 
  1. Laws of probability 
  1. Standard Deviation 
  1. Coefficient of Variation 

  

Topic 12 

Distributions and Data 

1. Normal Distribution and Z-Scores 
2. Chebyshev’s Theorem 
3. Histograms 
4. Correlation and Scatterplots 
5. Correlation Coefficient and Regression Equation 
6. Utility and Validity 

  

Software/Hardware Used 

Software 

  • Software: N/A 
  • Version: N/A 
  • Instructions:  N/A 
  • Additional resources or files: N/A 

Hardware 

  • N/A