Engineering Mathematics
The textbook for Engineering Mathematics is:
http://www.palgrave.com/companion/Singh-Engineering-Mathematics-Through-Applications/
Topic Videos and Test Questions
All the test questions below were developed by Dr Martin Greenhow and his team at Brunel University London. (You can enter any name and any number like 123 for your student number. Also don’t need to give your email address, just enter a school where it asks for your email address.) You can do the test as many times as you wish as the numbers change every time you refresh the page.
There are also test questions from Newcastle University using Numbas and these were developed by Bill Foster and Christian Perfect.
Mock Test on first week of engineering mathematics
Mock Test on second week of engineering mathematics
Engineering Mathematics Mock Exam
Chapter Introduction Arithmetic for Engineers
Test on Indices of Arithmetic - Section Intro B
Test on Arithmetic Indices - Section Introduction B
Test on Arithmetic of Fractions - Section Introduction D
Test on Arithmetic of Fractions - Section Introduction D
Test on Arithmetic of Fractions (Applied) - Section Introduction E
Test on Decimals - Section Introduction F
Test on Standard Form - Section Introduction G
Test on Arithmetic Operations - Introductory Chapter Section I
Test on Percentages - Section Introduction J
Test on Ratios - Section Introduction K
Chapter 1 Engineering Formulae
Test on Linear Equations
Test on Transposing Formulae - Section 1B
Test Questions on Transposing of Formulae - Section 1B
Test on Rearranging formulae - Section 1B and 5B
Test on Simplification of Algebra of Fractions- Section 1B
Test on Algebraic Fractions - Section 1B
Test on Indices - Section 1C
Test on Algebraic Indices - Section 1C
Test on Dimensional Analysis - Section 1D
Test on Expanding Brackets - Section 1E
Test on Expanding Brackets - Section 1E
Test on Factorisation - Section 1F
Test on Quadratic Equations - Section 1G
Test on Solving Quadratic Equations - Section 1G
Test on Simultaneous Equations - Section 1H
Chapter 2 Visualizing Engineering Formulae
Test on Completing the Square - Section 2D
Test on Completing the Square - Section 2D
Test on the binomial expansion using Pascal's triangle - Section 2F
Chapter 3 Functions in Engineering
Chapter 3: Functions Page 137-38
Chapter 3 Functions Pages 138-140
Test on Evaluation of Functions Section 3A
Chapter 3 Inverse functions pages 141 – 44
Test on Inverse Functions Section 3b
Test on Composite Functions Section 3d
Chapter 3: Limits of Functions pages 159-64
Test on Limits of functions Section 3E
Test on Limits of Functions – Section 3E
Test on Limits of Functions II – Section 3E
Chapter 4 Trigonometry and Waveforms
Chapter 4A Trigonometric Functions Pages 172-76
Chapter 4A Inverse Trigonometric Functions Pages 177-79
Test on Trigonometric Functions – Section 4A
Test on Trigonometric Ratios – Section 4A
Chapter 4B Angles and Graphs pages 181-186
Chapter 4E Radians pages 201-203
Test on Radians - Section 4E
Chapter 4G Trigonometric Identities pages 21-218
Chapter 4H Applications of Identities pages 219-222
Section 4h Engineering examples of trig identities
Chapter 4I Conversion pages 223-229
Section 4i Conversion Examples
Sections 4h and 4i examples.pdf
Test on Conversion of Trigonometric Functions - Section 4I
Chapter 5 Logarithmic, Exponential and Hyperbolic Functions
Chapter 5B The Exponential Function pages 239-240
Chapter 5B Exponential Function pages 240-244
Section 5B Exponential Function examples
Section 5B Exponential function examples part II
Section 5B Exponential function examples part II
Test on Exponential Functions
Chapter 5C The Logarithmic Function pages 245-248
Chapter 5C Logarithmic Function pages 247-252
Section 5C Logarithmic Function Examples
Section 5C Logarithmic Function Examples
Section 5C Logarithmic Function Examples
Test on Logarithmic Function - Section 5C
Chapter 5E Hyperbolic Functions pages 259-261
Chapter 5E Hyperbolic Functions pages 262-266
Hyperbolic Functions I Examples
Hyperbolic Function Examples II
Section 5E Hyperbolic Functions Examples.pdf
Test on Hyperbolic Functions - Section 5E
Chapter 6 Differentiation
Chapter 6A The Derivative pages 272-274
Chapter 6A The Derivative pages 274-279
Chapter 6B Derivatives of Functions Pages 282-85
Chapter 6B Derivatives of Functions pages 286-89
Section 6B Chain Rule examples
Section 6B Chain rule exam questions
Differentiating Algebraic Functions - Section 6B
Test on the chain rule section 6B
Test on Chain rule of functions - Section 6B
Test on Chain Rule - Section 6B
Chapter 6C Chain Rule Revisited pages 290-95
Section 6C Chain rule revisited examples
Section 6C Engineering Examples using the chain rule
Test on Differentiating Hyperbolic Functions –
Section 6C Test on Differentiating Logarthmic Functions –
Section 6C Test on Differentiating Trigonometric Functions – Section 6C
Chapter 6D Product and Quotient Rules pages 296-302
Product and Quotient rule examples.pdf
Test on Product Rule - Section 6D
Test on Quotient Rule - Section 6D
Test on Differentiating Exponential Functions - Section 6D
Chapter 6E Higher Derivative pages 302-306
Section 6E Higher Derivatives Examples
Chapter 6F Parametric Differentiation pages 308-314
Section 6F Parametric Differentiation Examples
Test on Parametric Differentiation - Section 6F
Section 6G Implicit Differentiation Page 315-318
Section 6G Implicit and log differentiation examples
Test on Implicit Differentiation - Section 6G
Section 6g Logarithmic Differentiation pages 319-321
Logarithmic Differentiation Notes
Test on Logarithmic Differentiation – Section 6G
Test on Differentiation - Chapter 6
Chapter 7 Engineering Applications of Differentiation
Section 7A Curve Sketching pages 327-334
Section 7A Curve Sketching Notes
Section 7a Exam questions 7 page 394
Section 7B Optimization pages 339-342
Section 7B Exercises 7b question 4
Section 7C First Derivative Test pages 345-348
Section 7c Exercises 7c question 2 page 348
Section 7F Series Expansion pages 358 to 362
Notes on Section 7F Series Expansion pages 358 to 362
Section 7f Series Expansion pages 362 to 363
Notes on Section 7f Series Expansion pages 362 to 363
F2: Maclaurin series of functions pages 364-65
Section 7F: Maclaurin Series for sin(x) Pages 363-365
Section F3: Taylor series of functions pages 366-369
Section G: Binomial Revisited pages 369-70
Section 7G: Binomial Revisited Pages 369-73
Test on Binomial Series - Section 7G
Section 7H: Introduction to Infinite Series Pages 375-77
Section 7H: Introduction to Infinite Series pages 377-79
Section 7H3: Examples of Geometric Series pages 379-83
Test on Geometric Series - Section 7H3
Section 7H4: Ratio Test pages 383-86
Section J Power Series – Ratio Test
Section 7J: General Power Series
Section 7J Interval of Convergence of Power Series
Section 7J Interval of Convergence examples
Chapter 8 Integration
Section 8A and 8B pages 400-413
Sections 8A and 8B Notes
Test on basic indefinite integration - Section 8A
The notes for 8b are here: SECTION 8B.pdf
Section 8C Part I pages 414-417
Test on Integration by Substitution – Section 8C
Section 8C Part II An Important Integral pages 417-420
The notes for 8c are here: SECTION 8C.pdf
Test on integration by substitution with algebraic integrand- Section 8C
Section 8D Engineering Applications of Integration pages 421 -426
The notes for 8d are here: SECTION 8D.one
The notes for 8d are here: SECTION 8D.pdf
The notes for exam questions is here EXAM QUESTIONS 8.pdf
Section 8E Integration by Parts pages 432-438
Integration by parts, Exercises 8e page 440
Integration by parts Exam questions page 466
Here are the notes for the above videos: section 8e.pdf
Test on Integration by Parts - Section 8E
Test on integration by parts with exponential function - Section 8E
Test on integration by parts involving logarithmic function - Section 8E
Test on challenging questions on integration by parts - Section 8E
Test on integration by parts with trigonometric functions- Section 8E
Section 8F Algebraic Fractions pages 440-446
Section 8F Improper Fractions pages 446-449
Integration by partial fractions Exercises 8g page 455
Exam questions on integration by partial fractions pages 466-67
Here are the notes for the above videos: Section 8g.pdf
Test on Partial Fractions with Linear Factors - Section 8F
Test on Algebraic Fractions - Section 8F
Test on Linear Partial Fractions - Section 8F
Test on Repeated Partial Fractions - Section 8F
Test on long divsion - Section 8F
Section 8G: Integration by Partial Fractions pages 450-452
Integration by Substitution Exercise 8h page 459
Here are the notes for the above videos: Section 8h.pdf
Test on Integration using Partial Fractions - Section 8G
Test on Calculus - Chapters 6 and 8
Trigonometric Techniques for integration Exercise 8i page 459
Here are the notes for the above videos: section 8 I.pdf
Chapter 9: Applications of Integration
Section 9C Engineering Applications of integration pages 489-492
Section 9C2 Mean and root mean square (RMS) values pages 492-95
Section 9C2 RMS values pages 495-97
Here are the notes for Section 9C section 9c.pdf
Exercise 9C Engineering applications of integration page 498
Here are the notes for Exercise 9C Section 9c examples.pdf
Test on the Trapezuim Rule – Section 9A
Section E3: OtherApplications of Integration pages 506-507
Chapter 10: Complex Numbers
Section 10a Arithmetic of complex numbers pages 514-523 Video
Test on Arithmetic of Complex Numbers - Section 10A
Section 10b Representation of complex numbers pages 525-531 Video
Test on Modulus and Argument of a Complex Number - Section 10B
Test on modulus, argument and conjugate of a complex number - Section 10B
Section 10c Multiplication and division in polar form pages 532-537 Video
Test on conversion between polar and Cartesian - Section 10B and 10C
Section 10D Powers and Roots of Complex numbers pages 538-543
Notes on Section 10D Powers and Roots of Complex numbers pages 538-543
Section 10D Powers and Roots of Complex Numbers Pages 544-547
Notes on Section 10D Powers and Roots of Complex Numbers Pages 544-547
Section 10E Exponential Form of Complex Numbers Pages 548-553
Notes on Section 10E Exponential Form of Complex Numbers Pages 548-553
Test on Exponential Form of complex number - Section 10E
Chapter 11 Matrices
Test on Arithmetic of Matrices - Section 11A
Test on Manipulation of Matrices - Section 11A
Test on Manipulation of Matrices II - Section 11A
Test on Square Matrices - Section 11B and 11C
Test on Gaussian Elimination - Section 11D
Test on Eigenvalues and Eigenvectors - Section 11F
Chapter 13: First Order Differential Equations
Test on Separable first-order differential equations - Section 13A
The following topics are not covered in the textbook.
Test on Bernoull Differential Equation
Test on Exact Differential Equation
Test on Converting First Order to Homogeneous Form
Test on Linear First Order Differential Equations - Sections 13A and 13B
Test on Ist Order Differential Equations -Section 13A and 13B
Test on Numerical Methods on solving First Order ODEs
Chapter 14: Second Order Linear Differential Equations
Section 14a Homogeneous Differential Equations pages 732-737
Notes on Section 14a Homogeneous Differential Equations pages 732-737
Online Test on homogeneous differential equations
Test on Direct Integration applied to 2nd Order ODEs
Section 14b Applications pages 738-740
Notes on Section 14b Applications pages 738-740
Section 14b Applications pages 740 – 744
Notes on Section 14b Applications pages 740 – 744
Test On Section 14B
Section 14c Non- homogenous Differential Eqns pages 746-751
Notes on Section 14c Non- homogenous Differential Eqns pages 746-751
Section 14c Non-Homogeneous DES pages 752 to 757
Notes on Section 14c Non- homogenous Differential Eqns pages 752-57
Test on Inhomogeneous equations Section 14C
Section 14D Particular solutions to 2nd order DES pages 759 to 762
Notes on Section 14D Particular solutions to 2nd order DES pages 759 to 762
Section 14D Particular solutions to 2nd Order DES pages 762-63
Notes on Section 14D Particular solutions to 2nd Order DES pages 762-63
Test on 2nd Order Differential Equations -Section 14D
Chapter 16 Probability and Statistics
Test on Data Summaries – Section 16B
Test on Probability Rules – Section 16C
Test on Probability Rules II – Section 16C
Test on Probability Rules III – Section 16C
Test on Combinations – Section 16D
Test on Permutations – Section 16D
Additional material which is freely available at:
Companion site for engineering mathematics
A glossary is available at the following URL:
Matlab notes available at the following URL:
Sample Engineering Mathematics Examination Questions:
Sample Examination Engineering Mathematics Questions
The following questions were developed by Laurence Taylor.
Here is a revision checklist was written by Laurence Taylor
Revision Checklist for Engineering Mathematics
The following are not in the book.
Chapter 17: Fourier Series
Some links on Fourier Series
A good link to visualize Fourier series is the following: Graphs
A useful application is here Sign your name in the circle and see how it is reproduced. If you click the theory link then you will see the relevance of Fourier series.
Another graphical link to Fourier series is the blog
Youtube video on Fourier series is here
Chapter 18 Laplace Transform
Test on Applying Laplace Transforms to Differential Equations
Test on Inverse Laplace Transforms
Test on Properties of Laplace Transforms
The year 2017-18 Videos
Lecture 5 on Logarithmic Function Section 5C
Lecture 6 on Hyperbolic Functions Section 5E
Lecture 7 Hyperbolic Functions Section 5E
Chapter 6 Differentiation
Derivatives of functions – Section 6B
Chain Rule Revisited – Section 6C
Product and Quotient Rules – Section 6D
Section 6F Parametric Differentiation
Section 6F Parametric Differentiation Part II
Section 6f Part II Notes
A book on Differential Calculus by Jaromir Kuben
A good book for lots of examples in
Differential Calculus for Functions of a Single Variable by Jaromir Kuben
A book on Integral Calculus by Jaromir Kuben
This is an excellent interactive book:
Integral Calculus
Differential Calculus for Functions of a Single Variable by Jaromir Kuben