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University of Edinburgh

Edinburgh MATH08075 Engineering Mathematics 1b: Topics and Practice

A study guide for Engineering Mathematics 1b (MATH08075) at Edinburgh: series, derivatives, partial derivatives, integrals and ODEs, with free practice.

University of Edinburgh Updated 3 min read

At a glance

Course code
MATH08075
Credits
20 SCQF credits (10 ECTS), SCQF Level 8
Taught
Year 1, Semester 2
Who takes it
Engineering students, as a compulsory part of their degree
Prerequisites
None listed; it follows on from Engineering Mathematics 1a (MATH08074)
Assessment
Written exam 80% (180 minutes), coursework 20%
Covers
Sequences and series, power series, differentiation, partial derivatives, Taylor series, integration, improper integrals, first-order differential equations
Practice here
Calculus 1 and Calculus 2

Try it yourself

Use the power rule to differentiate $x^3$.
\frac{d}{dx}\left(x^{3}\right)
f'(x) =
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On this page
  1. What MATH08075 covers
  2. MATH08075 topic map
  3. Where MATH08075 fits
  4. Example problems at the MATH08075 level
  5. How to do well in MATH08075

MATH08075 Engineering Mathematics 1b is the first calculus course for engineering students at the University of Edinburgh. It runs in Year 1, Semester 2, is worth 20 SCQF credits (10 ECTS) and follows Engineering Mathematics 1a (MATH08074), which deliberately leaves calculus out. In one semester it covers what many universities spread across Calculus 1 and Calculus 2, and it even touches partial derivatives. This guide maps every topic to free practice so you can build fluency one problem at a time.

What MATH08075 covers

According to the Edinburgh course catalogue (DRPS), the syllabus includes:

  • Sequences and series, limits, power series and radius of convergence.
  • Basic differentiation: rate of change, rules of differentiation, maxima and minima, and derivatives of polynomials, rational functions and circular (trig) functions.
  • The chain rule, derivatives of exponential and related functions, and derivatives of inverse functions.
  • Parametric and implicit differentiation, and higher derivatives.
  • Partial differentiation, directional derivatives, the multivariable chain rule, the total derivative and exact differentials.
  • L'Hopital's rule, Taylor's theorem and Maclaurin series.
  • Integration: antiderivatives, definite and indefinite integrals, substitution and integration by parts, and the Fundamental Theorem of Calculus.
  • Applications of integration: area, arc length, volume, mean values and rms values.
  • Improper integrals.
  • Differential equations: general and particular solutions, boundary values, separable equations and first-order linear equations with constant coefficients.

Skills are built with weekly online quizzes, and written assignments develop your mathematical writing.

MATH08075 topic map

MATH08075 topic Practice Read
Limits What is a limit? How to evaluate limits
Sequences and series Series and partial sums Convergence tests
Power series and radius of convergence Power series and radius Power series
Rules of differentiation Power rule Product rule, quotient rule
Chain rule, exponentials and inverses Chain rule Chain rule, inverse trig derivatives
Implicit and parametric differentiation Implicit differentiation Implicit differentiation
Maxima and minima Absolute extrema Optimization problems
Partial and directional derivatives Partial derivatives Gradient and directional derivatives
L'Hopital's rule L'Hopital's rule L'Hopital's rule
Taylor and Maclaurin series Maclaurin series Taylor series, Taylor's theorem
Substitution and integration by parts Integration by parts u-substitution, integration by parts
Fundamental Theorem of Calculus FTC part 2 Fundamental Theorem of Calculus
Area, arc length, volume, mean values Volumes with disks Volumes of revolution
Improper integrals Integrating to infinity Improper integrals
Separable and first-order ODEs Separable equations Differential equations practice

Where MATH08075 fits

Course When Focus
MATH08074 Engineering Mathematics 1a Year 1, Semester 1 Functions, complex numbers, vectors, matrices (no calculus)
MATH08075 Engineering Mathematics 1b Year 1, Semester 2 First calculus course for engineers

The catalogue lists Introduction to Mathematical Analysis (MATH08081) and Mathematics for the Natural Sciences 1b (MATH08073) as courses you cannot also take. The official page does not name a Year 2 follow-on course.

Example problems at the MATH08075 level

1. Implicit differentiation. For x^2 + y^2 = 25, differentiate both sides with respect to x:

2x + 2y\frac{dy}{dx} = 0 \quad\Rightarrow\quad \frac{dy}{dx} = -\frac{x}{y}

2. A partial derivative. For f(x, y) = x^2 y + \sin y,

\frac{\partial f}{\partial x} = 2xy, \qquad \frac{\partial f}{\partial y} = x^2 + \cos y

3. A separable ODE. Solve \frac{dy}{dx} = 3y with y(0) = 2. Separating gives \int \frac{dy}{y} = \int 3\,dx, so \ln|y| = 3x + C and

y = 2e^{3x}

How to do well in MATH08075

  • Do the weekly quizzes properly. The online questions give feedback on submission, so treat each one as practice, not a hurdle.
  • Practise in short daily sessions. One semester covers a lot of calculus, and rules like the chain rule need repetition to become automatic.
  • Keep the formulas close. The calculus formula sheet puts the standard derivatives and integrals on one page.
  • Rehearse under exam conditions. The exam is 180 minutes and worth 80%, so try timed practice exams before April.

Tip: many engineering integrals yield to either substitution or parts. Our lesson on choosing a strategy helps you decide quickly.

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The power rule

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Frequently asked questions

What is MATH08075 at Edinburgh?
Engineering Mathematics 1b is a 20-credit first-year course from the School of Mathematics. The course catalogue describes it as a first university-level course in calculus for engineering students, following on from Engineering Mathematics 1a (MATH08074).

Who can take Engineering Mathematics 1b?
The catalogue says the course is for engineering students only, restricted to those for whom it is a compulsory part of their degree programme. It is not available to visiting students.

What topics are in MATH08075?
Sequences and series, limits, power series and radius of convergence; differentiation including the chain rule, implicit and parametric differentiation; partial differentiation; L'Hopital's rule; Taylor and Maclaurin series; integration by substitution and by parts; areas, arc length, volumes and mean values; improper integrals; and separable and first-order linear differential equations.

How is MATH08075 assessed?
By a 180-minute written exam in the April/May diet worth 80% and coursework worth 20%. Students must pass both the exam and the course overall. Students repeating the course are assessed by exam only.

What textbook does MATH08075 use?
The catalogue names Engineering Mathematics by Glyn James as the course textbook, in a special edition available from Blackwell's on South Bridge or electronically.

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Related university courses

Edinburgh MATH08081 Calculus 1 Introduction to Mathematical Analysis A study guide for MATH08081 at the University of Edinburgh: real numbers, sequences, series, limits, continuity and differentiation, with free practice. Edinburgh MATH08082 Calculus 3 Further Analysis and Several Variable Calculus A study guide for MATH08082 at Edinburgh: rigorous integration, partial derivatives, multiple integrals, Stokes and the divergence theorem, with practice.