# 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.

Source: https://practicecalculus.com/courses/university-of-edinburgh-math08075
Updated: 2026-11-08

## 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](/learn/calculus-1) and [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH08075 is the first university calculus course for Edinburgh engineering students, taught in Year 1, Semester 2.
- It follows Engineering Mathematics 1a (MATH08074), which covers functions, complex numbers, vectors and matrices but not calculus.
- Its syllabus runs from limits and series through differentiation, partial derivatives and integration to first-order differential equations.
- It is assessed by an 80% written exam and 20% coursework, with weekly online quizzes for skills practice.

**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?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Sequences and series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Convergence tests](/blog/convergence-tests) |
| Power series and radius of convergence | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |
| Rules of differentiation | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Product rule](/rules/product-rule), [quotient rule](/rules/quotient-rule) |
| Chain rule, exponentials and inverses | [Chain rule](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/rules/chain-rule), [inverse trig derivatives](/practice-problems/inverse-trig-derivatives) |
| Implicit and parametric differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation](/blog/implicit-differentiation) |
| Maxima and minima | [Absolute extrema](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Optimization problems](/blog/optimization-problems) |
| Partial and directional derivatives | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Gradient and directional derivatives](/blog/gradient-and-directional-derivatives) |
| L'Hopital's rule | [L'Hopital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hopital's rule](/rules/lhopitals-rule) |
| Taylor and Maclaurin series | [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series), [Taylor's theorem](/theorems/taylors-theorem) |
| Substitution and integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [u-substitution](/blog/u-substitution), [integration by parts](/blog/integration-by-parts) |
| Fundamental Theorem of Calculus | [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Area, arc length, volume, mean values | [Volumes with disks](/learn/calculus-1/applications-of-integrals/volumes-disks) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Separable and first-order ODEs | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Differential equations practice](/practice-problems/differential-equations) |

## 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)](/courses/university-of-edinburgh-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](/rules/chain-rule) need repetition to become automatic.
- **Keep the formulas close.** The [calculus formula sheet](/formulas) 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](/practice) before April.

> **Tip:** many engineering integrals yield to either substitution or parts. Our lesson on [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) helps you decide quickly.

## 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.