# UI MTH 201 Mathematical Methods I: Study Guide and Practice

> Study guide for MTH 201 Mathematical Methods I at the University of Ibadan: Taylor series, partial derivatives, Lagrange multipliers and multiple integrals.

Source: https://practicecalculus.com/courses/university-of-ibadan-mth-201
Updated: 2026-11-03

## At a glance

- **Course code:** MTH 201 (Mathematical Methods I)
- **Credit units:** 2 units
- **Status:** Compulsory at 200 level in the Department of Mathematics
- **Covers:** The national CCMAS outline for MTH 201: review of calculus, mean value theorem, Taylor series, functions of several variables, partial derivatives, extrema, Lagrange multipliers, linear approximation, line and multiple integrals
- **Other 200 level maths:** MTH 202 Elementary Differential Equations, MTH 207 Real Analysis I, MTH 210 Vector Analysis and others
- **Practice here:** [Calculus 3](/learn/calculus-3) plus Taylor series in [Calculus 2](/learn/calculus-2)

## Key takeaways

- MTH 201 Mathematical Methods I is a compulsory 2-unit, 200 level course in the University of Ibadan Department of Mathematics.
- UI lists it under the national CCMAS code, whose outline covers Taylor series and the calculus of functions of several variables.
- It is the calculus course that follows MTH 102 in the UI list, taken alongside MTH 210 Vector Analysis.
- The Calculus 3 path on PracticeCalculus has a lesson for nearly every MTH 201 topic.

**MTH 201 Mathematical Methods I** is the 200 level calculus course in the **University of Ibadan (UI)** Department of Mathematics. The department lists it as a compulsory 2-unit course, alongside MTH 202 Elementary Differential Equations and MTH 210 Vector Analysis. Like UI's 100 level courses, it carries the national CCMAS code, so it follows the National Universities Commission outline for Mathematical Methods I. This guide maps each topic to free practice on PracticeCalculus.

## What UI MTH 201 covers

The UI course list gives the code, title, units and status. The CCMAS outline for MTH 201 begins with real-valued functions of one variable and a review of differentiation and integration. It then covers the mean value theorem and Taylor series before moving to functions of two and three variables: partial derivatives and the chain rule, extrema, Lagrange multipliers, increments, differentials and linear approximation, line integrals, and multiple integrals.

In a standard sequence these topics span the end of **Calculus 2** (Taylor series) and most of **Calculus 3**. The [NUC MTH 201 guide](/courses/nuc-mth-201) has the full national outline.

## UI MTH 201 topic map

| MTH 201 topic | Practice | Read |
| --- | --- | --- |
| Mean value theorem | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean value theorem](/blog/mean-value-theorem) |
| Taylor and Maclaurin series | [Common Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series), [power series](/blog/power-series) |
| Functions of two and three variables | [Functions of several variables](/learn/calculus-3/partial-derivatives/functions-of-several-variables) | [Partial derivatives](/blog/partial-derivatives) |
| Partial derivatives | [Partials with the chain and product rules](/learn/calculus-3/partial-derivatives/partials-with-rules) | [Clairaut's theorem](/theorems/clairauts-theorem) |
| Second partial derivatives | [Second partial derivatives](/learn/calculus-3/partial-derivatives/second-partial-derivatives) | [Partial derivatives](/blog/partial-derivatives) |
| Chain rule | [The multivariable chain rule](/learn/calculus-3/partial-derivatives/multivariable-chain-rule) | [Chain rule](/rules/chain-rule) |
| Extrema | [Critical points and the second-derivative test](/learn/calculus-3/partial-derivatives/critical-points-and-second-derivative-test) | [Optimization problems](/blog/optimization-problems) |
| Lagrange multipliers | [Lagrange multipliers](/learn/calculus-3/partial-derivatives/lagrange-multipliers) | [Lagrange multipliers](/blog/lagrange-multipliers) |
| Differentials and linear approximation | [Tangent planes and linear approximation](/learn/calculus-3/partial-derivatives/tangent-planes) | [Linear approximation](/blog/linear-approximation) |
| Line integrals | [Work and line integrals of vector fields](/learn/calculus-3/vector-calculus/line-integrals-of-vector-fields) | [Green's theorem](/theorems/greens-theorem) |
| Multiple integrals | [Double integrals over general regions](/learn/calculus-3/multiple-integrals/general-regions) | [Double integrals](/blog/double-integrals) |

## MTH 201 in the UI course list

| Course | Level | Units | Status |
| --- | --- | --- | --- |
| [MTH 102](/courses/university-of-ibadan-mth-102) Elementary Mathematics II | 100 | 2 | Compulsory |
| MTH 201 Mathematical Methods I | 200 | 2 | Compulsory |
| MTH 202 Elementary Differential Equations | 200 | 2 | Compulsory |
| MTH 207 Real Analysis I | 200 | 2 | Compulsory |
| MTH 210 Vector Analysis | 200 | 1 | Compulsory |

The national outline for MTH 210 (gradient, divergence, curl, lines and planes) is covered in the [NUC MTH 210 guide](/courses/nuc-mth-210).

## Example problems at the MTH 201 level

These are original practice problems, not past questions.

**1. A Taylor polynomial.** The Maclaurin series of $\cos x$ begins

$$\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \cdots$$

so $\cos(0.1) \approx 1 - 0.005 = 0.995$.

**2. Classifying a critical point.** For $f(x, y) = x^2 + xy + y^2 - 3x$, setting $f_x = 2x + y - 3 = 0$ and $f_y = x + 2y = 0$ gives $(2, -1)$. Then $f_{xx} = 2$, $f_{yy} = 2$, $f_{xy} = 1$, and

$$D = f_{xx}f_{yy} - f_{xy}^2 = 4 - 1 = 3 > 0$$

with $f_{xx} > 0$, so $(2, -1)$ is a local minimum.

**3. A double integral over a triangle.** Over the region $0 \le y \le x \le 1$:

$$\int_0^1 \int_0^x 2y\,dy\,dx = \int_0^1 x^2\,dx = \frac{1}{3}$$

## How to do well in UI MTH 201

- **Rebuild your MTH 102 speed.** Partial derivatives are ordinary derivatives with the other variables held fixed, so drill [mixed derivative rules](/learn/calculus-1/derivative-rules/derivative-rules-practice) if they feel rusty.
- **Draw every region.** Wrong limits cause most multiple integral errors. Sketch first, then decide the order of integration.
- **Use the second-derivative test carefully.** Compute $D$ before deciding anything, and remember that $D < 0$ means a saddle point.
- **Keep formulas close and practise often.** The [formula sheet](/formulas) and mixed [practice](/practice) sessions help you switch between single-variable and multivariable topics.

## Frequently asked questions

### What is MTH 201 at UI?

MTH 201 Mathematical Methods I is a compulsory 2-unit course at 200 level in the University of Ibadan Department of Mathematics. It uses the national CCMAS code; the CCMAS outline covers the mean value theorem, Taylor series, partial derivatives, extrema, Lagrange multipliers, linear approximation, line integrals and multiple integrals.

### What other mathematics courses are at UI 200 level?

The department lists MTH 202 Elementary Differential Equations, MTH 203 Sets, Logic and Algebra I, MTH 204 Linear Algebra I, MTH 205 Linear Algebra II, MTH 207 Real Analysis I, MTH 209 Introduction to Numerical Analysis and MTH 210 Vector Analysis, plus UI-MAT 221 Analysis I and UI-MAT 222 Analysis II.

### Is MTH 201 hard?

The pace is the main challenge, because the course moves from Taylor series to multiple integrals in only 2 units. If your MTH 102 differentiation is fluent, partial derivatives feel familiar quickly; Lagrange multipliers and multiple integral limits need the most practice.

### How do I prepare for UI MTH 201?

Revise MTH 102 differentiation and integration first, then work through partial derivatives and double integrals with short, regular practice sessions. Drawing the region before every multiple integral prevents most mistakes.