UNN MTH 242 Mathematical Methods I: Study Guide and Practice

UNN MTH 242, Mathematical Methods I, is the 200-level course where calculus at the University of Nigeria, Nsukka moves into several variables. It is a 3-unit major course in the second semester of the second year for mathematics students, and it builds directly on the single-variable calculus of MTH 121. This guide maps every MTH 242 topic to free practice, so you can learn each idea by solving problems with instant feedback.

What UNN MTH 242 covers

The department's description opens with real-valued functions of one real variable: a review of differentiation and integration and their applications, the mean value theorem and Taylor series. It then turns to real-valued functions of two or three variables, covering partial derivatives, the chain rule, extrema, Lagrange's multipliers, increments, differentials and linear approximations. The course closes with the evaluation of line integrals and multiple integrals.

In standard terms, MTH 242 combines the end of Calculus 2 (the mean value theorem and Taylor series) with most of a Calculus 3 course. The main Calculus 3 topics it does not list are the big vector calculus theorems, which UNN places in the 300-level course MTH 324 Vector and Tensor Analysis.

MTH 242 topic map

MTH 242 in the UNN sequence

MTH 221 and MTH 242 look at some of the same results from two angles: Real Analysis I proves them, while Mathematical Methods I uses them to compute. If you need to rebuild your foundation, revisit MTH 121 and MTH 111.

Example problems at the MTH 242 level

1. Partial derivatives. For f(x, y) = x^2 y + y^3,

2. A Lagrange multiplier problem. Maximize f = xy subject to x + y = 10.

Set \nabla f = \lambda \nabla g with g = x + y: y = \lambda and x = \lambda, so x = y. The constraint gives x = y = 5, and the maximum is f = 25.

3. A double integral.

4. A line integral. Evaluate \int_C x\,dx + y\,dy along \mathbf{r}(t) = (t, t^2) for 0 \le t \le 1.

Here dx = dt and dy = 2t\,dt, so

How to do well in UNN MTH 242

• Refresh single-variable calculus first. The course starts with a review, and every partial derivative is an ordinary derivative with the other variables held fixed. The calculus formula sheet keeps the standard results in one place.
• Draw the region before integrating. Most errors in multiple integrals come from wrong limits. Sketch the region, then practice double integrals over general regions.
• Check stationary points with the test. After solving f_x = f_y = 0, classify each point with the second-derivative test rather than guessing.
• Avoid classic slips. Read common calculus mistakes and see how Calculus 3 differs from earlier courses in Calculus 1 vs 2 vs 3.
• Rehearse with timed sets using practice exams before each test.

Tip: Lagrange multiplier problems always end with solving a small system of equations. Write out all the equations, including the constraint, before you start eliminating variables.