UI MTH 201 Mathematical Methods I: Study Guide and Practice

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 has the full national outline.

UI MTH 201 topic map

MTH 201 in the UI course list

The national outline for MTH 210 (gradient, divergence, curl, lines and planes) is covered in the NUC MTH 210 guide.

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

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

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:

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 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 and mixed practice sessions help you switch between single-variable and multivariable topics.