ABU MATH201 Mathematical Methods I: Study Guide and Practice

ABU MATH201, Mathematical Methods I, is the first 200-level calculus course at Ahmadu Bello University, Zaria. It carries 3 credit units in the first semester, and its listed prerequisite is MATH105 Differential and Integral Calculus or an equivalent. This guide maps every MATH201 topic to free practice, so you can learn each method by solving problems with instant feedback.

What ABU MATH201 covers

The department's outline has two blocks. The first, applications of calculus, revises the techniques of differentiation, then covers successive differentiation and Leibniz's theorem, Taylor's and Maclaurin's series, tangents and normals to plane curves, and curvature. On the integration side it covers definite integrals, methods of integration, reduction formulae, arc length of a plane curve, the area enclosed by a plane curve and improper integrals.

The second block is partial differentiation: real-valued functions of two and three variables, partial derivatives, the chain rule, the Jacobian, extrema, Lagrange's multipliers, increments, differentials and linear approximations.

In standard terms, the first block is mostly Calculus 2 (series, integration techniques, arc length and improper integrals) and the second is the differential half of Calculus 3.

MATH201 topic map

MATH201 in the ABU sequence

MATH201 and MATH203 run in the same semester and share the same prerequisite: MATH201 computes with calculus while Real Analysis I proves why it works. If your 100-level skills need work, revisit the MATH105 and MATH104 guides.

Example problems at the MATH201 level

1. Leibniz's theorem. Find the third derivative of y = x^2 e^x.

Only the first three terms survive, because the third derivative of x^2 is zero:

2. A Maclaurin series. For f(x) = \ln(1 + x), the derivatives at 0 give

3. A reduction formula. With I_n = \int_0^{\pi/2} \sin^n x\,dx, integration by parts gives I_n = \dfrac{n - 1}{n} I_{n - 2}. Since I_0 = \dfrac{\pi}{2},

4. An improper integral.

5. A Jacobian. For polar coordinates x = r\cos\theta, y = r\sin\theta,

How to do well in ABU MATH201

• Make integration by parts automatic. Reduction formulae, many improper integrals and Leibniz-style patterns all lean on it. Drill integration by parts and repeated parts.
• Memorize a few Maclaurin series. Knowing e^x, \sin x, \cos x and \ln(1 + x) by heart lets you build many others quickly. The calculus formula sheet lists them.
• Hold variables fixed deliberately. In partial differentiation, write which variables are constant before differentiating. It prevents the most common mistake in the second block.
• Review the classic errors in common calculus mistakes, especially sign errors in Taylor series and limits of improper integrals.
• Practice with timed sets from practice exams before each test.

Tip: when an improper integral looks hard, compare it with \int_1^{\infty} \frac{1}{x^p}\,dx first. Many convergence questions are settled by that one comparison.