MTH 201 Mathematical Methods I: Topics, Study Guide, Practice

MTH 201 Mathematical Methods I is the main 200 level calculus course in the National Universities Commission's Core Curriculum and Minimum Academic Standards (CCMAS). It is a compulsory 2-unit course in the B.Sc. Mathematics programme, and it also appears in the CCMAS computing programmes. It takes the single-variable calculus of MTH 102 and extends it to functions of several variables. This guide maps every MTH 201 topic to practice and reading on PracticeCalculus.

What MTH 201 covers

The CCMAS outline starts with real-valued functions of a real variable and a review of differentiation, integration and their applications. It then covers the mean value theorem and Taylor series. The second half moves to real-valued functions of two and three variables: partial derivatives and the chain rule, extrema, Lagrange multipliers, increments, differentials and linear approximation, the evaluation of line integrals, and multiple integrals.

The learning outcomes ask students to explain real-valued functions, solve problems with the mean value theorem and Taylor expansions, and evaluate line, surface and volume integrals.

Compared with a standard sequence, MTH 201 takes the series and approximation ideas of Calculus 2 and most of the differential and integral calculus of Calculus 3.

MTH 201 topic map

MTH 201 and the courses around it

MTH 201 and MTH 210 complement each other: MTH 201 supplies partial derivatives and multiple integrals, and MTH 210 supplies the vector language used for gradients and line integrals.

Example problems at the MTH 201 level

These are original practice problems.

1. A Maclaurin series. Expanding \ln(1 + x) about x = 0:

2. Partial derivatives. For f(x, y) = x^2 y + \sin(xy),

3. Lagrange multipliers. Maximise f = xy subject to x + y = 10. Setting \nabla f = \lambda \nabla g gives y = \lambda and x = \lambda, so x = y = 5 and the maximum is f = 25.

4. A double integral.

How to do well in MTH 201

• Refresh MTH 102 first. A partial derivative is an ordinary derivative with the other variables held constant, so weak differentiation rules show up immediately. The formula sheet is a quick refresher.
• Sketch regions before integrating. Most mistakes in multiple integrals come from wrong limits. Draw the region, then decide the order of integration.
• Use a checklist for Lagrange problems. Write \nabla f = \lambda \nabla g, list every equation including the constraint, then solve. The Lagrange multipliers guide walks through the method.
• Practice in short, regular sessions. Use practice to mix topics, and read the Calculus 1 vs 2 vs 3 guide to see how MTH 201 fits the wider calculus picture.