Entry requirements

Basic Course in Mathematics or Introduction to Studies in Mathematics participation (may be read in parallel with 1MA210).

Learning outcomes

On completion of the course, the student should be able to:

• give an account of the notion of limits both for real-valued functions and for sequences of numbers, and compute limits of functions and sequences using standard formulas;
• use rules of differentiation, and use derivatives to compute extreme values and sketch graphs of functions;
• give an account of the Riemann integral of a continuous function and its analytic and geometric meaning, decide convergence or divergence of generalized Riemann integrals, as well as proofs of the basic theorems in integral calculus;
• use variable substitution and integration by parts to compute integrals, and use the integrals in applications to geometric problems;
• give an account of basic notions, theorems and proofs in the theory of numerical series, Taylor series and power series;
• prove minor results and theorems in differential and integral calculus using fundamental theorems in these subjects.

Content

Real numbers: supremum and infimum, convergence of sequences. Functions: properties of certain functions, monotonicity and inverse, as well as inverses of elementary functions. Limits and continuity: notions, proof of existence and rules. The derivative: notions, differential rules, the chain rule, the mean value theorem with applications, extreme value problems, sketching graphs of functions. The integral: primitive function, Riemann integral, the fundamental theorem of integral calculus, integration techniques such as substitutions and integration by parts, improper integrals and their convergence, geometric applications of integral calculus such as calculations of areas, volumes and arclengths. Infinite series: notion of convergence. convergence criteria for positive and alternating series. notation of absolutely convergent series. Taylor's formula and power series.

Instruction

Lectures, teaching sessions and calculation exercises. Dugga or assignments

Assessment

Written examination at the end of the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other regulations

The course can not be included in higher education qualification together with any of the courses Single variable calculus, Derivatives and integrals or Analysis for engineers.