Course Objectives

The students should:

· become familiar with the basic concepts and solutions associated with differential and integral calculations and with differential equations.

· be able to model and solve problems through the use of differentials, integrals and differential equations.

· be able to use Maclaurin series in connection with integration, limit determinations and linear approximations.

· be able to use the computer programme Maple for symbolic and numeric calculations and for graphics in association with practical assignments and submitted assignments and projects.

Course Description

Differential calculations: the concepts of limits and continuity. Derivation and implicit derivation. Newton’s method. Differentials. Linear approximations and the computation of uncertainty. Inverse functions. Applications of differential calculations.

Integrals: Riemann sums and Riemann integrals. The Fundamental Theorem. Integration methods. Applications of integral calculations (areas, curve lengths, volumes and surfaces of rotating objects). Numerical integration (the rectangle method, the trapeze method, Simpson’s formula). Integration through the use of series development.

Differential equations: Differential equations and mathematical models. Direction fields and solution curves. Separable and linear first-order differential equations. Numerical solutions of first-order differential equations by Euler’s methods. Second-order differential equations with constant coefficients.

Exponential series: Maclaurin-series with applications within integral and limit-value calculations. Relationship with linear approximations.

Learning Methods

Lectures and practical assignments. Training and practice in the use of the computer programme Maple is an important aspect of the subject. In the practical assignments students will work with pencil and paper as well use Maple as a natural tool for handling graphics and more complex numerical and symbolic calculations. Seven of the practical assignments will be organised as maths-labs with obligatory participation and submission of reports.

Assessment Methods

• Continuous assessment:
  • Two obligatory Maple projects in groups must be approved.
  • At least 5 of the 7 obligatory mathematics-lab practical assignments with resulting reports must be approved.
  • Individual written mid-term test - all printed and written aids allowed (30%)

• Individual written final examination (70%), which consists of:
  • Part 1 – all printed and written aids allowed
  • Part 2 – all examination aids permitted, including calculators and laptop computers with Maple

In order to earn a passing grade for the course, the final examination must receive an E grade or better.

Minor adjustments may occur during the academic year, subject to the decision of the Dean