Differential and Integral Calculus, 5 op

Core content

• Antiderivative and basic integration techniques. Proper and improper integrals.
• Ordinary linear differential equations of first and second order. Separable first order differential equations.
• Limit of a sequence, increasing and decreasing sequences.
• Series (geometric, with positive terms, alternating, Taylor series) and their convergence.

Complementary knowledge

• Applications of integration in, e.g., determining areas and volumes of geometrical shapes, and computing the length of a curve.
• Higher order differential equations. Modeling specific real world problems, such as growth of populations, with differential equations.
• Approximating a function with a polynomial.
• Using Matlab as a tool in solving the exercise problems.

Specialist knowledge

• Numerical integration, trapezoid rule and Simpson's formula. Computing the Riemann sums.
• Existence and uniqueness results, matrix notation for linear systems.
• Testing convergence. Computing limits and integrals using series. Estimating the error in polynomial approximations of functions.