Fundamentals of Differential and Integral Calculus, 5 cr

Core content

• Functions, limits and continuity. Composite function. Inverse function.
• Derivative. Derivative by limit of a difference quotient. Chain rule. Differentiation of elementary functions.
• Integration. Simple integration techniques (such as integration by parts and integration by substitution). Riemann integral.
• Ordinary differential equations. Linear and separable first order differential equations.
• Second order differential equations.

Complementary knowledge

• Hyperbolic functions and their inverse functions.
• Differentiation of an inverse function. Mean value theorem.
• Applications of integrals such as area, arc length, volume and surface area of a solid of revolution.
• Applications of differential equations.
• Higher order differential equations with constant coefficients.
  

Specialist knowledge

• Epsilon-delta proof of limits.
• L'Hospital's rule.
• Numerical integration.
• Numeric methods for solving differential equations.
• Systems of differential equations.