Differential and Integral CalculusLaajuus (3 ECTS)

Objective

The student is aware of the meaning of continuity and differentiability in solving equations and finding maximum and minimum values of a function. The student knows how to estimate the accuracy of the results when using numerical methods. The student knows general principles to write down the differential and the definite integral in application problems and is able to recognize a differential equation.

The student knows how to test whether a given function is a solution of a differential equation.

The student is able to differentiate most common functions up to the case where the inner function is of the form kx + b. He or she is able to solve an equation numerically using interval bisection method and Newtons method The student can solve optimization problems with the help of the derivative of the function.

The student is able to integrate most common functions up to the case where the inner function is of the form kx + b. He or she is able to use definite integrals to determine areas, volumes, and mean values of a given function. The student is able to differentiate and integrate numerically and make an estimation of the accuracy of the result.

Content

Rules to determine the derivative of any given (common) function. Numerical methos to solve equations: interval bisection method and Newtons method. Extremal values and optimization problems solved by using differentiation.

Integral function and definite integral. Connection of these concepts. Integration techniques: basic functions and their linear combinations, integration of a composed function if the inner function is simply multiplication by a constant.

Differential and its use to determine the uncertainty of the result calculated from uncertain values. Differential as a base for definite integral. Applications of integral calculus: areas, volumes, different mean values.

The concept of a differential equation and its solution.

Qualifications

Systems of equations and matrices, Functions with an introduction to differentiation