Obligatory base module 1
Learning outcomes
After passing this cource the student should come to:
* identify, transform and use elementary functions, especially in their common applications;
* understand, compute and estimate derivatives algebraically, graphically, numerically, and verbally;
* understand and use basic methods of integral calculus, including analytical, graphical and numerical techniques of integration;
* apply techniques of slicing and summing to a variety of physical problems in geometry, physics and economics;
* use common functions like polynomials and sinusoidal functions as building blocks in approximations of more complicated functions;
* understand and use simple differential equations to model and analyze problems in biology, geology and other scientific fields;
* distinguish between convergent and divergent series and integrals;
* understand and appreciate the interplay between discrete and continuous variables;
* understand of the concepts and methods of linear algebra;
* use matrix algebra fluently, including the ability to put systems of linear equation in matrix format and solve them using matrix multiplication and the matrix inverse.
More general goals include developing students' abilities to
* improve logical thinking and think critically;
* apply knowledge of mathematics to identify, formulate, and solve problems, particularly problems related to the environment;
* work effectively in heterogeneous teams;
* communicate effectively, especially by writing precisely about technical things;
* use technological tools such as graphing calculators and equation editors in an appropriate manner; and
* engage in life-long learning.
Brief description of content
In this course, we will engage in the full mathematics process, which includes searching for patterns, order and reason; creating models of real world situations to clarify and predict better what happens around us; understanding and explaining ideas clearly; and applying the mathematics we know to solve unfamiliar problems. Some classical mathematical concepts and methods from different branches of advanced mathematics (mathematical analysis, linear algebra and analytic geometry) are studied. Main topics include functions, limits, differentiation, sequences, integration, differential equations, matrix algebra and determinants.
