## DIM701 Mathematics

 Code DIM701 Name Mathematics Status Compulsory/Courses of Limited Choice Level and type Undergraduate Studies, Academic Field of study Mathematics and Statistics Faculty Academic staff Inta Volodko, Aleksandrs Kovancovs, Irina Eglīte, Ilona Dzenīte, Vladislavs Kremeņeckis, Ilze Karpinska, Valentīna Koliškina, Marija Dobkeviča, Sergejs Smirnovs, Jeļena Mihailova, Tabita Treilande, Kaspars Krauklis, Jeļena Liģere Credit points 9.0 (13.5 ECTS) Parts 2 Annotation Linear algebra: matrices, determinants, systems of linear equations. Analytical geometry: vectors, lines, surfaces. Introduction to analysis: limits, continuity. Differential calculus: derivative,differential and their applications.. Integral calculus: indefinite and definite integrals, their applications. Multiple integrals. Ordinary differentialequations. The Laplace transform. Series.. Goals and objectives of the course in terms of competences and skills Deliver basic mathematical concepts that are necessary to understand data handling processes and algorithms. Develop students’ logical thinking and skills to analyze basic aspects of special subjects with the objective to analyze more complicated problems. Learning outcomes and assessment After successful completion of the course students will be able to solve systems of linear equations and perform operations on matrices. Can perform operations on vectors. - Evaluation of students’ work is based on the results of homework assignments, tests and the final exam. Can find equation of a straight line in a plane and three-dimensional space; Find equation of a plane in three-dimensional space; Recognize second-order curves and plot they in a plane. - Students’ knowledge and abilities are assessed using homework assignments, tests and final exam. Can compute simple limits; find derivatives of functions; can analyze the behavior of a function using limits and derivatives and plot the graph of a function. - Two tests, two homework assignments and several problems on the final exam are used to assess students’ knowledge on these topics. Can find partial derivatives of a function of several variables; find equations of a tangent plane and normal line to a surface; determine extrema of a function of two variables. - Students’ work is tested using homework assignment and problem on the final exam. Can perform operations on complex numbers in algebraic, trigonometric and exponential form. - Corresponding problems are included in the final exam. Can integrate simple functions; find the area of a plane figure, length of a curve and volume of a body of revolution using definite integral. - Three tests, two homework assignments and problems on the final exam are used to test students’ knowledge on the above mentioned topics. Can solve simple first and second order ordinary differential equations. Can solve ordinary differential equations by means of the method of the Laplace transform. - Students’ knowledge is assessed using homework assignment, test and problems on the final exam. Can determine whether a series is convergent or divergent; find the domain of convergence of functional series; expand a function into power series; use series to compute a definite integral. - One test, one homework assignment and a problem on the final exam are used to assess students’ knowledge on these topics. Can evaluate more complicated integrals, solve ordinary differential equations and other problems using Mathematica 5. - Students’ knowledge is tested on the pass/fail system. The test consists of six problems, three points maximum for each problem. Students’ have to score at least 10 points in order to pass the course. Course prerequisites Course is based on knowledge that is acquired in secondary school.

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