Course code:  MT2A 
Course title in language of instruction:  Mathematics II 
Course title in Czech:  Mathematics II 
Course title in English:  Mathematics II 
Mode of completion and number of credits:  Exam (6 credits) (1 ECTS credit = 28 hours of workload) 
Mode of delivery/Timetabled classes:  fulltime, 2/2 (hours of lectures per week / hours of seminars per week) 
Language of instruction:  English 
Level of course:  bachelor 
Semester:  SS 2019/2020 
Name of lecturer:  RNDr. Karel Mikulášek, Ph.D. (supervisor) 
Prerequisites:  Mathematics I 

Aims of the course: 
Students should get an understanding of functions of two variables, partial derivatives and their applications. They should know how to solve simple first and second order differential equations, learn the basics of difference equations, finding roots of polynomials, and fitting the data with curves. Using suitable examples they will test the methods and skills they have learned to be able to tackle simple mathematical problems they may come across in practice. 

Course contents: 
1.  Calculus of functions of 2 variables (allowance 10/10)   a.  Functions of 2 variables, domain, properties  b.  Partial derivatives, directional derivatives, tangent plane  c.  Local, relative absolute maxima/minima of twofunctions 
 2.  Differential and difference equations (allowance 10/10)   a.  First order ordinary differential equation separable, homogeneous  b.  Second order ordinary linear differential equation with constant coefficients 
 3.  Difference equations (allowance 4/4)   a.  Homogeneous difference equations  b.  Nonhomogeneous difference equations 
 4.  Polynomials and approximation (allowance 4/4)   a.  Polynomials and finding their roots  b.  Lagrange approximation polynomial  c.  Fitting data with curves 



Learning outcomes and competences: 
Generic competences:     Ability to apply knowledge    Ability to solve problems    Ability to work independently    Basic computing skills    General knowledge 
 Specific competences:     Student is able with use of basic integration methods calculate indefinite integral    Student is able with using limits and integration methods solve improper integral.    Student knows to solve basic types of difference equations of 1st and 2nd order.    Student knows to solve basic types of ordinary differential equations of 1st and 2nd order.    Student knows to use calculation derivative of two variables function for determination of its maximal and minimal value.    Student knows with use of definite integral calculate surface area and volume of rotate solids. 


Type of course unit:  required 
Year of study:  Not applicable  the subject could be chosen at anytime during the course of the programme. 
Work placement:  There is no compulsory work placement in the course unit. 
Recommended study modules:   

Learning activities and study load (hours of study load): 
Type of teaching method  Daily attendance  Direct teaching  lecture  28 h  practice  28 h  Selfstudy  preparation for exam  46 h  preparation for regular assessment  20 h  preparation for regular testing  46 h  Total  168 h 


Assessment methods: 
At midterm, in a written test, students are required to submit solutions to several practical problems for them to see the improvement needed. To complete the course a written test consisting of practical and theoretical parts is required. In the practical part, students have to solve 3 to 4 problems and, in the theoretical part, to give correct answers to 3 to 4 questions to see whether they have a good understanding of the background theory. The points obtained in both parts are then added. To pass the examination, a student has to achieve at least 50 percent of the total number of points. 

Recommended reading: 
Type  Author  Title  Published in  Publisher  Year  ISBN 

RQ  BENCE, S.  HOBSON, M.  RILEY, K.  Mathematical Methods for Physics and Engineering  Cambridge  Cambridge University Press  2009  9780521679718  RQ  STROUD, K.  Engineering Mathematics  New York  Palgrave Macmillan  2001  9781403942463  RQ  STROUD, K.  Advanced Engineering Mathematics  New York  Industrial Press, Inc.  2003  9780831131692 
