Study Guide

Objectives

In this Course, you will learn the calculation and mathematical modeling skills you need in the engineering profession. The sub-area is differential and integral calculus

At the end of the course, you
• recognize exponential and logarithmic functions
• can solve exponential and logarithmic equations and apply them in engineering problems
• you know the basic calculations of matrices and know some applications
• can use the concepts and notations related to limit value, derivative and integral
• can interpret the derivative as a rate of change
• can determine the derivative and integral graphically, numerically and symbolically
• know how to solve application tasks, the modeling of which requires the use of a derivative or an integral
• are able to present and justify logically chosen solutions
• you know how to evaluate the reasonableness and correctness of the solutions you make

Content

• exponential and logarithmic function
• exponential equation, logarithmic equation
• basic matrix concepts and calculations (sum, multiplication by a number, product, determinant, inverse matrix)
• solving a group of linear equations with matrices
• some matrix applications
• the concept of limit value in brief
• derivative of the graph
• derivative numerically
• calculating the derivative using the rules of derivation
• higher derivatives (used at the entry level)
• some applications of the derivative (e.g. differential and total differential, error estimation and extreme values)
• the definite integral graphically
• definite integral numerically
• calculating the integral function using integration rules
• basic theorem of analysis, definite integral symbolically
• some applications of the integral (e.g. distance, work, area, center of gravity, average, mean square)

Assessment criteria, satisfactory (1-2)

Student

• recognizes exponential and logarithmic functions
• can solve simple exponential and logarithmic equations
• knows basic calculations of matrices
• knows how to use some concepts and notations related to derivatives and integrals
• knows the principle of the derivative as a rate of change
• can determine the derivative and integral graphically, numerically and symbolically, similar to the simple examples used in class
• the presentations and justifications of the chosen solutions may be incomplete
• there may be shortcomings in evaluating the reasonableness and correctness of the solutions made

Assessment criteria, good (3-4)

Student

• recognizes exponential and logarithmic functions
• can solve exponential and logarithmic equations and apply them in engineering problems
• knows the basic calculations of matrices and knows some applications
• knows how to use concepts and notations related to limit value, derivative and integral
• can interpret the derivative as a rate of change
• can determine the derivative and integral graphically, numerically and symbolically
• can solve application tasks, the modeling of which requires the use of a derivative or an integral
• is able to present and justify logically chosen solutions
• knows how to evaluate the reasonableness and correctness of the decisions he makes

Assessment criteria, excellent (5)

n addition to the previous, the student has a comprehensive understanding of the subjects of the course and knows how to apply them to more demanding problems. The student has the ability to present and justify logically chosen solutions. Solutions are presented clearly and mathematical concepts are used precisely. The student is highly motivated and takes full responsibility for their own and the group's performance.