Basics of Mathematics 4030-PMAT
The scope of the lecture and accompanying exercises is aligned and includes the following topics:
1. Logic.
2. Basic elementary functions:
• exponential, power, polynomial, logarithmic, and trigonometric functions;
• logarithmic scale and its applications.
3. Sequences and numerical series:
• mathematical induction;
• limits and convergence of infinite sequences;
• infinite sums illustrated by the geometric series.
4. Fundamentals of financial mathematics:
• simple and compound interest; fixed and decreasing installment loans;
• financial deposits and savings.
5. Concept of compositefunctions, continuous functions; properties of continuous functions.
6. Differential and integral calculus and its applications:
• definition of the derivative, tangent line to the graph of a function;
• derivatives of elementary functions, arithmetic properties of derivatives, derivative of a composite function;
• determining properties of a function based on its derivative, use of differential calculus in optimization problems;
• the indefinite integral as the inverse operation to differentiation, concept of the definite integral;
• geometric interpretation of the definite integral, applications of integrals.
Type of course
Mode
Course coordinators
Learning outcomes
Upon completion of the course (lecture and exercises), the student:
• understands the basics of logic;
• has knowledge of the fundamental concepts of mathematical analysis (numerical sequence, convergence, function, continuity, derivative, composite function, definite and indefinite integrals);
• understands the concept of the derivative of a continuous single-variable function;
• is able to compute basic limits of sequences, as well as derivatives and definite/indefinite integrals of elementary single-variable functions;
• is familiar with basic elementary functions: exponential, logarithmic, power, polynomial, and trigonometric functions;
• understands the concept of the logarithmic scale and its applications;
• possesses basic knowledge of financial mathematics: is able to calculate the installment amount (and its components) for fixed-rate and decreasing-rate loans, and can compare financial investment offers from different institutions in terms of profitability;
• can use differential calculus to find (when they exist) local and global extrema of single-variable functions, determine intervals of monotonicity, and write the equation of the tangent line to a function at a given point;
• knows and understands the concept of the integral of a single-variable function, including the geometric interpretation of the definite integral;
• additionally achieves the learning outcomes specified by the codes: K_W09, K_W10, K_U03, K_K03, K_K05.
Assessment criteria
A necessary condition for receiving a positive final grade is having no more than two (2) unexcused absences from the exercise sessions.
The final grade will be based on the result of a written exam, consisting of a multiple-choice test (60 points) and a problem-solving section (40 points).
Homework assignments and quizzes, aimed at continuously assessing the student’s knowledge and understanding of the material, are not mandatory.
A student has the right to retake the exam even if they have already received a passing grade. In such a case, the final grade will be the one obtained in the retake.
Practical placement
Not applicable
Bibliography
Dariusz Wrzosek, Matematyka dla biologów, Wydawnictwa Uniwersytetu Warszawskiego, Warszawa 2008.
Marek Bodnar, Zbiór zadań z matematyki dla biologów, Wydawnictwa Uniwersytetu Warszawskiego, Warszawa 2008.
Włodzimierz Krysicki, Lech Włodarski, Analiza matematyczna w zadaniach część 1, Państwowe Wydawnictwo Naukowe, Warszawa 1977.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: