Veidlapa Nr. M-3 (8)
Study Course Description
Mathematical Methods
Course Code
SL_105
Branch of Science
Mathematics
ECTS
6.00
Target Audience
Life Science
LQF
Level 7
Study Type And Form
Full-Time; Part-Time
Study Course Implementer
Course Supervisor
Ilze Balode
Structure Unit Manager
Andrejs Ivanovs
Structural Unit
Statistics Unit
Contacts
23 Kapselu street, 2nd floor, Riga, statistika@rsu.lv, +371 67060897
About Study Course
Objective
This course aims at providing mathematical background for further calculus-based learning of statistics. The main objective of this course is to allow students to understand mathematical concepts that are necessary to follow proofs and reasoning in subsequent courses. Students are not expected to spend much time understanding proofs of calculus theorems, but rather to build intuition of fundamental ideas of calculus and linear algebra, and their role and application in statistics.
Preliminary Knowledge
Students must have the necessary mathematical background to understand key statistical techniques and their derivation, if they involve concepts covered in the course. In addition, good knowledge of high school algebra as well as understanding of the notion of a function and its graph.
Learning Outcomes
Knowledge
1.• the student is able to demonstrate deeper knowledge, understands and explains the concepts of limit, derivative, integral, infinite series; • recognizes and uses the notation of matrices and determinants; • independently utilize basic methods to do computations involving mathematical objects studied in the course; • qualitatively describes examples of the practical application of mathematical objects studied in the course, understands how to use them in the research.
Skills
1.• student independently uses limit concept and limit laws to predict the behaviour of a given function; • finds derivative and indefinite integral of a function, computes definite integral; • performs computations with matrices and determinants; • applies rules and methods of mathematical objects studied in the course to solve a practical problem related to these objects.
Competences
1.Students have an comprehension of how calculus generalize pre-calculus mathematics using the limit process and how that can be further integrated to other real-world situations if necessary. Students are competent formulate their tasks into mathematical problems and choose the appropriate method to solve them.
Assessment
Individual work
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Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Individual work |
-
|
-
|
|
1) Individual work with required and additional literature – careful reading of the chapters corresponding to current topics for each lecture to create theoretical bases.
2) Thorough review of solutions for provided examples to sum up the material for all practical classes.
In order to evaluate the quality of the study course as a whole, the student must fill out the study course evaluation questionnaire on the Student Portal.
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Examination
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Examination |
-
|
10 points
|
|
1) Practical tasks - 50% 2) Written exam – 50%. |
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Study Course Theme Plan
FULL-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Functions and their graphs. Domain and range of the function. Combining functions.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Functions and their graphs. Domain and range of the function. Combining functions.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Limit of a function, limit laws. The precise definition of a limit.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Limit of a function, limit laws. The precise definition of a limit.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Continuity. Limits involving infinity.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Derivative, differentiation rules.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
The chain rule. Linearization and differentials.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Applications of derivatives: extreme values, monotonicity, concavity.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Applications of derivatives: extreme values, monotonicity, concavity.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Applications of derivatives: extreme values, monotonicity, concavity.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Applications of derivatives: extreme values, monotonicity, concavity.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Applied optimization problems, Newton’s method to solve equations. Antiderivative.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Applied optimization problems, Newton’s method to solve equations. Antiderivative.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Estimating area with finite sums. Limits of finite sums. Definite integral.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
The Fundamental theorem of calculus. Indefinite integral.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Substitution method for indefinite and definite integral. Applications of definite integral.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Other techniques of integration.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Infinite sequences and series.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Vectors and the geometry of spaces.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Matrix, matrix operations.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Determinants. Inverse matrix.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Determinants. Inverse matrix.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Eigenvalues, eigenvectors and diagonalization of a matrix.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Eigenvalues, eigenvectors and diagonalization of a matrix.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
48 Academic Hours
Final Examination:
Exam (Written)
PART-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Functions and their graphs. Domain and range of the function. Combining functions.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Limit of a function, limit laws. The precise definition of a limit.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Limit of a function, limit laws. The precise definition of a limit.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Continuity. Limits involving infinity.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Continuity. Limits involving infinity.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Continuity. Limits involving infinity.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Derivative, differentiation rules.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
The chain rule. Linearization and differentials.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
The chain rule. Linearization and differentials.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Applications of derivatives: extreme values, monotonicity, concavity.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Applied optimization problems, Newton’s method to solve equations. Antiderivative.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Applied optimization problems, Newton’s method to solve equations. Antiderivative.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Estimating area with finite sums. Limits of finite sums. Definite integral.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Estimating area with finite sums. Limits of finite sums. Definite integral.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
The Fundamental theorem of calculus. Indefinite integral.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Substitution method for indefinite and definite integral. Applications of definite integral.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Other techniques of integration.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Infinite sequences and series.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Vectors and the geometry of spaces.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Matrix, matrix operations.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Matrix, matrix operations.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Determinants. Inverse matrix.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Eigenvalues, eigenvectors and diagonalization of a matrix.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Study room
|
2
|
Topics
|
Eigenvalues, eigenvectors and diagonalization of a matrix.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
32 Academic Hours
Final Examination:
Exam (Written)
Bibliography
Required Reading
1.
Strang, G. (2006). Linear algebra and its applications. 4th Edition, Brooks Cole.Suitable for English stream
2.
Hass, J., Heil, C., Weir, M. D., & Thomas, G. B. (2018). Thomas' calculus. 14th Edition, Pearson.Suitable for English stream
Additional Reading
1.
Stewart, J. (2016). Calculus: Early Transcendentals. 8th Edition, Cengage Learning.Suitable for English stream
2.
Lay, D. C. (2012). Linear algebra and its applications. Boston: Addison-Wesley.Suitable for English stream