Bi8688 Introduction to Scientific Computing

Faculty of Science
Autumn 2014
Extent and Intensity
1/1. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. Walter Gander (lecturer), prof. RNDr. Jiří Hřebíček, CSc. (deputy)
prof. RNDr. Jiří Hřebíček, CSc. (alternate examiner)
Guaranteed by
prof. RNDr. Ladislav Dušek, Ph.D.
RECETOX – Faculty of Science
Contact Person: prof. RNDr. Jiří Hřebíček, CSc.
Supplier department: RECETOX – Faculty of Science
Prerequisites
Passing the core courses of mathematical analysis
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of this course the student will be able to understand what is contained in scientific computing using Maple and Matlab
Syllabus
  • Lecture 1. Finite Precision Arithmetic. Matlab, Octave, Maple . 1.1 Real Numbers and Machine Numbers 1.2 IEEE Standard, 1.3 Rounding Errors , Condition, Stability 1.4 Machine Independent Algorithms 1.5 Problems and Exercises Lecture 2. Linear Systems of Equations (direct and iterative solver) 2.1 Algorithms for dense Systems 2.2 Gaussian Elimination, Condition, Pivoting 2.3 LU and QR-decomposition 2.4 Algorithms for Large Sparse Systems 2.5 Classical Stationary Iterative Methods 2.6 Krylov Subspace Methods 2.7 Problems and Exercises Lecture 3. Nonlinear Equations . 3.1 Scalar Nonlinear Equations 3.2 Determinants and Zeros of Polynomials 3.3 Nonlinear Systems of Equations 3.4 Problems and Exercises Lecture 4. Least Squares Problems 4.1 Linear Least Squares Problem and the Normal Equations 4.2 Singular Value Decomposition (SVD) 4.3 Condition of the Linear Least Squares Problem 4.4 Algorithms Using Orthogonal Matrices 4.5 Nonlinear Least Squares Problems 4.6 Least Squares with Constraints 4.7 Problems and Exercises Lecture 5. Numerical Ordinary Differential Equations 5.1 Theoretical Background, Notation 5.2 Taylor Expansions, Truncation Error 5.3 Runge-Kutta Methods 5.4 Linear Multistep Methods 5.5 Special Cases 5.6 Problems and Exercise
Literature
    recommended literature
  • Gander, Walter, Gander, Martin J., Kwok, Felix. Scientific Computing - An Introduction using Maple and MATLAB. Springer, 2014.
Teaching methods
Lectures and following exercises
Assessment methods
The final evaluation will be a written test.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught only once.
The course is taught: in blocks.
Note related to how often the course is taught: 15.-19. prosince 2014.
General note: 15.-19. prosince 2014.
  • Enrolment Statistics (recent)
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