Course modules
Unit 01: Introduction
Unit 01: Introduction
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PageLecture 1 Introduction and basic concepts, e.g. normed function spaces and setting up the approximation task. Lecture 1 Introduction and basic concepts, e.g. normed function spaces and setting up the approximation task.Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 2 Introduction (Cont.): periodic functions, trigonometric polynomials, Weierstrass and Jackson theorems Lecture 2 Introduction (Cont.): periodic functions, trigonometric polynomials, Weierstrass and Jackson theoremsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Unit 02: Interpolation
Unit 02: Interpolation
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PageLecture 3: Interpolation Lecture 3: InterpolationScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 4: Optimality and Interpolation Lecture 4: Optimality and InterpolationScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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AssignmentAssignment 1 Assignment 1Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Unit 03: Best Approximations
Unit 03: Best Approximations
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PageLecture 5: Existence of best approximations Lecture 5: Existence of best approximationsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Unit 04: Characterization of Best Approximations
Unit 04: Characterization of Best Approximations
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PageLecture 6: Characterization Lecture 6: CharacterizationScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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AssignmentAssignment 2 Assignment 2Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Unit 05: Best Approximations in Euclidean Spaces
Unit 05: Best Approximations in Euclidean Spaces
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PageLecture 7: Finite dimensional subspaces, Gramian and Projections Lecture 7: Finite dimensional subspaces, Gramian and ProjectionsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 8: Orthogonal Polynomials and Chebychev Sums Lecture 8: Orthogonal Polynomials and Chebychev SumsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 9: Fast Fourier Transformation (FFT) Lecture 9: Fast Fourier Transformation (FFT)Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 10: Best approximation of periodic functions by trigonometric polynomials Lecture 10: Best approximation of periodic functions by trigonometric polynomialsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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AssignmentAssignment 3 Assignment 3Score at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
Unit 06: Chebychev Approximation (max-norm)
Unit 06: Chebychev Approximation (max-norm)
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PageLecture 11: Best Tschebychev Approximation Lecture 11: Best Tschebychev ApproximationScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 12: Continuation + Remez Algorithm Lecture 12: Continuation + Remez AlgorithmScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 13: More on Remez and Approximation Operators Lecture 13: More on Remez and Approximation OperatorsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 14: Weierstrass Approximation Theorem for Algebraic Polynomials Lecture 14: Weierstrass Approximation Theorem for Algebraic PolynomialsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
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PageLecture 16: Weierstrass Theorem for Trigonometric Polynomials Lecture 16: Weierstrass Theorem for Trigonometric PolynomialsScore at least Must score at least to complete this module item Scored at least Module item has been completed by scoring at least Score at least % Must score at least % to complete this module item Scored at least % Module item has been completed by scoring at least % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark completed Must mark this module item done in order to complete Marked completed Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
