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MATHEMATICS FOR BIOMECHANICS |
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KAAP686 |
Discussion
Schedule |
Spring
2017 |
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Date |
Topic (subject to change) |
Reading1 |
Homework |
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Tue 2/07 |
Introduction. Calculus review 1. Derivatives, finding extremes. Example: maximum power from muscle. |
Chapter(s) on derivatives from any calculus textbook |
HW1 (due Tue 2/14) |
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Thu 2/09 |
Calculus review 1, continued |
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Tue 2/14 |
Intro to Signals; dB; sinusoids |
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Thu 2/16 |
No class (majority of students are at C.S.M. meeting) |
Parts 1, 2 of HW1 due. |
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Tue 2/21 |
Numerical Differentiation. HW1 presentations. |
Part 3 of HW 1 due. Start HW2. |
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Thu 2/23 |
HW1 presentations. Numerical Differentiation. |
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Tue 2/28 |
Continue Intro to Signals Sinusoidal signals |
fft_test1.m, fft_test1a.m, fft_test2.m |
HW2 due. Start HW3 (due Tue 3/07) |
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Thu 3/02 |
Frequency content of signals. Fourier series. Complex numbers (?) (skip maybe) |
fft_examples.xls dft_examples1.html dft_examples2.html |
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The schedule after 3/02 is not finalized. |
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Tue 3/07 |
Fourier series 2. Power spectrum analysis |
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Thu 3/09 |
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Tue 3/14 |
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Thu 3/16 |
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Tue 3/21 |
Calculus review 3: Vectors & motion in space. Add, subtract vectors. Segment axes. |
Introduction to vectors in any math book. |
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Thu 3/23 |
Calculus review 3, continued. |
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HW3 due. |
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Tue 4/04 |
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Thu 4/06 |
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Tue 4/11 |
Matrices, continued: Rotations in 2D. Rotations in 3D. |
Winter, sections 7.0, 7.1 |
HW4 (due 3/14) |
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Matrices, continued: Rotations in 3D. |
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Complex numbers, sinusoidal signals, Fourier series |
SSS ch.3 Winter sect. 2.5.2; Thomas Appendix A.4; SSS ch.1, SSS ch.2. fft_test1.m, fft_test1a.m, fft_test2.m |
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Thu 4/13 |
Fourier series 2 Power spectrum analysis |
fft_examples.xls dft_examples1.html dft_examples2.html |
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Tue 4/18 |
Filter design Guide |
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Thu 4/20 |
Analog filtering and filter comparisons |
Filter Design Guide, pp. 6 to end |
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Tue 4/25 |
Data processing: sampling signals; noise |
Winter 2.5.3, 2.5.4 |
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Thu 4/27 |
Data processing: smoothing and fitting; digital filtering |
Winter 2.5.5, 2.5.6 |
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Tue 5/02 |
Digital filtering example: Force from instrumented treadmill (low pass) |
Treadmill data files; pwr spectrum code; alternate pwr spectrum code; residual analysis code |
HW 5 due |
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Thu 5/04 |
Digital filtering example: Remove noise from ECG (band
stop) |
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Tue 5/09 |
Lab exercise |
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Thu 5/11 |
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Tue 5/16 Last Day |
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Topics to cover if time allows:
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EMG analysis |
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Matrix eigenvalues and eigenvectors |
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Journal article discussion |
Buchanan et al., Neuromusculoskeletal Modeling, J. Appl. Biomech 20: 367-395, 2004. Notes |
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Center of pressure analysis. |
\reserve\cop |
1. Winter: David A. Winter, Biomechanics and Motor Control of Human Movement, 4th ed., 2009.
SSS: W. M. Hartmann, Signals, Sound, and Sensation, 1997.