Applied Maple for Engineers and Scientists
| Date: 06 May 2011, 19:47
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Author shows how real-world engineering problems can be solved using MAPLE as the principal tool. Features practical examples and detailed explanations.
MAPLE is easy-to-use software that performs numerical and symbolic analysis to solve complex mathematical problems. A reference for engineers, scientists, and application developers, it shows you how to tap the full power of MAPLE in solving real-world engineering problems in circuit theory, control theory, curve fitting, mechanics and digital signal processing. The book includes more than 65 figure, 100 equatiions, and accompanying software that includes exercises, MAPLE features and MAPLE subroutines.
Contents
Chapter 1
Introduction
What is a CAS ?
Numbers
Symbols
More about Maple
Maple: a tutorial
Help
Maple as a calculator
Maple as a programmable calculator
Chapter 2
Active filter design and analysis
Case I: analog low-pass filter design and analysis
Use of Laplace transform explained
Constituent relationships derived
Designing a 1-kHz Butterworth LPF
Bode magnitude and phase plots
Improvement on the 1-kHz Butterworth LPF
Butterworth LPF component sensitivity analysis
Unequal resistance values in the Butterworth LPF topology
Butterworth LPF test setup
Design iteration of LPFs for newer filtering requirements
Unit step response
Conclusion
Case II: comb filter analysis and design
Filter derivation and analysis
Separating a known signal from an interfering neighboring background design
Cascading comb filters
Conclusion
Chapter 3
Curve fitting
Introduction
Case study: Gaussian peak estimator filter example with regressive curve fitting
Starting the Maple regression session
Linear regression using a logarithmic representation of the Gaussian model
Problem data set for linear regression
Nonlinear regression: the Levenberg-Marquardt algorithm
General polynomial regression
High-order polynomial regression fit problems
Quick moral about curve fitting
Conclusion
Chapter 4
Mathematical models: working with differential equations
ODE tools: a tour
The dsolve function
The DEtools package
The difforms package
Series methods
Modeling dynamic systems
A simple shock absorber
A twin mass shock absorber
A nonlinear system
Chapter 5
Continuous control application theory
Linear control system analysis
Frequency-domain approach
Partial fraction expansion
Time-domain approach
Time-invariant versus time-variant systems
Analysis of a time-invariant system: fundamentals
The state transition matrix
Conclusion
Chapter 6
Discrete control applications
The pulse transfer function
Transforming continuous signals
Calculating the time response
State space equations and their canonical forms
Applied Maple for Engineers and Scientists
Transfer function to state space (the controllable canonical form)
Observable canonical form
Chapter 7
Discrete data processing
Maple plots
The plot structure
Image conversion
Togreyscale
Normalize
Tofalsecolor
Conclusion
Linear filters
Differencing
Moving average
Moving median
Exponential filtering
Conclusion
Chapter 8
Switching topologies
Steady-state method
Pulse width modulator driver
Switching power supply
Fourier method
Appendix A
Appendix B
Glossary
About the authors
Index
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