APPLIED MAPLE

By D. FAURO

Chapter 1 Introduction 1 What is a CAS ? 2 Numbers 2 Symbols 3 More about Maple 5 Maple: a tutorial 5 Help 6 Maple as a calculator 9 Maple as a programmable calculator 27 Chapter 2 Active filter design and analysis 39 Case I: analog low-pass filter design and analysis 40 Use of Laplace transform explained 41 Constituent relationships derived 41 Designing a 1-kHz Butterworth LPF 47 Bode magnitude and phase plots 49 Improvement on the 1-kHz Butterworth LPF 53 Butterworth LPF component sensitivity analysis 55 Unequal resistance values in the Butterworth LPF topology 57 Butterworth LPF test setup 60 Design iteration of LPFs for newer filtering requirements 64 Unit step response 68 Conclusion 70 Case II: comb filter analysis and design 71 Filter derivation and analysis 72 Separating a known signal from an interfering neighboring background design 81 Cascading comb filters 87 Conclusion 91 Chapter 3 Curve fitting 93 Introduction 93 Case study: Gaussian peak estimator filter example with regressive curve fitting 95 Starting the Maple regression session 96 Linear regression using a logarithmic representation of the Gaussian model 96 Problem data set for linear regression 111 Nonlinear regression: the Levenberg-Marquardt algorithm 115 General polynomial regression 121 High-order polynomial regression fit problems 126 Quick moral about curve fitting 131 Conclusion 132 Chapter 4 Mathematical models: working with differential equations 133 ODE tools: a tour 134 The dsolve function 134 The DEtools package 137 The difforms package 143 Series methods 144 Modeling dynamic systems 152 A simple shock absorber 152 A twin mass shock absorber 158 A nonlinear system 166 Chapter 5 Continuous control application theory 173 Linear control system analysis 173 Frequency-domain approach 175 Partial fraction expansion 179 Time-domain approach 194 Time-invariant versus time-variant systems 194 Analysis of a time-invariant system: fundamentals 195 The state transition matrix 200 Conclusion 210 Chapter 6 Discrete control applications 213 The pulse transfer function 215 Transforming continuous signals 216 Calculating the time response 234 State space equations and their canonical forms 242 Transfer function to state space (the controllable canonical form) 242 Observable canonical form 247 Chapter 7 Discrete data processing 249 Maple plots 249 The plot structure 250 Image conversion 252 Togreyscale 260 Normalize 263 Tofalsecolor 269 Conclusion 272 Linear filters 273 Differencing 273 Moving average 276 Moving median 282 Exponential filtering 288 Conclusion 296 Chapter 8 Switching topologies 301 Steady-state method 302 Pulse width modulator driver 302 Switching power supply 316 Fourier method 330