2012-03-01 central difference formulas

8/16/2019 2012-03-01 Central Difference Formulas

1/54

3 5 9

0.5

0 0 0.227837

1 0 -0.124966 -0.188736

2 0 -0.149636 0.066519 0.092643

3 0 0.008071 0.165028 0.20705

4 0 0.18042 0.011405 0.021301 0.036824

5 0 0.030881 -0.201597 -0.264866 -0.307299

6 0 -0.222775 -0.034989 -0.034785 -0.018356

7 0 -0.039097 0.130402 0.155918 0.151721

8 0 0.038028 0.142693 0.185856 0.222478

9 0 0.24629 -0.103993 -0.154061 -0.192414

10 0 -0.169958 -0.050272 -0.070583 -0.08136

11 0 0.145746 0.125317 0.170667 0.212645

12 0 0.080675 0.0288 0.004733 -0.008002

13 0 0.203346 0.076683 0.02624 -0.010112

14 0 0.234041 0.427226 0.475263 0.4892

15 1 1.057798 0.489549 0.577196 0.63768

16 1 1.213139 0.025991 -0.038869 -0.100985

17 1 1.10978 -0.048403 -0.076395 -0.071013

18 1 1.116333 0.045152 0.05929 0.064066

19 1 1.200084 0.053877 0.081418 0.110678

20 1 1.224086 -0.102646 -0.147042 -0.194472

21 1 0.994791 0.007208 0.033399 0.055012

22 1 1.238502 -0.04008 -0.014504 0.025858

23 1 0.914631 -0.240824 -0.328747 -0.41663

24 1 0.756854 0.085971 0.144972 0.215419

25 1 1.086572 0.058757 0.063128 0.044324

26 1 0.874367 0.005313 -0.005314 -0.011808

27 1 1.097199 0.015631 0.017015 0.022193

28 1 0.905629 0.017649 0.019931 0.009348

29 1 1.132496 0.005971 0.028908

30 1 0.917571 -0.143328 -0.20387

31 1 0.845841 0.070628

32 1 1.058828

sinc function

-20 0.045647

-19.95 0.044682

-19.9 0.0436

-19.85 0.042404

-19.8 0.041095

-19.75 0.039676

-19.7 0.038151

-19.65 0.036522

-19.6 0.034794

2 4 6 8 10 12

-1

-0.5

0

0.5

1

1.5

2

0 5 10

-1

-0.5

0

0.5

1

1.5

2

0.2

0.4

0.6

0.8

1

1.2


2/54

-19.55 0.03297

-19.5 0.031053

-19.45 0.029049

-19.4 0.026962

-19.35 0.024797

-19.3 0.022558

-19.25 0.020251

-19.2 0.017881

-19.15 0.015454

-19.1 0.012976

-19.05 0.010452

-19 0.007888

-18.95 0.005292

-18.9 0.002668

-18.85 2.36E-005

-18.8 -0.002635

-18.75 -0.005301

-18.7 -0.007968

-18.65 -0.010629

-18.6 -0.013278

-18.55 -0.015908

-18.5 -0.018512

-18.45 -0.021085

-18.4 -0.023618

-18.35 -0.026105

-18.3 -0.028541

-18.25 -0.030919

-18.2 -0.033233

-18.15 -0.035475

-18.1 -0.037642

-18.05 -0.039726

-18 -0.041722

-17.95 -0.043624

-17.9 -0.045428

-17.85 -0.047128

-17.8 -0.048719

-17.75 -0.050198

-17.7 -0.051558

-17.65 -0.052798

-17.6 -0.053912

-17.55 -0.054897

-17.5 -0.05575

-17.45 -0.056468

-17.4 -0.057049

-17.35 -0.057491

-17.3 -0.05779

-17.25 -0.057947

-17.2 -0.057959

-25 -20 -15 -10 -5 0 5 10 15

-0.4

-0.2

0


3/54

-17.15 -0.057826

-17.1 -0.057548

-17.05 -0.057123

-17 -0.056553

-16.95 -0.055837

-16.9 -0.054978

-16.85 -0.053975

-16.8 -0.052831

-16.75 -0.051548

-16.7 -0.050128

-16.65 -0.048574

-16.6 -0.046889

-16.55 -0.045076

-16.5 -0.043139

-16.45 -0.041081

-16.4 -0.038909

-16.35 -0.036626

-16.3 -0.034236

-16.25 -0.031747

-16.2 -0.029162

-16.15 -0.026488

-16.1 -0.023731

-16.05 -0.020898

-16 -0.017994

-15.95 -0.015027

-15.9 -0.012004

-15.85 -0.008931

-15.8 -0.005817

-15.75 -0.002668

-15.7 0.000507

-15.65 0.003702

-15.6 0.006907

-15.55 0.010116

-15.5 0.01332

-15.45 0.016512

-15.4 0.019683

-15.35 0.022825

-15.3 0.025931

-15.25 0.028992

-15.2 0.032

-15.15 0.034948

-15.1 0.037828

-15.05 0.040632

-15 0.043353

-14.95 0.045983

-14.9 0.048516

-14.85 0.050944

-14.8 0.05326


4/54

-14.75 0.055459

-14.7 0.057534

-14.65 0.059478

-14.6 0.061287

-14.55 0.062954

-14.5 0.064476

-14.45 0.065845

-14.4 0.06706

-14.35 0.068114

-14.3 0.069005

-14.25 0.069729

-14.2 0.070284

-14.15 0.070666

-14.1 0.070873

-14.05 0.070904

-14 0.070758

-13.95 0.070433

-13.9 0.069929

-13.85 0.069245

-13.8 0.068384

-13.75 0.067344

-13.7 0.066128

-13.65 0.064737

-13.6 0.063174

-13.55 0.06144

-13.5 0.05954

-13.45 0.057476

-13.4 0.055252

-13.35 0.052873

-13.3 0.050344

-13.25 0.047669

-13.2 0.044854

-13.15 0.041905

-13.1 0.038829

-13.05 0.035632

-13 0.032321

-12.95 0.028903

-12.9 0.025386

-12.85 0.021778

-12.8 0.018087

-12.75 0.014322

-12.7 0.010491

-12.65 0.006603

-12.6 0.002668

-12.55 -0.001304

-12.5 -0.005306

-12.45 -0.009326

-12.4 -0.013355


5/54

-12.35 -0.017384

-12.3 -0.021401

-12.25 -0.025397

-12.2 -0.029363

-12.15 -0.033288

-12.1 -0.037161

-12.05 -0.040973

-12 -0.044714

-11.95 -0.048375

-11.9 -0.051944

-11.85 -0.055414

-11.8 -0.058773

-11.75 -0.062014

-11.7 -0.065127

-11.65 -0.068103

-11.6 -0.070933

-11.55 -0.073611

-11.5 -0.076126

-11.45 -0.078473

-11.4 -0.080643

-11.35 -0.08263

-11.3 -0.084426

-11.25 -0.086027

-11.2 -0.087427

-11.15 -0.088619

-11.1 -0.089599

-11.05 -0.090364

-11 -0.090908

-10.95 -0.091229

-10.9 -0.091324

-10.85 -0.091191

-10.8 -0.090827

-10.75 -0.090232

-10.7 -0.089405

-10.65 -0.088346

-10.6 -0.087054

-10.55 -0.085532

-10.5 -0.083781

-10.45 -0.081802

-10.4 -0.079599

-10.35 -0.077174

-10.3 -0.074533

-10.25 -0.071678

-10.2 -0.068615

-10.15 -0.06535

-10.1 -0.061888

-10.05 -0.058237

-10 -0.054402


6/54

-9.95 -0.050392

-9.9 -0.046216

-9.85 -0.041881

-9.8 -0.037396

-9.75 -0.032771

-9.7 -0.028017

-9.65 -0.023142

-9.6 -0.018159

-9.55 -0.013078

-9.5 -0.007911

-9.45 -0.002669

-9.4 0.002636

-9.35 0.00799

-9.3 0.013382

-9.25 0.018799

-9.2 0.024227

-9.15 0.029654

-9.1 0.035066

-9.05 0.040449

-9 0.045791

-8.95 0.051077

-8.9 0.056294

-8.85 0.061429

-8.8 0.066468

-8.75 0.071397

-8.7 0.076203

-8.65 0.080874

-8.6 0.085395

-8.55 0.089755

-8.5 0.09394

-8.45 0.097938

-8.4 0.101738

-8.35 0.105327

-8.3 0.108695

-8.25 0.111831

-8.2 0.114723

-8.15 0.117363

-8.1 0.119739

-8.05 0.121845

-8 0.12367

-7.95 0.125207

-7.9 0.126448

-7.85 0.127388

-7.8 0.128018

-7.75 0.128335

-7.7 0.128334

-7.65 0.128009

-7.6 0.127358


7/54

-7.55 0.126378

-7.5 0.125067

-7.45 0.123423

-7.4 0.121447

-7.35 0.119138

-7.3 0.116498

-7.25 0.113528

-7.2 0.110232

-7.15 0.106611

-7.1 0.102672

-7.05 0.098418

-7 0.093855

-6.95 0.088991

-6.9 0.083832

-6.85 0.078387

-6.8 0.072664

-6.75 0.066673

-6.7 0.060425

-6.65 0.053931

-6.6 0.047203

-6.55 0.040253

-6.5 0.033095

-6.45 0.025743

-6.4 0.018211

-6.35 0.010514

-6.3 0.002669

-6.25 -0.005309

-6.2 -0.013402

-6.15 -0.021592

-6.1 -0.029863

-6.05 -0.038195

-6 -0.046569

-5.95 -0.054967

-5.9 -0.063369

-5.85 -0.071755

-5.8 -0.080104

-5.75 -0.088396

-5.7 -0.096611

-5.65 -0.104728

-5.6 -0.112726

-5.55 -0.120584

-5.5 -0.12828

-5.45 -0.135794

-5.4 -0.143105

-5.35 -0.150191

-5.3 -0.157032

-5.25 -0.163607

-5.2 -0.169895


8/54

-5.15 -0.175877

-5.1 -0.181532

-5.05 -0.186841

-5 -0.191785

-4.95 -0.196344

-4.9 -0.200501

-4.85 -0.204236

-4.8 -0.207534

-4.75 -0.210377

-4.7 -0.21275

-4.65 -0.214635

-4.6 -0.21602

-4.55 -0.216889

-4.5 -0.217229

-4.45 -0.217028

-4.4 -0.216273

-4.35 -0.214955

-4.3 -0.213062

-4.25 -0.210586

-4.2 -0.207518

-4.15 -0.203851

-4.1 -0.19958

-4.05 -0.194698

-4 -0.189201

-3.95 -0.183086

-3.9 -0.17635

-3.85 -0.168994

-3.8 -0.161015

-3.75 -0.152416

-3.7 -0.143199

-3.65 -0.133366

-3.6 -0.122922

-3.55 -0.111873

-3.5 -0.100224

-3.45 -0.087983

-3.4 -0.075159

-3.35 -0.061762

-3.3 -0.047802

-3.25 -0.033291

-3.2 -0.018242

-3.15 -0.002669

-3.1 0.013413

-3.05 0.029988

-3 0.04704

-2.95 0.06455

-2.9 0.0825

-2.85 0.100869

-2.8 0.119639


9/54

-2.75 0.138786

-2.7 0.158289

-2.65 0.178125

-2.6 0.19827

-2.55 0.218699

-2.5 0.239389

-2.45 0.260312

-2.4 0.281443

-2.35 0.302755

-2.3 0.32422

-2.25 0.34581

-2.2 0.367498

-2.15 0.389255

-2.1 0.411052

-2.05 0.43286

-2 0.454649

-1.95 0.47639

-1.9 0.498053

-1.85 0.519608

-1.8 0.541026

-1.75 0.562278

-1.7 0.583332

-1.65 0.604161

-1.6 0.624734

-1.55 0.645022

-1.5 0.664997

-1.45 0.68463

-1.4 0.703893

-1.35 0.722758

-1.3 0.741199

-1.25 0.759188

-1.2 0.776699

-1.15 0.793708

-1.1 0.810189

-1.05 0.826117

-1 0.841471

-0.95 0.856227

-0.9 0.870363

-0.85 0.883859

-0.8 0.896695

-0.75 0.908852

-0.7 0.920311

-0.65 0.931056

-0.6 0.941071

-0.55 0.95034

-0.5 0.958851

-0.45 0.96659

-0.4 0.973546


10/54

-0.35 0.979708

-0.3 0.985067

-0.25 0.989616

-0.2 0.993347

-0.15 0.996254

-0.1 0.998334

-0.05 0.999583

2.98E-013 1

0.05 0.999583

0.1 0.998334

0.15 0.996254

0.2 0.993347

0.25 0.989616

0.3 0.985067

0.35 0.979708

0.4 0.973546

0.45 0.96659

0.5 0.958851

0.55 0.95034

0.6 0.941071

0.65 0.931056

0.7 0.920311

0.75 0.908852

0.8 0.896695

0.85 0.883859

0.9 0.870363

0.95 0.856227

1 0.841471

1.05 0.826117

1.1 0.810189

1.15 0.793708

1.2 0.776699

1.25 0.759188

1.3 0.741199

1.35 0.722758

1.4 0.703893

1.45 0.68463

1.5 0.664997

1.55 0.645022

1.6 0.624734

1.65 0.604161

1.7 0.583332

1.75 0.562278

1.8 0.541026

1.85 0.519608

1.9 0.498053

1.95 0.47639

2 0.454649


11/54

2.05 0.43286

2.1 0.411052

2.15 0.389255

2.2 0.367498

2.25 0.34581

2.3 0.32422

2.35 0.302755

2.4 0.281443

2.45 0.260312

2.5 0.239389

2.55 0.218699

2.6 0.19827

2.65 0.178125

2.7 0.158289

2.75 0.138786

2.8 0.119639

2.85 0.100869

2.9 0.0825

2.95 0.06455

3 0.04704

3.05 0.029988

3.1 0.013413

3.15 -0.002669

3.2 -0.018242

3.25 -0.033291

3.3 -0.047802

3.35 -0.061762

3.4 -0.075159

3.45 -0.087983

3.5 -0.100224

3.55 -0.111873

3.6 -0.122922

3.65 -0.133366

3.7 -0.143199

3.75 -0.152416

3.8 -0.161015

3.85 -0.168994

3.9 -0.17635

3.95 -0.183086

4 -0.189201

4.05 -0.194698

4.1 -0.19958

4.15 -0.203851

4.2 -0.207518

4.25 -0.210586

4.3 -0.213062

4.35 -0.214955

4.4 -0.216273


12/54

4.45 -0.217028

4.5 -0.217229

4.55 -0.216889

4.6 -0.21602

4.65 -0.214635

4.7 -0.21275

4.75 -0.210377

4.8 -0.207534

4.85 -0.204236

4.9 -0.200501

4.95 -0.196344

5 -0.191785

5.05 -0.186841

5.1 -0.181532

5.15 -0.175877

5.2 -0.169895

5.25 -0.163607

5.3 -0.157032

5.35 -0.150191

5.4 -0.143105

5.45 -0.135794

5.5 -0.12828

5.55 -0.120584

5.6 -0.112726

5.65 -0.104728

5.7 -0.096611

5.75 -0.088396

5.8 -0.080104

5.85 -0.071755

5.9 -0.063369

5.95 -0.054967

6 -0.046569

6.05 -0.038195

6.1 -0.029863

6.15 -0.021592

6.2 -0.013402

6.25 -0.005309

6.3 0.002669

6.35 0.010514

6.4 0.018211

6.45 0.025743

6.5 0.033095

6.55 0.040253

6.6 0.047203

6.65 0.053931

6.7 0.060425

6.75 0.066673

6.8 0.072664


13/54

6.85 0.078387

6.9 0.083832

6.95 0.088991

7 0.093855

7.05 0.098418

7.1 0.102672

7.15 0.106611

7.2 0.110232

7.25 0.113528

7.3 0.116498

7.35 0.119138

7.4 0.121447

7.45 0.123423

7.5 0.125067

7.55 0.126378

7.6 0.127358

7.65 0.128009

7.7 0.128334

7.75 0.128335

7.8 0.128018

7.85 0.127388

7.9 0.126448

7.95 0.125207

8 0.12367

8.05 0.121845

8.1 0.119739

8.15 0.117363

8.2 0.114723

8.25 0.111831

8.3 0.108695

8.35 0.105327

8.4 0.101738

8.45 0.097938

8.5 0.09394

8.55 0.089755

8.6 0.085395

8.65 0.080874

8.7 0.076203

8.75 0.071397

8.8 0.066468

8.85 0.061429

8.9 0.056294

8.95 0.051077

9 0.045791

9.05 0.040449

9.1 0.035066

9.15 0.029654

9.2 0.024227


14/54

9.25 0.018799

9.3 0.013382

9.35 0.00799

9.4 0.002636

9.45 -0.002669

9.5 -0.007911

9.55 -0.013078

9.6 -0.018159

9.65 -0.023142

9.7 -0.028017

9.75 -0.032771

9.8 -0.037396

9.85 -0.041881

9.9 -0.046216

9.95 -0.050392

10 -0.054402

10.05 -0.058237

10.1 -0.061888

10.15 -0.06535

10.2 -0.068615

10.25 -0.071678

10.3 -0.074533

10.35 -0.077174

10.4 -0.079599

10.45 -0.081802

10.5 -0.083781

10.55 -0.085532

10.6 -0.087054

10.65 -0.088346

10.7 -0.089405

10.75 -0.090232

10.8 -0.090827

10.85 -0.091191

10.9 -0.091324

10.95 -0.091229

11 -0.090908

11.05 -0.090364

11.1 -0.089599

11.15 -0.088619

11.2 -0.087427

11.25 -0.086027

11.3 -0.084426

11.35 -0.08263

11.4 -0.080643

11.45 -0.078473

11.5 -0.076126

11.55 -0.073611

11.6 -0.070933


15/54

11.65 -0.068103

11.7 -0.065127

11.75 -0.062014

11.8 -0.058773

11.85 -0.055414

11.9 -0.051944

11.95 -0.048375

12 -0.044714

12.05 -0.040973

12.1 -0.037161

12.15 -0.033288

12.2 -0.029363

12.25 -0.025397

12.3 -0.021401

12.35 -0.017384

12.4 -0.013355

12.45 -0.009326

12.5 -0.005306

12.55 -0.001304

12.6 0.002668

12.65 0.006603

12.7 0.010491

12.75 0.014322

12.8 0.018087

12.85 0.021778

12.9 0.025386

12.95 0.028903

13 0.032321

13.05 0.035632

13.1 0.038829

13.15 0.041905

13.2 0.044854

13.25 0.047669

13.3 0.050344

13.35 0.052873

13.4 0.055252

13.45 0.057476

13.5 0.05954

13.55 0.06144

13.6 0.063174

13.65 0.064737

13.7 0.066128

13.75 0.067344

13.8 0.068384

13.85 0.069245

13.9 0.069929

13.95 0.070433

14 0.070758


16/54

14.05 0.070904

14.1 0.070873

14.15 0.070666

14.2 0.070284

14.25 0.069729

14.3 0.069005

14.35 0.068114

14.4 0.06706

14.45 0.065845

14.5 0.064476

14.55 0.062954

14.6 0.061287

14.65 0.059478

14.7 0.057534

14.75 0.055459

14.8 0.05326

14.85 0.050944

14.9 0.048516

14.95 0.045983

15 0.043353

15.05 0.040632

15.1 0.037828

15.15 0.034948

15.2 0.032

15.25 0.028992

15.3 0.025931

15.35 0.022825

15.4 0.019683

15.45 0.016512

15.5 0.01332

15.55 0.010116

15.6 0.006907

15.65 0.003702

15.7 0.000507

15.75 -0.002668

15.8 -0.005817

15.85 -0.008931

15.9 -0.012004

15.95 -0.015027

16 -0.017994

16.05 -0.020898

16.1 -0.023731

16.15 -0.026488

16.2 -0.029162

16.25 -0.031747

16.3 -0.034236

16.35 -0.036626

16.4 -0.038909


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16.45 -0.041081

16.5 -0.043139

16.55 -0.045076

16.6 -0.046889

16.65 -0.048574

16.7 -0.050128

16.75 -0.051548

16.8 -0.052831

16.85 -0.053975

16.9 -0.054978

16.95 -0.055837

17 -0.056553

17.05 -0.057123

17.1 -0.057548

17.15 -0.057826

17.2 -0.057959

17.25 -0.057947

17.3 -0.05779

17.35 -0.057491

17.4 -0.057049

17.45 -0.056468

17.5 -0.05575

17.55 -0.054897

17.6 -0.053912

17.65 -0.052798

17.7 -0.051558

17.75 -0.050198

17.8 -0.048719

17.85 -0.047128

17.9 -0.045428

17.95 -0.043624

18 -0.041722

18.05 -0.039726

18.1 -0.037642

18.15 -0.035475

18.2 -0.033233

18.25 -0.030919

18.3 -0.028541

18.35 -0.026105

18.4 -0.023618

18.45 -0.021085

18.5 -0.018512

18.55 -0.015908

18.6 -0.013278

18.65 -0.010629

18.7 -0.007968

18.75 -0.005301

18.8 -0.002635


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18.85 2.36E-005

18.9 0.002668

18.95 0.005292

19 0.007888

19.05 0.010452

19.1 0.012976

19.15 0.015454

19.2 0.017881

19.25 0.020251

19.3 0.022558

19.35 0.024797

19.4 0.026962

19.45 0.029049

19.5 0.031053

19.55 0.03297

19.6 0.034794

19.65 0.036522

19.7 0.038151

19.75 0.039676

19.8 0.041095

19.85 0.042404

19.9 0.0436

19.95 0.044682

20 0.045647


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!o"in# a"e$a#e

7 sample 11 sample 7+5 sampl

-9

-8

-7 -0.007167

-6 -0.0453

-5 -0.022015 0.002281 -0.006165

-4 0.034545 -0.005181 -0.0039

-3 0.009113 0.013513 0.007415

-2 0.004159 0.045602 0.026247

-1 0.011273 0.066145 0.041572

0 0.072147 0.145907 0.091119

1 0.111167 0.253385 0.169281

2 0.256848 0.374526 0.282584

3 0.39497 0.479565 0.411444

4 0.577789 0.585207 0.564482

5 0.716445 0.674097 0.717549

6 0.87636 0.779984 0.864727

7 1.02218 0.879325 0.980503

8 1.130859 0.955139 1.06002

1.156674 1.005458 1.097471

1.114029 1.082961 1.104907

1.063611 1.066285 1.081301

1.05936 1.055745 1.048906

1.012829 1.037186 1.022494

0.994702 1.038656 1.003135

0.981965 1.012973 0.984712

0.966821 0.978587 0.978137

0.967241 0.984408 0.974394

0.979954 0.972502

0.97599

14 16

Column C

Column D

Column E

Column G

15 20 25 30 35

Column


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20 25


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29/54


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31/54


32/54


33/54


34/54


35/54


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e

Column C

7 sample

11 sample

7+5 sample


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2012-03-01 central difference formulas

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