Muutke küpsiste eelistusi

Calculus for Cognitive Scientists: Derivatives, Integrals and Models 1st ed. 2016 [Kõva köide]

  • Formaat: Hardback, 507 pages, kõrgus x laius: 235x155 mm, kaal: 1212 g, 105 Illustrations, color; XXXI, 507 p. 105 illus. in color., 1 Hardback
  • Sari: Cognitive Science and Technology
  • Ilmumisaeg: 11-Feb-2016
  • Kirjastus: Springer Verlag, Singapore
  • ISBN-10: 9812878726
  • ISBN-13: 9789812878724
Teised raamatud teemal:
  • Kõva köide
  • Hind: 141,35 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Tavahind: 166,29 €
  • Säästad 15%
  • Raamatu kohalejõudmiseks kirjastusest kulub orienteeruvalt 2-4 nädalat
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Tellimisaeg 2-4 nädalat
  • Lisa soovinimekirja
Calculus for Cognitive Scientists: Derivatives, Integrals and Models 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 507 pages, kõrgus x laius: 235x155 mm, kaal: 1212 g, 105 Illustrations, color; XXXI, 507 p. 105 illus. in color., 1 Hardback
  • Sari: Cognitive Science and Technology
  • Ilmumisaeg: 11-Feb-2016
  • Kirjastus: Springer Verlag, Singapore
  • ISBN-10: 9812878726
  • ISBN-13: 9789812878724
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789812878724.html
Märksõnad:
This book provides a self-study program on how mathematics, computer science and science can be usefully and seamlessly intertwined. Learning to use ideas from mathematics and computation is essential for understanding approaches to cognitive and biological science. As such the book covers calculus on one variable and two variables and works through a number of interesting first-order ODE models. It clearly uses MatLab in computational exercises where the models cannot be solved by hand, and also helps readers to understand that approximations cause errors – a fact that must always be kept in mind.

Arvustused

The introductory remarks in this book address the concern that many presentations of mathematics focus so heavily on traditional content that the usefulness of mathematics in other fields can be overlooked. the approach is both demanding and thorough, but the brief exercise sets remain focused on providing opportunities for straightforward practice of the principles at hand. Summing Up: Recommended. Lower- and upper-division undergraduates. (N. W. Schillow, Choice, Vol. 54 (4), December, 2016)

Part I Introduction
1 Introductory Remarks
3(22)
1.1 Our Design Philosophy
5(2)
1.2 Insights from Other Fields
7(2)
1.3 How Should You Study?
9(3)
1.4 Code
12(1)
1.5 Some Glimpses of Modeling
13(5)
1.5.1 West Nile Virus Models
14(1)
1.5.2 Simple Brain Models
15(2)
1.5.3 A Cancer Model
17(1)
1.6 A Roadmap to the Text
18(4)
1.7 Final Thoughts
22(3)
References
22(3)
Part II Using One Variable
2 Viability Selection
25(36)
2.1 A Basic Evolutionary Model
25(3)
2.1.1 Examples
27(1)
2.1.2 Homework
28(1)
2.2 The Next Generation
28(3)
2.2.1 Examples
30(1)
2.2.2 Homework
30(1)
2.3 A Difference Equation
31(2)
2.3.1 Examples
32(1)
2.3.2 Homework
33(1)
2.4 The Functional Form of the Frequency
33(6)
2.4.1 Examples
35(1)
2.4.2 Homework
36(1)
2.4.3 Biology and the Model
37(2)
2.5 A Gentle Introduction to MatLab
39(12)
2.5.1 Matlab Vectors
40(3)
2.5.2 Graphing a Function
43(2)
2.5.3 A Simple Virus Infection Model
45(6)
2.6 Long Term Consequences
51(1)
2.7 The Domestication of Wheat
52(9)
2.7.1 Project
58(2)
References
60(1)
3 Limits and Basic Smoothness
61(18)
3.1 Limits
64(15)
3.1.1 The Humble Square Root
64(2)
3.1.2 A Cool Polynomial Trick
66(3)
3.1.3 Change and More Change!
69(2)
3.1.4 How Many Do We Have?
71(5)
3.1.5 This Function Is Smooth!
76(3)
4 Continuity and Derivatives
79(22)
4.1 Continuity
79(6)
4.1.1 Example
82(2)
4.1.2 Homework
84(1)
4.2 Differentiability
85(4)
4.2.1 Example
87(1)
4.2.2 Homework
88(1)
4.3 Simple Derivatives
89(4)
4.3.1 Examples
92(1)
4.3.2 Homework
92(1)
4.4 The Quotient Rule
93(4)
4.4.1 Examples
95(1)
4.4.2 Homework
96(1)
4.5 Chain Rule
97(4)
4.5.1 Examples
99(1)
4.5.2 Homework
99(2)
5 Sin, Cos and All That
101(12)
5.1 Sin, Cos and All That!
101(5)
5.1.1 The Sin and Cos Functions
101(5)
5.2 A New Power Rule
106(2)
5.2.1 Examples
107(1)
5.2.2 Homework
107(1)
5.3 Derivatives of Complicated Things
108(5)
6 Antiderivatives
113(8)
6.1 Simple Integer Power Antiderivatives
113(3)
6.1.1 Examples
115(1)
6.1.2 Homework
116(1)
6.2 Simple Fractional Power Antiderivatives
116(3)
6.2.1 Examples
118(1)
6.2.2 Homework
118(1)
6.3 Simple Trigonometric Function Antiderivatives
119(2)
6.3.1 Examples
119(1)
6.3.2 Homework
120(1)
7 Substitutions
121(8)
7.1 Simple Substitution Polynomials
121(4)
7.2 Substitution for Polynomials Quick and Dirty
125(2)
7.2.1 Homework
126(1)
7.3 Sin's and Cos's
127(2)
7.3.1 Examples
127(1)
7.3.2 Homework
128(1)
8 Riemann Integration
129(36)
8.1 Riemann Sums
129(5)
8.1.1 Examples
133(1)
8.1.2 Homework
133(1)
8.2 Riemann Sums in MatLab
134(3)
8.2.1 Homework
135(2)
8.3 Graphing Riemann Sums
137(11)
8.3.1 Automating Riemann Sums
141(4)
8.3.2 Uniform Partition Riemann Sums
145(3)
8.4 Riemann Integrals
148(4)
8.4.1 The Riemann Integral as a Limit
149(1)
8.4.2 Properties
150(2)
8.5 The Fundamental Theorem of Calculus
152(3)
8.6 The Cauchy Fundamental Theorem of Calculus
155(3)
8.6.1 Examples
157(1)
8.6.2 Homework
158(1)
8.7 Riemann Integration with Substitution
158(2)
8.7.1 Homework
159(1)
8.8 Integration with Jumps
160(5)
8.8.1 Removable Discontinuity
160(2)
8.8.2 Jump Discontinuity
162(1)
8.8.3 Homework
163(2)
9 The Logarithm and Its Inverse
165(14)
9.1 The Natural Logarithm Function
165(2)
9.2 Logarithm Functions
167(4)
9.2.1 Worked Out Examples: Derivatives
168(1)
9.2.2 Homework: Derivatives
169(1)
9.2.3 Worked Out Examples: Integrals
170(1)
9.2.4 Homework: Integrals
171(1)
9.3 The Exponential Function
171(2)
9.4 Exponential Functions
173(4)
9.4.1 Worked Out Examples: Derivatives
173(1)
9.4.2 Homework: Exponential Derivatives
174(1)
9.4.3 Worked Out Examples: Exponential Integrals
175(1)
9.4.4 Homework: Exponential Integrals
176(1)
9.5 Our Antiderivatives So Far
177(2)
10 Exponential and Logarithm Function Properties
179(26)
10.1 Positive Integer Powers of e
179(3)
10.1.1 Homework
181(1)
10.2 Negative Integer Powers of e
182(3)
10.2.1 Homework
184(1)
10.3 Adding Natural Logarithms
185(6)
10.3.1 Adding Logarithms: Both Logarithms are Bigger Than 1
185(3)
10.3.2 Adding Logarithms: One Logarithm Less Than 1 and One Bigger Than 1
188(2)
10.3.3 Generalizing These Results
190(1)
10.3.4 Doing Subtracts in General
190(1)
10.4 Fractional Powers
191(2)
10.5 The Logarithm Function Properties
193(2)
10.5.1 Homework
195(1)
10.6 The Exponential Function Properties
195(10)
10.6.1 Properties of the Exponential Function
198(6)
10.6.2 Homework
204(1)
11 Simple Rate Equations
205(24)
11.1 Solving a Simple Rate Problem: Indefinite Approach
209(5)
11.1.1 Resolution of the Absolute Value
211(1)
11.1.2 Examples
211(2)
11.1.3 Homework
213(1)
11.2 Solving a Simple Rate Problem: Definite Approach
214(4)
11.2.1 Examples
215(2)
11.2.2 Homework
217(1)
11.3 The Half Life in Exponential Decay Problems
218(4)
11.4 The Carbon Dating Problem
222(2)
11.4.1 A Simple Dating Problem
223(1)
11.4.2 Homework
223(1)
11.4.3 Further Caveats
224(1)
11.5 Simple Rate Problems with Jumps
224(5)
11.5.1 Homework
227(1)
References
227(2)
12 Simple Protein Models
229(28)
12.1 The Integrating Factor Approach
229(3)
12.1.1 Examples
230(2)
12.1.2 Homework
232(1)
12.2 The Integrating Factor Approach with a Constant on the Right
232(3)
12.2.1 Homework
235(1)
12.3 Protein Synthesis
235(9)
12.3.1 The Underlying Biology
237(3)
12.3.2 Worked Out Examples
240(3)
12.3.3 Homework
243(1)
12.4 The Response Time in Protein Synthesis Problems
244(3)
12.4.1 Homework
246(1)
12.5 Signal On and Off Scenarios
247(3)
12.5.1 Homework
248(2)
12.6 Transcription Error Rates
250(7)
12.6.1 A First Attempt to Explain the Error Rate
251(2)
12.6.2 The Second Attempt: Kinetic Proofreading
253(4)
13 Logistics Models
257(22)
13.1 The Model
257(9)
13.1.1 An Integration Side Trip: Partial Fraction Decompositions
258(2)
13.1.2 Examples
260(6)
13.2 The General Solution Method
266(8)
13.2.1 A Streamlined Solution
272(2)
13.3 Solving a Logistics Model on Paper
274(5)
13.3.1 Homework
274(3)
Reference
277(2)
14 Function Approximation
279(22)
14.1 Taylor Polynomials
279(3)
14.1.1 Fundamental Tools
280(2)
14.2 The Zeroth Order Taylor Polynomial
282(2)
14.2.1 Examples
283(1)
14.2.2 Homework
283(1)
14.3 The First Order Taylor Polynomial
284(5)
14.3.1 Examples
286(3)
14.3.2 Homework
289(1)
14.4 Quadratic Approximations
289(6)
14.4.1 Examples
290(2)
14.4.2 Homework
292(3)
14.5 Exponential Approximations
295(6)
14.5.1 Example
297(1)
14.5.2 Homework
298(3)
15 Extreme Values
301(14)
15.1 Extremal Values
301(2)
15.1.1 Example
302(1)
15.1.2 Homework
303(1)
15.2 The Newton Cooling Project
303(12)
15.2.1 Homework
305(1)
15.2.2 Your Newton Cooling Project
305(3)
15.2.3 Your Report
308(1)
15.2.4 Some Sample Calculations
309(6)
16 Numerical Methods Order One ODEs
315(32)
16.1 Euler's Method
315(25)
16.1.1 Approximating the Solution to First Order Differential Equations
317(4)
16.1.2 Euler Approximates Again
321(3)
16.1.3 Euler Approximates the Last Time
324(5)
16.1.4 Euler's Algorithm
329(2)
16.1.5 Adding Time to Euler's Method
331(1)
16.1.6 Simple MatLab Experiments
332(3)
16.1.7 Matlab Euler Functions
335(1)
16.1.8 Homework
336(1)
16.1.9 The True Versus the Euler Approximate Solution
337(3)
16.1.10 Homework
340(1)
16.2 Runge-Kutta Methods
340(7)
16.2.1 The MatLab Implementation
341(4)
16.2.2 Homework
345(1)
References
345(2)
17 Advanced Protein Models
347(24)
17.1 Binding Time Estimates
347(2)
17.2 The Bound Fraction
349(3)
17.2.1 Example
352(1)
17.2.2 Homework
352(1)
17.3 Transcription Regulation
352(7)
17.3.1 Example
356(3)
17.3.2 Homework
359(1)
17.4 Simple Regulations
359(4)
17.4.1 Example
362(1)
17.4.2 Homework
362(1)
17.5 Feedback Loops
363(8)
17.5.1 Examples
366(1)
17.5.2 Homework
367(1)
References
368(3)
Part III Using Multiple Variables
18 Matrices and Vectors
371(14)
18.1 Matrices
371(4)
18.1.1 The Zero Matrices
372(1)
18.1.2 Square Matrices
373(1)
18.1.3 The Identity Matrices
373(1)
18.1.4 The Transpose of a Matrix
374(1)
18.1.5 Homework
375(1)
18.2 Operations on Matrices
375(3)
18.2.1 Homework
377(1)
18.3 Vectors
378(1)
18.4 Operations on Vectors
379(1)
18.5 The Magnitude of a Vector
379(4)
18.5.1 Homework
382(1)
18.5.2 Some Matrix--Vector Calculations
382(1)
18.6 The Inner Product of Two Column Vectors
383(2)
18.6.1 Homework
384(1)
19 A Cancer Model
385(14)
19.1 Two Allele TSG Models
387(4)
19.2 Model Assumptions
391(1)
19.3 Solving the Top Pathway Exactly
392(2)
19.3.1 The X0 -- X1 Subsystem
392(1)
19.3.2 Solving for X2
393(1)
19.4 Approximation of the Top Pathway
394(5)
19.4.1 Approximating X0
394(1)
19.4.2 Approximating X1
395(1)
19.4.3 Approximating X2
396(2)
References
398(1)
20 First Order Multivariable Calculus
399(30)
20.1 Functions of Two Variables
399(7)
20.1.1 Drawing an Annotated Surface
400(6)
20.1.2 Homework
406(1)
20.2 Continuity
406(2)
20.3 Partial Derivatives
408(8)
20.3.1 Homework
414(2)
20.4 Tangent Planes
416(5)
20.4.1 The Tangent Plane to a Surface
416(2)
20.4.2 Examples
418(1)
20.4.3 Homework
419(1)
20.4.4 Computational Results
419(2)
20.4.5 Homework
421(1)
20.5 Derivatives in Two Dimensions!
421(4)
20.6 The Chain Rule
425(4)
20.6.1 Examples
426(1)
20.6.2 Homework
427(2)
21 Second Order Multivariable Calculus
429(24)
21.1 Tangent Plane Approximation Error
429(1)
21.2 Second Order Error Estimates
430(2)
21.2.1 Examples
431(1)
21.2.2 Homework
432(1)
21.3 Hessian Approximations
432(5)
21.3.1 Ugly Error Estimates!
433(3)
21.3.2 Homework
436(1)
21.4 Extrema Ideas
437(5)
21.4.1 Examples
440(2)
21.4.2 Homework
442(1)
21.5 A Regression to Regression
442(7)
21.5.1 Example
447(1)
21.5.2 Homework
447(2)
21.6 Regression and Covariances
449(4)
21.6.1 Example
450(1)
21.6.2 Homework
451(1)
Reference
452(1)
22 Hamilton's Rule in Evolutionary Biology
453(26)
22.1 How Do We Define Altruism
454(7)
22.1.1 A Shared Common Good Model
454(3)
22.1.2 The Abstract Version
457(4)
22.2 Hamilton's Rule
461(3)
22.2.1 Example
464(1)
22.2.2 Homework
464(1)
22.3 Gene Survival
464(3)
22.3.1 Back to Covariance!
466(1)
22.4 Altruism Spread Under Additive Fitness
467(2)
22.4.1 Example
469(1)
22.4.2 Homework
469(1)
22.5 Altruism Spread Under Additive Genetics
469(4)
22.5.1 Examples
472(1)
22.5.2 Homework
473(1)
22.6 The Optimization Approach
473(6)
22.6.1 Example
474(1)
22.6.2 Homework
474(1)
References
475(4)
Part IV Summing It All Up
23 Final Thoughts
479(4)
References
480(3)
Part V Advise to the Beginner
24 Background Reading
483(4)
References
484(3)
Glossary 487(12)
Index 499
Dr. James Peterson is an Associate Professor in Mathematical Sciences and Biological Sciences at Clemson University, USA. His formal training is in mathematics but he has worked as an aerospace engineer and a software engineer also. He enjoys working on very hard problems that require multiple disciplines to make sense out of and he reads, studies and plays in cutting edge areas a lot as part of his interests.