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دانلود کتاب Calculus BLUE Multivariable Volume 2: Derivatives
دانلود کتاب Calculus BLUE Multivariable Volume 2: مشتقات
مشخصات کتاب
Calculus BLUE Multivariable Volume 2: Derivatives
ویرایش:
نویسندگان: Robert Ghrist
سری:
ISBN (شابک) : 9781944655044
ناشر:
سال نشر: 2016
تعداد صفحات: 475
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 238 مگابایت
قیمت کتاب (تومان) : 48,000
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توضیحاتی درمورد کتاب به خارجی
فهرست مطالب
BLUE 2 INTRO COVER Title Page Table of Contents Instructions LET’S GO! SONG 19 BLUE 2 PROLOGUE TITLE CHORUS We got it… CHORUS Change is… How it all works CASE: Gradients CASE: Linearization CASE: Optimization CASE: Lagrange BUT SO WHAT? CASE: Approximation CASE: the IFT CASE: Statistics CHORUS SO MUCH MORE! ONWARD! Chapter 1 - multivariate functions TITLE CALCULUS! CHORUS Graphing functions 1-D Graphing functions 2-D Functions! CHORUS CASE: curves CASE: surfaces CASE: level set curves CASE: level set surfaces CASE: color, time, & more CHORUS CASE: weather CASE: weather CASE: weather CHORUS CASE: coordinate change CASE: coordinate change CASE: coordinate change CHORUS CASE: market equilibrium CASE: market equilibrium CASE: epidemic models CHORUS CASE: robot kinematics CASE: data CHORUS Spin the Dials! CHORUS The BIG PICTURE PROBLEMS PROBLEMS ACKNOWLEDGEMENTS Chapter 2 - partial derivatives TITLE Remember… The derivative DEFINITION: partial derivative DEFINITION: partial derivative CHORUS EXAMPLE: partial & implicit differentiation NOTATION: partial derivatives CHORUS Slopes & derivatives LET\'S SEE: Slopes & derivatives CHORUS EXAMPLE: inputs & outputs CASE: managing a bakery CHORUS It’s the question that drives you The BIG PICTURE PROBLEMS PROBLEMS Chapter 3 - the derivative TITLE What is the derivative? It’s a matrix! BUT SO WHAT? IMPORTANT! CHORUS Curves & rates of change Surfaces & rates of change NOTATION: partial derivatives EXAMPLE: rates of change EXAMPLE: polar coordinates Seeing derivatives CHORUS EXAMPLE: sensitivity SUMMARY CAUTION The BIG PICTURE PROBLEMS PROBLEMS Chapter 4 - differentiation TITLE DEFINITION: derivative The Derivative EXAMPLE: linear functions CHORUS An unusual annoyance OK, so what? Oh wait. YOU CAN SEE: the wrinkle PANIC!!! CHORUS EXAMPLE: squaring square matrices EXAMPLE: AHHA... CHORUS THINK ABOUT IT Like, seriously, think! CHORUS The BIG PICTURE PROBLEMS PROBLEMS ACKNOWLEDGEMENTS Chapter 5 - the chain rule TITLE Remember… 1-d chain rule In other words… CHORUS It’s time… THEOREM: Chain Rule CHORUS EXAMPLE: evaluation EXAMPLE: higher dimensions CHORUS EXAMPLE: chain rule FALSE CHORUS Classical chain rules Classical chain rules CHORUS The BIG PICTURE PROBLEMS PROBLEMS Chapter 6 - differentiation rules TITLE CHORUS Linearity EXAMPLE: linear & affine functions CHORUS EXAMPLE: dot products CHORUS The product rule, REDUX CHORUS EXAMPLE: quadratic forms …continued CHORUS The material derivative Material derivative derivation EXAMPLE: BOOP! FORESHADOWING The BIG PICTURE PROBLEMS PROBLEMS Chapter 7 - the inverse function theorem TITLE CHORUS Recall: inverse rule for derivatives CHORUS DEFINITION: inverse functions EXAMPLE: local nonlinear inverses The BIG IDEA CHORUS The inverse rule for derivatives EXAMPLE: derivative of an inverse CHORUS THEOREM: Inverse Function Theorem CHORUS EXAMPLE: polar coordinates, redux CHORUS EXAMPLE: solving nonlinear equations CHORUS EXAMPLE: inverse kinematics The BIG PICTURE PROBLEMS PROBLEMS Chapter 8 - the implicit function theorem TITLE Remember… The classical case EXAMPLE: classical case CHORUS EXAMPLE: implicit function CHORUS THEOREM: implicit function theorem EXAMPLE: implicit function theorem CHORUS EXAMPLE: price equilibria EXAMPLE: price equilibria CHORUS EXAMPLE: GPS accuracy EXAMPLE: GPS accuracy EXAMPLE: GPS accuracy CHORUS The BIG PICTURE PROBLEMS PROBLEMS ACKNOWLEDGEMENTS Chapter 9 - gradients TITLE CHORUS Level sets in 2-d… …are curves Level sets in 3-d? Nonlinear classifiers CHORUS Vectors or Matrices? DEFINITION: gradient The Gradient CHORUS EXAMPLE: computing gradients CHORUS Gradients & level sets You can see this in 2-d You can see this in 3-d EXAMPLE: spheres CHORUS FALSE CHORUS DEFINITION: vectors Dictionary BONUS: stochastic gradient descent FORESHADOWING: gradients fields CHORUS Remember this… The BIG PICTURE PROBLEMS PROBLEMS Chapter 10 - tangent spaces TITLE CHORUS Tangent planes EXAMPLE: tangent planes CHORUS Parametrized curves CHORUS Parametrized surfaces EXAMPLE: parametrized tangent planes EXAMPLE: continued… But what about…? CHORUS BONUS! Kernels & images Tangent spaces: implicit Tangent spaces: parametric The BIG PICTURE PROBLEMS PROBLEMS Please sign… Chapter 11 - linearization TITLE CHORUS Linearization to approximate curves Linearization to approximate surfaces CHORUS Differentials or derivatives? CHORUS EXAMPLE: numerical approximation EXAMPLE: tolerances and error CHORUS Relative rates EXAMPLE: beam deflection error EXAMPLE: beam deflection error Do you see a pattern? CHORUS Accuracy of linear approximation Taylor time! The BIG PICTURE PROBLEMS PROBLEMS ACKNOWLEDGEMENTS Chapter 12 - taylor series TITLE Remember… Let’s recall: Taylor series What a Taylor polynomial means CHORUS What a Taylor polynomial means 2 The FORMULA RELAX!!! CHORUS NOTATION: variables NOTATION: powers EXAMPLE: multi-index monomials NOTATION: factorials CHORUS NOTATION: derivatives EXAMPLE: higher derivatives IMPORTANT! CHORUS FORMULA: Taylor series about 0 FORMULA: Taylor series about a CHORUS Remarks The BIG PICTURE PROBLEMS PROBLEMS Chapter 13 - computing taylor series TITLE Let’s see some… CHORUS EXAMPLE: 2-d Taylor series CHORUS EXAMPLE: Taylor the hard way EXAMPLE: Taylor the easy way CHORUS EXAMPLE: Using the chain rule BUT SO WHAT? EXAMPLE: local solutions to equations CHORUS WHY? DEFINITION: Hessian BONUS! CAUTION! The BIG PICTURE PROBLEMS Chapter 14 - critical points and optimization TITLE Remember… CHORUS Time for a definition DEFINTION: critical points LEMMA: critical points CHORUS EXAMPLE: finding critical points Graphing critical points A saddle! CHORUS The second derivative Trace-determinant method The second derivative test EXAMPLE: classification Degenerate critical points CHORUS CAUTION: boundaries CHORUS The BIG PICTURE PROBLEMS Please sign… Chapter 15 - optimization - linear regression TITLE Linear regression CHORUS Least squares problem Take a partial derivative Take another partial derivative Solve for the critical point CHORUS Solve for the critical point The solution! CHORUS Check minimality BONUS! Linear regression Nonlinear regression? Topological data analysis?! The BIG PICTURE PROBLEMS Chapter 16 - optimization - nash equilibria TITLE It\'s time for some CHORUS Payoff matrices EXAMPLE: rock, scissors, paper EXAMPLE: even-odd EXAMPLE: Mendelsohn CHORUS Playing at random Expected payoffs from random play CHORUS EXAMPLE: even-odd mixed strategy …continued A saddle point equilibrium Nash equilibria LET\'S SEE: Nash equilibrium BONUS! EXAMPLE: Nash equilibria CHORUS THINK! The BIG PICTURE PROBLEMS ACKNOWLEDGEMENTS Chapter 17 - constrained optimization TITLE CHORUS CASES: constraints CHORUS RECALL: 1-d bounded optimization BUT SO WHAT? CHORUS EXAMPLE: a simple constraint …continued …continued CHORUS EXAMPLE: an optimal box …continued CHORUS EXAMPLE: a parametrized boundary …continued …continued Higher dimensions? Yikes! The BIG PICTURE PROBLEMS Chapter 18 - the lagrange multipler TITLE CHORUS EXAMPLE: a simple constraint CHORUS EXAMPLE: a simple constraint Think gradient… CHORUS You can see it…3D You can see it…2D THIS WORKS! CHORUS THEOREM: Lagrange multiplier EXAMPLE: Lagrange The BIG IDEA The Lagrange equations WHAT IS IT? Interpretations of Lagrange CHORUS BONUS! Lagrange & rates of change Lagrange multiplier: A PICTURE! CHORUS The BIG PICTURE PROBLEMS Chapter 19 - using the lagrange equation TITLE The Lagrange equations CHORUS EXAMPLE: supply chains CHORUS EXAMPLE: inscribing a cone CHORUS EXAMPLE: hard & in 3-d …continued …continued CHORUS EXAMPLE: resource allocation CHORUS EXAMPLE: algebraic-geometric inequality …continued FORESHADOWING The BIG PICTURE PROBLEMS PROBLEMS BLUE 2 EPILOGUE TITLE SO MUCH MORE! CHORUS You should… OPTIMIZATION Multi-Lagrange …continued CHORUS EIGENVALUES CHORUS DYNAMICAL SYSTEMS Linear ODE systems The matrix exponential Classification of equilibria CHORUS Nonlinear dynamics CHORUS OW MY HEAD! SO MUCH MORE! BLUE 2 FORESHADOW TITLE CHORUS FAIL!!! The definite integral CHORUS One weird trick… CHORUS Take it to the limit CHORUS APPLICATION: mass APPLICATION: probability CHORUS the BIG THEOREM CHORUS Coordinate systems APPLICATION: surface area Higher dimensions… The BIG PICTURE LET’S GO! BLUE 2 CLOSE SONG 20 COVER About the Author REFERENCES Where credit is due Publisher of Beautiful Mathematics
