![]() ![]() n-Dimensional Euclidean Space Review Exercises for Chapter 1 2.1 The Geometry of Real-Valued Functions 2.2 Limits and Continuity 2.3 Differentiation 2.4 Introduction to Paths and Curves 2.5 Properties of the Derivative 2.6 Gradients and Directional Derivatives Review Exercises for Chapter 2 3.1 Iterated Partial Derivatives 3.2 Taylor's Theorem 3.3 Extrema of Real-Valued Functions 3.4 Constrained Extrema and Lagrange Multipliers 3.5 The Implicit Function Theorem Review Exercises for Chapter 3 4.1 Acceleration and Newton's Second Law 4.2 Arc Length 4.3 Vector Fields 4.4 Divergence and Curl Review Exercises for Chapter 4 5.1 Introduction 5.2 The Double Integral Over a Rectangle 5.3 The Double Integral Over More General Regions 5.4 Changing the Order of Integration 5.5 The Triple Integral Review Exercises for Chapter 5 6.1 The Geometry of Maps from R^2 to R^2 6.2 The Change of Variables Theorem 6.3 Applications 6.4 Improper Integrals Review Exercises for Chapter 6 7.1 The Path Integral 7.2 Line Integrals 7.3 Parametrized Surfaces 7.4 Area of a Surface 7.5 Integrals of Scalar Functions Over Surfaces 7.6 Surface Integrals of Vector Fields 7.7 Applications to Differential Geometry, Physics, and Forms of Life Review Exercises for Chapter 7 8.1 Green's Theorem 8.2 Stokes' Theorem 8.3 Conservative Fields 8.4 Gauss' Theorem 8. The videos, which include real-life examples to illustrate the concepts, are ideal for high school students, college students, and anyone interested in learning the basics of calculus.Ġ.1 Distance and Speed // Height and SlopeĠ.2 The Changing Slope of \(y=x^2\) and \(y=x^n\)Ġ.4 Video Summaries and Practice ProblemsĬhapter 1: Introduction to Calculus (PDF)Ģ.5 The Product and Quotient and Power RulesĬhapter 3: Applications of the Derivative (PDF)ģ.3 Second Derivatives: Bending and Accelerationģ.8 The Mean Value Theorem and 1’Hôpital’s RuleĬhapter 4: Derivatives by the Chain Rule (PDF)Ĥ.2 Implicit Differentiation and Related RatesĤ.3 Inverse Functions and Their Derivativesĥ.4 Indefinite Integrals and Substitutionsĥ.6 Properties of the Integral and Average Valueĥ.7 The Fundamental Theorem and Its ApplicationsĬhapter 6: Exponentials and Logarithms (PDF)Ħ.3 Growth and Decay in Science and EconomicsĦ.5 Separable Equations Including the Logistic EquationĬhapter 7: Techniques of Integration (PDF)Ĭhapter 8: Applications of the Integral (PDF)Ĭhapter 9: Polar Coordinates and Complex Numbers (PDF)ĩ.3 Slope, Length, and Area for Polar Curvesġ0.4 The Taylor Series for \(e^x\), \(\sin\)ġ2.2 Plane Motion: Projectiles and Cycloidsġ2.4 Polar Coordinates and Planetary Motionġ3.3 Tangent Planes and Linear Approximationsġ3.4 Directional Derivatives and Gradientsġ3.7 Constraints and Lagrange Multipliersġ4.1.1 Vectors in Two- and Three-Dimensional Space 1.2 The Inner Product, Length, and Distance 1.3 Matrices, Determinants, and the Cross Product 1.4 Cylindrical and Spherical Coordinates 1.5. MIT Professor Gilbert Strang has created a series of videos to show ways in which calculus is important in our lives. The complete textbook (PDF) is also available as a single file. There is also an online Instructor’s Manual and a student Study Guide. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. The directional derivative in the direction of the vector (1,1,0) is found by taking the dot product of V I and the unit vector in this direction. At the point (1,2,3) this has the value (6,3,2). ![]() First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike. 160 Vector Calculus Solutions to Exercises for Chapter 3 3.1 I xyz, so VI (yz,xz,xy).
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