348-367ĩ.2 Polar Equations and Graphs, pp. 328-335ĩ: Polar Coordinates and Complex Numbers, pp. 311-319Ĩ.3 Area of a Surface of Revolution, pp. 311-347Ĩ.1 Areas and Volumes by Slices, pp. 294-299Ĩ: Applications of the Integral, pp. 283-310ħ.3 Trigonometric Substitutions, pp. 259-266Ħ.6 Powers Instead of Exponentials, pp. 242-251Ħ.5 Separable Equations Including the Logistic Equation, pp. 228-282Ħ.3 Growth and Decay in Science and Economics, pp. 213-219Ħ: Exponentials and Logarithms, pp. 206-212ĥ.7 The Fundamental Theorem and Its Consequences, pp. 195-200ĥ.6 Properties of the Integral and the Average Value, pp.
187-194ĥ.4 Indefinite Integrals and Substitutions, pp. 164-170Ĥ.4 Inverses of Trigonometric Functions, pp. 160-163Ĥ.3 Inverse Functions and Their Derivatives, pp. 154-159Ĥ.2 Implicit Differentiation and Related Rates, pp. 146-153Ĥ.1 Derivatives by the Charin Rule, pp. 137-145ģ.8 The Mean Value Theorem and l’Hôpital’s Rule, pp. 130-136ģ.7 Newton’s Method and Chaos, pp. 105-111ģ.5 Ellipses, Parabolas, and Hyperbolas, pp. 96-104ģ.3 Second Derivatives: Minimum vs. 91-153ģ.2 Maximum and Minimum Problems, pp. 71-77ģ: Applications of the Derivative, pp.
64-70Ģ.5 The Product and Quotient and Power Rules, pp. 58-63Ģ.4 Derivative of the Sine and Cosine, pp. 44-49Ģ.3 The Slope and the Tangent Line, pp. 34-35Ģ.1 The Derivative of a Function, pp.
#Calculus 2 pdf#
Answers to Odd-Numbered Problems ( PDF - 2.4MB)ġ.3 The Velocity at an Instant, pp.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. MIT Professor Gilbert Strang has created a series of videos to show ways in which calculus is important in our lives. The complete textbook is also available as a single file.
#Calculus 2 manual#
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. Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. We close off this section with Taylor series in two variables and using Lagrange multipliers to determine optima. In the context of surfaces we consider families of level curves, tangent planes, directional derivatives and optima.
#Calculus 2 how to#
We see the graphs of functions of two variables as surfaces and consider what it means for limits of such functions to exist and how to define continuity. We parametrise space curves, find arc lengths, and determine the intersection of surfaces as curves. Three-dimensional geometry: Our primary interest here is in space curves and surfaces. We study the Fundamental Theorem of Calculus and use some integration techniques such as integration by substitution and integration by parts. Integration: We define integration in the context of areas under curves and use Riemann sums to determine definite integrals from first principles. We shall consider summation techniques with particular interest in the relationship with Riemann sums. Series of particular interest are the p-series, geometric series, and Taylor and Maclaurin expansions. To do this we use a variety of different tests for convergence and also look at approximation errors. Sequences, series and summation: We shall define sequences and series and consider the convergence of infinite sequences and series.
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