book

Quick Calculus, 3rd Edition

by Daniel Kleppner, Peter Dourmashkin, Norman Ramsey

April 2022

Beginner to intermediate

304 pages

7h 21m

English

Jossey-Bass

Read now

Unlock full access

1.1 A Few Preliminaries1.2 Functions1.3 Graphs1.4 Linear and Quadratic Functions1.5 Angles and Their Measurements1.6 Trigonometry1.7 Exponentials and LogarithmsSummary of Chapter 1Notes
2.1 The Limit of a Function2.2 Velocity2.3 Derivatives2.4 Graphs of Functions and Their Derivatives2.5 Differentiation2.6 Some Rules for Differentiation2.7 Differentiating Trigonometric Functions2.8 Differentiating Logarithms and Exponentials2.9 Higher‐Order Derivatives2.10 Maxima and Minima2.11 Differentials2.12 A Short Review and Some ProblemsConclusion to Chapter 2Summary of Chapter 2
3.1 Antiderivative, Integration, and the Indefinite Integral3.2 Some Techniques of Integration3.3 Area Under a Curve and the Definite Integral3.4 Some Applications of Integration3.5 Multiple IntegralsConclusion to Chapter 3Summary of Chapter 3Notes
4.1 Taylor Series4.2 Numerical Integration4.3 Differential Equations4.4 Additional Problems for Chapter 4Summary of Chapter 4Conclusion (frame 449)
A.1 Trigonometric Functions of Sums of AnglesA.2 Some Theorems on LimitsA.3 Exponential FunctionA.4 Proof ThatA.5 DifferentiatingA.6 Differentiating Trigonometric FunctionsA.7 Differentiating the Product of Two FunctionsA.8 Chain Rule for DifferentiatingA.9 Differentiating ln xA.10 Differentials When Both Variables Depend on a Third VariableA.11 Proof That if Two Functions Have the Same Derivative They Differ Only by a ConstantA.12 Limits Involving Trigonometric Functions
B.1 Implicit DifferentiationB.2 Differentiating the Inverse Trigonometric FunctionsB.3 Partial DerivativesB.4 Radial Acceleration in Circular MotionB.5 Resources for Further Study

Answers to Selected Problems from the Text
Chapter 1Chapter 2Chapter 3
Table 1: DerivativesTable 2: Integrals

Content preview from Quick Calculus, 3rd Edition

APPENDIX ADerivations

This appendix presents derivations of certain formulas and theorems not derived earlier.

A.1 Trigonometric Functions of Sums of Angles

Formulas for the sine of the sum of two angles, and , can easily be derived with the aid of this drawing in which the radius of the circle is unity.

$StartLayout 1st Row 1st Column sine left-parenthesis theta plus phi right-parenthesis 2nd Column equals italic upper A upper D equals italic upper F upper E plus italic upper A upper G 2nd Row 1st Column Blank 2nd Column equals italic OF sine theta plus italic upper A upper F cosine theta 3rd Row 1st Column Blank 2nd Column equals sine theta cosine phi plus cosine theta sine phi period EndLayout$

In a similar fashion with the same ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.

Start your free trial

Calculus For Dummies, 2nd Edition

Mark Ryan

Calculus I

W. Michael Kelley

Applied Calculus 5th Edition

Deborah Hughes-Hallett, Patti Frazer Lock, Andrew M. Gleason, Daniel E. Flath, David Lovelock, Douglas Quinney, Eric Connally, Guadalupe I. Lonzano, Karen R. Rhea, Selin Kalaycýoðlu, William G. McCallum, Adam H. Speigler, Brigitte Lahme, Brad G. Osgood

Make: Calculus

Joan Horvath, Rich Cameron

Publisher Resources

ISBN: 9781119743194