[PDF] 3000 Solved Problems in Calculus by Elliot Mendelson

3000 Solved Problems in Calculus Contents

• Chapter 1 Inequalities
• Chapter 2 Absolute Value
• Chapter 3 Lines
• Chapter 4 Circles
• Chapter 5 Functions And Their Graphs
• Chapter 6 Limits
• Chapter 7 Continuity
• Chapter 8 The Derivative
• Chapter 9 The Chain Rule
• Chapter 10 Trigonometric Functions And Their Derivatives
• Chapter 11 Rolle’s Theorem, The Mean Value Theorem, And The Sign Of The Derivative
• Chapter 12 Higher-Order Derivatives And Implicit Differentiation
• Chapter 13 Maxima And Minima
• Chapter 14 Related Rates
• Chapter 15 Curve Sketching (Graphs)
• Chapter 16 Applied Maximum And Minimum Problems
• Chapter 17 Rectilinear Motion
• Chapter 18 Approximation By Differentials
• Chapter 19 Antiderivatives (Indefinite Integrals)
• Chapter 20 The Definite Integral And The Fundamental Theorem Of Calculus
• Chapter 21 Area And Arc Length
• Chapter 22 Volume
• Chapter 23 The Natural Logarithm
• Chapter 24 Exponential Functions
• Chapter 25 L’hopital’s Rule
• Chapter 26 Exponential Growth And Decay
• Chapter 27 Inverse Trigonometric Functions
• Chapter 28 Integration By Parts
• Chapter 29 Trigonometric Integrands And Substitutions
• Chapter 30 Integration Of Rational Functions: The Method Of Partial Fractions
• Chapter 31 Integrals For Surface Area, Work, Centroids Surface Area Of A Solid Of Revolution / Work / Centroid Of A Planar Region 
• Chapter 32 Improper Integrals
• Chapter 33 Planar Vectors
• Chapter 34 Parametric Equations, Vector Functions, Curvilinear Motion Parametric Equations Of Plane Curves / Vector-Valued Functions /
• Chapter 35 Polar Coordinates
• Chapter 36 Infinite Sequences
• Chapter 37 Infinite Series
• Chapter 38 Power Series
• Chapter 39 Taylor And Maclaurin Series
• Chapter 40 Vectors In Space. Lines And Planes
• Chapter 41 Functions Of Several Variables Multivariate Functions And Their Graphs / Cylindrical And Spherical Coordinates /
• Chapter 42 Partial Derivatives
• Chapter 43 Directional Derivatives And The Gradient. Extreme Values
• Chapter 44 Multiple Integrals And Their Applications
• Chapter 45 Vector Functions In Space. Divergence And Curl. Line Integrals
• Chapter 46 Differential Equations

Preface to 3000 Solved Problems in Calculus PDF

To the Student

This collection of solved problems covers elementary and intermediate calculus and much of advanced calculus. We have aimed at presenting the broadest range of problems that you are likely to encounter the old chestnuts, all the current standard types, and some not so standard. Each chapter begins with very elementary problems.

Their difficulty usually increases as the chapter progresses, but there is no uniform pattern. It is assumed that you have available a calculus textbook, including tables for the trigonometric, logarithmic, and exponential functions.

Our ordering of the chapters follows the customary order found in many textbooks, but as no two textbooks have exactly the same sequence of topics, you must expect an occasional discrepancy from the order followed in your course.

The printed solution that immediately follows a problem statement gives you all the details of one way to solve the problem.

You might wish to delay consulting that solution until you have outlined an attack in your own mind. You might even disdain to read it until, with pencil and paper, you have solved the problem yourself (or failed gloriously).

Used thus, 3000 Solved Problems in Calculus can almost serve as a supplement to any course in calculus, or even as an independent refresher course.

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