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Calculus I with Integrated Precalculus

Calculus I with Integrated Precalculus


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About the Book

Taalman’s Calculus I with Integrated Precalculus helps students with weak mathematical backgrounds be successful in the calculus sequence, without retaking a precalculus course.  Taalman’s innovative text is the only book to interweave calculus with precalculus and algebra in a manner suitable for math and science majors— not a rehashing or just-in-time review of precalculus and algebra, but rather a new approach that uses a calculus-level toolbox to examine the structure and behavior of algebraic and transcendental functions. This book was written specifically to tie in with the material covered in Taalman/Kohn Calculus. Students who begin their calculus sequence with Calculus I with Integrated Precalculus can easily continue on to Calculus II using the Taalman/Kohn text.

Table of Contents:
I Differential Calculus 0 Functions and Precalculus 0.1 Numbers and Sets 0.2 Equations 0.3 Inequalities 0.4 Functions and Graphs 0.5 A Basic Library of Functions 0.6 Operations, Transformations, and Inverses 0.7 Logic and Mathematical Thinking* Chapter Review, Self-Test, and Capstones 1 Limits 1.1 An Intuitive Introduction to Limits 1.2 Formal Definition of a Limit 1.3 Delta-Epsilon Proofs* 1.4 Continuity and Its Consequences 1.5 Limit Rules and Calculating Basic Limits 1.6 Infinite Limits and Indeterminate Forms Chapter Review, Self-Test, and Capstones 2 Derivatives 2.1 An Intuitive Introduction to Derivatives 2.2 Formal Definition of the Derivative 2.3 Rules for Calculating Basic Derivatives 2.4 The Chain Rule and Implicit Differentiation Chapter Review, Self-Test, and Capstones 3 Applications of the Derivative 3.1 The Mean Value Theorem 3.2 The First Derivative and Curve Sketching 3.3 The Second Derivative and Curve Sketching 3.4 Optimization 3.5 Related Rates Chapter Review, Self-Test, and Capstones II Exploring Functions with Calculus 4 Calculus with Power, Polynomial, and Rational Functions 4.1 Advanced Algebraic Techniques 4.2 Power Functions 4.3 Polynomial Functions 4.4 Rational Functions Chapter Review, Self-Test, and Capstones 5 Calculus with Exponential and Logarithmic Functions 5.1 Defining Exponential and Logarithmic Functions 5.2 Limits of Exponential and Logarithmic Functions 5.3 Derivatives of Exponential and Logarithmic Functions 5.4 Applications of Exponential Functions 5.5 L’Hopital’s Rule Chapter Review, Self-Test, and Capstones 6 Calculus with Trignometric and Inverse Trigonometric Functions 6.1 Defining the Trigonometric Functions 6.2 Trigonometric Identities 6.3 Limits and Derivatives of Trigonometric Functions 6.4 Inverse Trigonometric Functions Chapter Review, Self-Test, and Capstones III Integral Calculus 7 Definite Integrals 7.1 Addition and Accumulation 7.2 Riemann Sums 7.3 Definite Integrals 7.4 Indefinite Integrals 7.5 The Fundamental Theorem of Calculus 7.6 Areas and Average Values 7.7 Functions Defined by Integrals Chapter Review, Self-Test, and Capstones 8 Techniques of Integration 8.1 Integration by Substitution 8.2 Integration by Parts 8.3 Partial Fractions and Other Algebraic Techniques 8.4 Trigonometric Integrals 8.5 Trigonometric Substitution 8.6 Improper Integrals 8.7 Numerical Integration* Chapter Review, Self-Test, and Capstones 9 Applications of Integration 9.1 Volumes by Slicing 9.2 Volumes by Shells 9.3 Arc Length and Surface Area 9.4 Real-World Applications of Integration 9.5 Differential Equations* Chapter Review, Self-Test, and Capstones Answers to Odd Problems Index


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Product Details
  • ISBN-13: 9781319353780
  • Publisher: MacMillan Learning
  • Publisher Imprint: W.H.Freeman & Co Ltd
  • Language: English
  • Returnable: Y
  • ISBN-10: 1319353789
  • Publisher Date: 24 Sep 2019
  • Binding: Digital download and online
  • No of Pages: 880


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