University Calculus: Early Transcendentals, Global Edition (4^th Ed.) University Calculus Early Transcendentals

For 3-semester or 4-quarter courses covering single variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.
University Calculus: Early Transcendentals helps students generalise and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. In the 4th SI Edition, new co-authors Chris Heil (Georgia Institute of Technology) and Przemyslaw Bogacki (Old Dominion University) partner with author Joel Hass to preserve the text's time-tested features while revisiting every word and figure with today's students in mind.

1. Functions

1.1    Functions and Their Graphs

1.2    Combining Functions; Shifting and Scaling Graphs

1.3    Trigonometric Functions

1.4    Graphing with Software

1.5    Exponential Functions

1.6    Inverse Functions and Logarithms

2.    Limits and Continuity 

2.1    Rates of Change and Tangent Lines to Curves

2.2    Limit of a Function and Limit Laws

2.3    The Precise Definition of a Limit

2.4    One-Sided Limits

2.5    Continuity

2.6    Limits Involving Infinity; Asymptotes of Graphs

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

3.    Derivatives

3.1    Tangent Lines and the Derivative at a Point

3.2    The Derivative as a Function

3.3    Differentiation Rules

3.4    The Derivative as a Rate of Change

3.5    Derivatives of Trigonometric Functions

3.6    The Chain Rule

3.7    Implicit Differentiation

3.8    Derivatives of Inverse Functions and Logarithms

3.9    Inverse Trigonometric Functions

3.10 Related Rates

3.11 Linearization and Differentials

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

4.    Applications of Derivatives

4.1    Extreme Values of Functions on Closed Intervals

4.2    The Mean Value Theorem

4.3    Monotonic Functions and the First Derivative Test

4.4    Concavity and Curve Sketching

4.5    Indeterminate Forms and L’Hôpital’s Rule

4.6    Applied Optimization

4.7    Newton’s Method

4.8    Antiderivatives

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

5.    Integrals

5.1    Area and Estimating with Finite Sums

5.2    Sigma Notation and Limits of Finite Sums

5.3    The Definite Integral

5.4    The Fundamental Theorem of Calculus

5.5    Indefinite Integrals and the Substitution Method

5.6   Definite Integral Substitutions and the Area Between Curves

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

6.    Applications of Definite Integrals

6.1    Volumes Using Cross-Sections

6.2    Volumes Using Cylindrical Shells

6.3    Arc Length

6.4    Areas of Surfaces of Revolution

6.5    Work

6.6    Moments and Centers of Mass

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

7.    Integrals and Transcendental Functions

7.1    The Logarithm Defined as an Integral

7.2    Exponential Change and Separable Differential Equations

7.3    Hyperbolic Functions

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

8.    Techniques of Integration  

8.1    Integration by Parts

8.2    Trigonometric Integrals

8.3    Trigonometric Substitutions

8.4    Integration of Rational Functions by Partial Fractions

Teach calculus the way you want to teach it, and at a level that prepares students for their STEM majors

· New co-author Chris Heil and co-author Joel Hass aim to develop students’ mathematical maturity and proficiency by going beyond memorization of formulas and routine procedures and showing how to generalize key concepts once they are introduced.

· Key topics are presented both formally and informally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Ideas are introduced with examples and intuitive explanations that are then generalized so that students are not overwhelmed by abstraction.

· Results are both carefully stated and proved throughout the book, and proofs are clearly explained and motivated. Students and instructors who proceed through the formal material will find it as carefully presented and explained as the informal development. If the instructor decides to downplay formality at any stage, it will not cause problems with later developments in the text.

· Expanded - PowerPoint^® lecture slides now include examples as well as key theorems, definitions, and figures. The files are fully editable making them a robust and flexible teaching tool.

Assess student understanding of key concepts and skills through a wide range of time-tested exercises

· Updated - Strong exercise sets feature a great breadth of problems — progressing from skills problems to applied and theoretical problems — to encourage students to think about and practice the concepts until they achieve mastery. In the 4th SI Edition, the authors added new exercises and exercise types throughout, many of which are geometric in nature.

· Writing exercises throughout the text ask students to explore a