Thomas' Calculus, Si Units 15th Edition

By (author) Hass, Joel; By (author) Heil, Christopher E.; By (author) Weir Maurice
Description

Thomas'' Calculus goes beyond memorizing formulas and routine procedures to help you develop deeper understanding. It guides you to a level of mathematical proficiency, with additional support if needed through its clear and intuitive explanations, current applications and generalized concepts. Technology exercises in every section use the calculator or computer for solving problems, and Computer Explorations offer exercises requiring a computer algebra system like Maple or Mathematica. The 15th Edition adds exercises, revises figures and language for clarity, and updates many applications; new online chapters cover Complex Functions, Fourier Series and Wavelets.

 

Table of contents
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
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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 Limits Involving Infinity; Asymptotes of Graphs
• 2.6 Continuity
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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 Related Rates
• 3.10 Linearization and Differentials
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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 Applied Optimization
• 4.6 Newton''s Method
• 4.7 Antiderivatives
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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
• Technology Application Projects

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 and Fluid Forces
• 6.6 Moments and Centers of Mass
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

7. Transcendental Functions

• 7.1 Inverse Functions and Their Derivatives
• 7.2 Natural Logarithms
• 7.3 Exponential Functions
• 7.4 Exponential Change and Separable Differential Equations
• 7.5 Indeterminate Forms and L''Hôpital''s Rule
• 7.6 Inverse Trigonometric Functions
• 7.7 Hyperbolic