Thomas Calculus 12th Edition PDF Free Download

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Thomas Calculus 12th Edition PDF Book Description

This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).

Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas’ Calculus, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.

Thomas Calculus 12th Edition Features

  • 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.
  • Figures are conceived and rendered to provide insight for students and support conceptual reasoning.
  • The flexible table of contents divides complex topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students. For example, the precise definition of the limit is contained in its own section and may be skipped.
  • Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.
  • A robust MyMathLab course contains 7,900 assignable exercises, a complete e-book, and built-in tutorials so students can get help whenever they need it.
  • A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.

Recent Edition: Thomas Calculus 13th Edition PDF Free Download

Thomas Calculus 12th Edition PDF 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 Calculators and Computers

2. Limits and Continuity

2.1 Rates of Change and Tangents 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

3. Differentiation

3.1 Tangents 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 Related Rates
3.9 Linearization and Differentials

4. Applications of Derivatives

4.1 Extreme Values of Functions
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

5. Integration

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 Substitution and Area Between Curves

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

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 Functions
7.8 Relative Rates of Growth

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
8.5 Integral Tables and Computer Algebra Systems
8.6 Numerical Integration
8.7 Improper Integrals

9. First-Order Differential Equations

9.1 Solutions, Slope Fields, and Euler’s Method
9.2 First-Order Linear Equations
9.3 Applications
9.4 Graphical Solutions of Autonomous Equations
9.5 Systems of Equations and Phase Planes

10. Infinite Sequences and Series

10.1 Sequences
10.2 Infinite Series
10.3 The Integral Test
10.4 Comparison Tests
10.5 The Ratio and Root Tests
10.6 Alternating Series, Absolute and Conditional Convergence
10.7 Power Series
10.8 Taylor and Maclaurin Series
10.9 Convergence of Taylor Series
10.10 The Binomial Series and Applications of Taylor Series

11. Parametric Equations and Polar Coordinates

11.1 Parametrizations of Plane Curves
11.2 Calculus with Parametric Curves
11.3 Polar Coordinates
11.4 Graphing in Polar Coordinates
11.5 Areas and Lengths in Polar Coordinates
11.6 Conic Sections
11.7 Conics in Polar Coordinates

12. Vectors and the Geometry of Space

12.1 Three-Dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Lines and Planes in Space
12.6 Cylinders and Quadric Surface

13. Vector-Valued Functions and Motion in Space

13.1 Curves in Space and Their Tangents
13.2 Integrals of Vector Functions; Projectile Motion
13.3 Arc Length in Space
13.4 Curvature and Normal Vectors of a Curve
13.5 Tangential and Normal Components of Acceleration
13.6 Velocity and Acceleration in Polar Coordinates

14. Partial Derivatives

14.1 Functions of Several Variables
14.2 Limits and Continuity in Higher Dimensions
14.3 Partial Derivatives
14.4 The Chain Rule
14.5 Directional Derivatives and Gradient Vectors
14.6 Tangent Planes and Differentials
14.7 Extreme Values and Saddle Points
14.8 Lagrange Multipliers
14.9 Taylor’s Formula for Two Variables
14.10 Partial Derivatives with Constrained Variables

15. Multiple Integrals

15.1 Double and Iterated Integrals over Rectangles
15.2 Double Integrals over General Regions
15.3 Area by Double Integration
15.4 Double Integrals in Polar Form
15.5 Triple Integrals in Rectangular Coordinates
15.6 Moments and Centers of Mass
15.7 Triple Integrals in Cylindrical and Spherical Coordinates
15.8 Substitutions in Multiple Integrals

16. Integration in Vector Fields

16.1 Line Integrals
16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
16.3 Path Independence, Conservative Fields, and Potential Functions
16.4 Green’s Theorem in the Plane
16.5 Surfaces and Area
16.6 Surface Integrals
16.7 Stokes’ Theorem
16.8 The Divergence Theorem and a Unified Theory

17. Second-Order Differential Equations (online)

17.1 Second-Order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.3 Applications
17.4 Euler Equations
17.5 Power-Series Solutions

Appendices

  1. Real Numbers and the Real Line
  2. Mathematical Induction
  3. Lines, Circles, and Parabolas
  4. Proofs of Limit Theorems
  5. Commonly Occurring Limits
  6. Theory of the Real Numbers
  7. Complex Numbers
  8. The Distributive Law for Vector Cross Products
  9. The Mixed Derivative Theorem and the Increment Theorem

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