TAILIEUCHUNG - Ebook Calculus - Single and multivariable (5th edition): Part 1

Calculus teachers recognize Calculus as the leading resource among the reform projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The book continues the effort to promote courses in which understanding and computation reinforce each other. | 5th Edition Chapter One A LIBRARY OF Contents Functions and Change. 2 The Rule of Four. 2 Examples of Domain and Range. 3 Linear Functions . 4 Families of Linear Functions. 5 Increasing versus Decreasing Functions . 6 Proportionality. 6 Exponential Functions . 10 Concavity. 11 Elimination of a Drug from the Body . 11 The General Exponential Function. 12 Half-Life and Doubling Time. 12 The Family of Exponential Functions . 13 Exponential Functions with Base e. 13 New Functions from Old . 17 Shifts and Stretches. 17 Composite Functions. 18 Odd and Even Functions Symmetry. 19 Inverse Functions. 19 Logarithmic Functions. 24 Logarithms to Base 10 and to Base e . 24 Solving Equations Using Logarithms . 26 Trigonometric Functions. 30 Radians. 30 The Sine and Cosine Functions. 31 The Tangent Function. 34 The Inverse Trigonometric Functions . 34 Powers Polynomials and Rational Functions 38 Power Functions. 38 Dominance. 39 Polynomials. 40 Rational Functions. 42 Introduction to Continuity . 47 Graphical Viewpoint. 47 The Intermediate Value Theorem. 48 Numerical Viewpoint. 49 Limits. 51 The Idea of a Limit. 51 Definition of Limit. 51 Definition of Continuity . 56 REVIEW PROBLEMS. 60 CHECK YOUR UNDERSTANDING . 65 PROJECTS. .

• Toán học
• Rule of Four
• Functions and change
• Exponential functions
• Logarithmic functions
• Trigonometric functions
• The Derivative
• Short cuts to differentiation
• Functions os several variables
• A fundamental tool
• Differentiating functions of several variables